# Heat and Fluid

- Working Group
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## Fluid Mechanics Laboratory

### Responsible Faculty Member

- Makina Mühendisliği Binası (Z64)

- +90 232 750 6770

## Heat & Mass Research Laboratory

### Responsible Faculty Member

- Mechanical Engineering Building (142)

- +90 232 750 6744

## Micro/Nano Engineering Laboratory

### Responsible Faculty Member

- Mechanical Engineering Building (162)

- +90 232 750 6785

## 2016 |

Pham, An Truong; Barisik, Murat; Kim, BoHung Interfacial thermal resistance between the graphene-coated copper and liquid water Journal Article INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 97 , pp. 422-431, 2016, ISSN: 0017-9310. @article{ISI:000374616900038, title = {Interfacial thermal resistance between the graphene-coated copper and liquid water}, author = {An Truong Pham and Murat Barisik and BoHung Kim}, doi = {10.1016/j.ijheatmasstransfer.2016.02.040}, issn = {0017-9310}, year = {2016}, date = {2016-06-01}, journal = {INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, volume = {97}, pages = {422-431}, abstract = {The thermal coupling at water-solid interfaces is a key factor in controlling thermal resistance and the performance of nanoscale devices. This is especially important across the recently engineered nano-composite structures composed of a graphene-coated-metal surface. In this paper, a series of molecular dynamics simulations were conducted to investigate Kapitza length at the interface of liquid water and nano-composite surfaces of graphene-coated-Cu(111). We found that Kapitza length gradually increased and converged to the value measured on pure graphite surface with the increase of the number of graphene layers inserted on the Cu surface. Different than the earlier hypothesis on the ``transparency of graphene,'' the Kapitza length at the interface of mono-layer graphene coated Cu and water was found to be 2.5 times larger than the value of bare Cu surface. This drastic change of thermal resistance with the additional of a single graphene is validated by the surface energy calculations indicating that the mono-layer graphene allows only similar to 18% van der Waals energy of underneath Cu to transmit. We introduced an ``overall interaction strength'' value for the nano-composites based the quantitative contribution of pair interaction potentials of each material with water into the total surface energy in each case. Similar to earlier studies, results revealed that Kapitza length shows exponentially variation as a function of the estimated interaction strength of the nano-composite surfaces. The effect of Cu/graphene coupling on thermal behavior between the nano-composite with water was characterized. The Kapitza length was found to decrease significantly with increased Cu/graphene strength in the case of weak coupling, while this behavior becomes negligible with strong coupling of Cu and graphene. (C) 2016 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The thermal coupling at water-solid interfaces is a key factor in controlling thermal resistance and the performance of nanoscale devices. This is especially important across the recently engineered nano-composite structures composed of a graphene-coated-metal surface. In this paper, a series of molecular dynamics simulations were conducted to investigate Kapitza length at the interface of liquid water and nano-composite surfaces of graphene-coated-Cu(111). We found that Kapitza length gradually increased and converged to the value measured on pure graphite surface with the increase of the number of graphene layers inserted on the Cu surface. Different than the earlier hypothesis on the ``transparency of graphene,'' the Kapitza length at the interface of mono-layer graphene coated Cu and water was found to be 2.5 times larger than the value of bare Cu surface. This drastic change of thermal resistance with the additional of a single graphene is validated by the surface energy calculations indicating that the mono-layer graphene allows only similar to 18% van der Waals energy of underneath Cu to transmit. We introduced an ``overall interaction strength'' value for the nano-composites based the quantitative contribution of pair interaction potentials of each material with water into the total surface energy in each case. Similar to earlier studies, results revealed that Kapitza length shows exponentially variation as a function of the estimated interaction strength of the nano-composite surfaces. The effect of Cu/graphene coupling on thermal behavior between the nano-composite with water was characterized. The Kapitza length was found to decrease significantly with increased Cu/graphene strength in the case of weak coupling, while this behavior becomes negligible with strong coupling of Cu and graphene. (C) 2016 Elsevier Ltd. All rights reserved. |

Vo, Truong Quoc; Barisik, Murat; Kim, BoHung Atomic density effects on temperature characteristics and thermal transport at grain boundaries through a proper bin size selection Journal Article JOURNAL OF CHEMICAL PHYSICS, 144 (19), 2016, ISSN: 0021-9606. @article{ISI:000377712600039, title = {Atomic density effects on temperature characteristics and thermal transport at grain boundaries through a proper bin size selection}, author = {Truong Quoc Vo and Murat Barisik and BoHung Kim}, doi = {10.1063/1.4949763}, issn = {0021-9606}, year = {2016}, date = {2016-05-01}, journal = {JOURNAL OF CHEMICAL PHYSICS}, volume = {144}, number = {19}, abstract = {This study focuses on the proper characterization of temperature profiles across grain boundaries (GBs) in order to calculate the correct interfacial thermal resistance (ITR) and reveal the influence of GB geometries onto thermal transport. The solid-solid interfaces resulting from the orientation difference between the (001), (011), and (111) copper surfaces were investigated. Temperature discontinuities were observed at the boundary of grains due to the phonon mismatch, phonon backscattering, and atomic forces between dissimilar structures at the GBs. We observed that the temperature decreases gradually in the GB area rather than a sharp drop at the interface. As a result, three distinct temperature gradients developed at the GB which were different than the one observed in the bulk solid. This behavior extends a couple molecular diameters into both sides of the interface where we defined a thickness at GB based on the measured temperature profiles for characterization. Results showed dependence on the selection of the bin size used to average the temperature data from the molecular dynamics system. The bin size on the order of the crystal layer spacing was found to present an accurate temperature profile through the GB. We further calculated the GB thickness of various cases by using potential energy (PE) distributions which showed agreement with direct measurements from the temperature profile and validated the proper binning. The variation of grain crystal orientation developed different molecular densities which were characterized by the average atomic surface density (ASD) definition. Our results revealed that the ASD is the primary factor affecting the structural disorders and heat transfer at the solid-solid interfaces. Using a system in which the planes are highly close-packed can enhance the probability of interactions and the degree of overlap between vibrational density of states (VDOS) of atoms forming at interfaces, leading to a reduced ITR. Thus, an accurate understanding of thermal characteristics at the GB can be formulated by selecting a proper bin size. Published by AIP Publishing.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This study focuses on the proper characterization of temperature profiles across grain boundaries (GBs) in order to calculate the correct interfacial thermal resistance (ITR) and reveal the influence of GB geometries onto thermal transport. The solid-solid interfaces resulting from the orientation difference between the (001), (011), and (111) copper surfaces were investigated. Temperature discontinuities were observed at the boundary of grains due to the phonon mismatch, phonon backscattering, and atomic forces between dissimilar structures at the GBs. We observed that the temperature decreases gradually in the GB area rather than a sharp drop at the interface. As a result, three distinct temperature gradients developed at the GB which were different than the one observed in the bulk solid. This behavior extends a couple molecular diameters into both sides of the interface where we defined a thickness at GB based on the measured temperature profiles for characterization. Results showed dependence on the selection of the bin size used to average the temperature data from the molecular dynamics system. The bin size on the order of the crystal layer spacing was found to present an accurate temperature profile through the GB. We further calculated the GB thickness of various cases by using potential energy (PE) distributions which showed agreement with direct measurements from the temperature profile and validated the proper binning. The variation of grain crystal orientation developed different molecular densities which were characterized by the average atomic surface density (ASD) definition. Our results revealed that the ASD is the primary factor affecting the structural disorders and heat transfer at the solid-solid interfaces. Using a system in which the planes are highly close-packed can enhance the probability of interactions and the degree of overlap between vibrational density of states (VDOS) of atoms forming at interfaces, leading to a reduced ITR. Thus, an accurate understanding of thermal characteristics at the GB can be formulated by selecting a proper bin size. Published by AIP Publishing. |

Barisik, Murat; Beskok, Ali ``Law of the nano-wall'' in nano-channel gas flows Journal Article MICROFLUIDICS AND NANOFLUIDICS, 20 (3), 2016, ISSN: 1613-4982. @article{ISI:000372866300003, title = {``Law of the nano-wall'' in nano-channel gas flows}, author = {Murat Barisik and Ali Beskok}, doi = {10.1007/s10404-016-1713-6}, issn = {1613-4982}, year = {2016}, date = {2016-03-01}, journal = {MICROFLUIDICS AND NANOFLUIDICS}, volume = {20}, number = {3}, abstract = {Molecular dynamics simulations of force-driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas-wall interactions. This duality enables definition of an inner-layer scaling, y*, based on the molecular dimensions. For gas-wall interactions determined by Lennard-Jones potential, the velocity distribution for y* <= 3 exhibits a universal behavior as a function of the local Knudsen number and gas-wall interaction parameters, which can be interpreted as the ``law of the nano-wall.'' Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok-Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1): 43-77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Molecular dynamics simulations of force-driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas-wall interactions. This duality enables definition of an inner-layer scaling, y*, based on the molecular dimensions. For gas-wall interactions determined by Lennard-Jones potential, the velocity distribution for y* <= 3 exhibits a universal behavior as a function of the local Knudsen number and gas-wall interaction parameters, which can be interpreted as the ``law of the nano-wall.'' Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok-Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1): 43-77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows. |

## 2015 |

Cetkin, Erdal Constructal Vascular Structures With High-Conductivity Inserts for Self-Cooling Journal Article JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME, 137 (11), 2015, ISSN: 0022-1481. @article{ISI:000362512900008, title = {Constructal Vascular Structures With High-Conductivity Inserts for Self-Cooling}, author = {Erdal Cetkin}, doi = {10.1115/1.4030906}, issn = {0022-1481}, year = {2015}, date = {2015-11-01}, journal = {JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME}, volume = {137}, number = {11}, abstract = {In this paper, we show how a heat-generating domain can be cooled with embedded cooling channels and high-conductivity inserts. The volume of cooling channels and high-conductivity inserts is fixed, so is the volume of the heat-generating domain. The maximum temperature in the domain decreases with high-conductivity inserts even though the coolant volume decreases. The locations and the shapes of high-conductivity inserts corresponding to the smallest peak temperatures for different number of inserts are documented}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, we show how a heat-generating domain can be cooled with embedded cooling channels and high-conductivity inserts. The volume of cooling channels and high-conductivity inserts is fixed, so is the volume of the heat-generating domain. The maximum temperature in the domain decreases with high-conductivity inserts even though the coolant volume decreases. The locations and the shapes of high-conductivity inserts corresponding to the smallest peak temperatures for different number of inserts are documented |

Vo, Truong Quoc; Barisik, Murat; Kim, BoHung Near-surface viscosity effects on capillary rise of water in nanotubes Journal Article PHYSICAL REVIEW E, 92 (5), 2015, ISSN: 1539-3755. @article{ISI:000364413300003, title = {Near-surface viscosity effects on capillary rise of water in nanotubes}, author = {Truong Quoc Vo and Murat Barisik and BoHung Kim}, doi = {10.1103/PhysRevE.92.053009}, issn = {1539-3755}, year = {2015}, date = {2015-11-01}, journal = {PHYSICAL REVIEW E}, volume = {92}, number = {5}, abstract = {In this paper, we present an approach for predicting nanoscale capillary imbibitions using the Lucas-Washburn (LW) theory. Molecular dynamics (MD) simulations were employed to investigate the effects of surface forces on the viscosity of liquid water. This provides an update to the modified LW equation that considered only a nanoscale slip length. An initial water nanodroplet study was performed to properly elucidate the wetting behavior of copper and gold surfaces. Intermolecular interaction strengths between water and corresponding solid surfaces were determined by matching the contact angle values obtained by experimental measurements. The migration of liquid water into copper and gold capillaries was measured by MD simulations and was found to differ from the modified LW equation. We found that the liquid layering in the vicinity of the solid surface induces a higher density and viscosity, leading to a slower MD uptake of fluid into the capillaries than was theoretically predicted. The near-surface viscosity for the nanoscale-confined water was defined and calculated for the thin film of water that was sheared between the two solid surfaces, as the ratio of water shear stress to the applied shear rate. Considering the effects of both the interface viscosity and slip length of the fluid, we successfully predicted the MD-measured fluid rise in the nanotubes.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, we present an approach for predicting nanoscale capillary imbibitions using the Lucas-Washburn (LW) theory. Molecular dynamics (MD) simulations were employed to investigate the effects of surface forces on the viscosity of liquid water. This provides an update to the modified LW equation that considered only a nanoscale slip length. An initial water nanodroplet study was performed to properly elucidate the wetting behavior of copper and gold surfaces. Intermolecular interaction strengths between water and corresponding solid surfaces were determined by matching the contact angle values obtained by experimental measurements. The migration of liquid water into copper and gold capillaries was measured by MD simulations and was found to differ from the modified LW equation. We found that the liquid layering in the vicinity of the solid surface induces a higher density and viscosity, leading to a slower MD uptake of fluid into the capillaries than was theoretically predicted. The near-surface viscosity for the nanoscale-confined water was defined and calculated for the thin film of water that was sheared between the two solid surfaces, as the ratio of water shear stress to the applied shear rate. Considering the effects of both the interface viscosity and slip length of the fluid, we successfully predicted the MD-measured fluid rise in the nanotubes. |

Ma, Zhiyuan; Korucu, Ayse; Miller, Richard Steven A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers Journal Article COMBUSTION THEORY AND MODELLING, 19 (6), pp. 807-832, 2015, ISSN: 1364-7830. @article{ISI:000366248600006, title = {A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers}, author = {Zhiyuan Ma and Ayse Korucu and Richard Steven Miller}, doi = {10.1080/13647830.2015.1100753}, issn = {1364-7830}, year = {2015}, date = {2015-11-01}, journal = {COMBUSTION THEORY AND MODELLING}, volume = {19}, number = {6}, pages = {807-832}, abstract = {Direct Numerical Simulation (DNS) data on high pressure H-2/O-2 and H-2/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Direct Numerical Simulation (DNS) data on high pressure H-2/O-2 and H-2/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number. |

Barisik, Murat; Yazicioglu, Almila Guevenc; Cetin, Barbaros; Kakac, Sadik Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects Journal Article INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 67 , pp. 81-88, 2015, ISSN: 0735-1933. @article{ISI:000362143700012, title = {Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects}, author = {Murat Barisik and Almila Guevenc Yazicioglu and Barbaros Cetin and Sadik Kakac}, doi = {10.1016/j.icheatmasstransfer.2015.05.004}, issn = {0735-1933}, year = {2015}, date = {2015-10-01}, journal = {INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER}, volume = {67}, pages = {81-88}, abstract = {The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram-Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number. (C)2015 Published by Elsevier Ltd.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram-Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number. (C)2015 Published by Elsevier Ltd. |

Cetkin, Erdal; Oliani, Alessandro The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain Journal Article JOURNAL OF APPLIED PHYSICS, 118 (2), 2015, ISSN: 0021-8979. @article{ISI:000357961000033, title = {The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain}, author = {Erdal Cetkin and Alessandro Oliani}, doi = {10.1063/1.4926620}, issn = {0021-8979}, year = {2015}, date = {2015-07-01}, journal = {JOURNAL OF APPLIED PHYSICS}, volume = {118}, number = {2}, abstract = {Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L-0, where L-0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change. (c) 2015 AIP Publishing LLC.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L-0, where L-0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change. (c) 2015 AIP Publishing LLC. |

Barisik, Murat; Beskok, Ali Molecular free paths in nanoscale gas flows Journal Article MICROFLUIDICS AND NANOFLUIDICS, 18 (5-6), pp. 1365-1371, 2015, ISSN: 1613-4982. @article{ISI:000353819900057, title = {Molecular free paths in nanoscale gas flows}, author = {Murat Barisik and Ali Beskok}, doi = {10.1007/s10404-014-1535-3}, issn = {1613-4982}, year = {2015}, date = {2015-05-01}, journal = {MICROFLUIDICS AND NANOFLUIDICS}, volume = {18}, number = {5-6}, pages = {1365-1371}, abstract = {Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas-surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas-surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported. |

Cetkin, Erdal CONSTRUCTAL STRUCTURES FOR SELF-COOLING: MICROVASCULAR WAVY AND STRAIGHT CHANNELS Journal Article JOURNAL OF THERMAL ENGINEERING, 1 (5, 1), pp. 166-174, 2015, ISSN: 2148-7847. @article{ISI:000434616100004, title = {CONSTRUCTAL STRUCTURES FOR SELF-COOLING: MICROVASCULAR WAVY AND STRAIGHT CHANNELS}, author = {Erdal Cetkin}, doi = {10.18186/jte.10873}, issn = {2148-7847}, year = {2015}, date = {2015-02-01}, journal = {JOURNAL OF THERMAL ENGINEERING}, volume = {1}, number = {5, 1}, pages = {166-174}, abstract = {This paper shows that a conductive domain which is subjected to heating from its bottom can be cooled with embedded microvascular cooling channels in it. The volume of the domain and the coolant are fixed. The actively cooled domain is mimicked from the human skin (which regulates temperature with microvascular blood vessels). The effect of the shape of cooling channels (sinusoidal or straight) and their locations in the direction perpendicular to the bottom surface on the peak and average temperatures are studied. In addition, the effect of pressure difference in between the inlet and outlet is varied. The pressure drop in the sinusoidal channel configurations is greater than the straight channel configurations for a fixed cooling channel volume. The peak and average temperatures are the smallest with straight cooling channels located at y = 0.7 mm. Furthermore, how the cooling channel configuration should change when the heat is generated throughout the volume is studied. The peak and average temperatures are smaller with straight channels than the sinusoidal ones when the pressure drop is less than 420 Pa, and they become smaller with sinusoidal channel configurations when the pressure drop is greater than 420 Pa. In addition, the peak and average temperatures are the smallest with sinusoidal channels for a fixed flow rate. Furthermore, the peak temperatures for multiple cooling channels is documented, and the multiple channel configurations promise to the smallest peak temperature for a fixed pressure drop value. This paper uncovers that there is no optimal cooling channel design for any condition, but there is one for specific objectives and conditions.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper shows that a conductive domain which is subjected to heating from its bottom can be cooled with embedded microvascular cooling channels in it. The volume of the domain and the coolant are fixed. The actively cooled domain is mimicked from the human skin (which regulates temperature with microvascular blood vessels). The effect of the shape of cooling channels (sinusoidal or straight) and their locations in the direction perpendicular to the bottom surface on the peak and average temperatures are studied. In addition, the effect of pressure difference in between the inlet and outlet is varied. The pressure drop in the sinusoidal channel configurations is greater than the straight channel configurations for a fixed cooling channel volume. The peak and average temperatures are the smallest with straight cooling channels located at y = 0.7 mm. Furthermore, how the cooling channel configuration should change when the heat is generated throughout the volume is studied. The peak and average temperatures are smaller with straight channels than the sinusoidal ones when the pressure drop is less than 420 Pa, and they become smaller with sinusoidal channel configurations when the pressure drop is greater than 420 Pa. In addition, the peak and average temperatures are the smallest with sinusoidal channels for a fixed flow rate. Furthermore, the peak temperatures for multiple cooling channels is documented, and the multiple channel configurations promise to the smallest peak temperature for a fixed pressure drop value. This paper uncovers that there is no optimal cooling channel design for any condition, but there is one for specific objectives and conditions. |

Cetkin, E; Lorente, S; Bejan, A Vascularization for cooling and reduced thermal stresses Journal Article INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 80 , pp. 858-864, 2015, ISSN: 0017-9310. @article{ISI:000345202100080, title = {Vascularization for cooling and reduced thermal stresses}, author = {E Cetkin and S Lorente and A Bejan}, doi = {10.1016/j.ijheatmasstransfer.2014.09.027}, issn = {0017-9310}, year = {2015}, date = {2015-01-01}, journal = {INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, volume = {80}, pages = {858-864}, abstract = {This paper documents the effect of thermal expansion on a vascularized plate that is heated and loaded mechanically. Vascular cooling channels embedded in a circular plate provide cooling and mechanical strength. The coolant enters the plate from the center and leaves after it cools the plate to an allowable temperature limit. The mechanical strength of the plate decreases because of the embedded cooling channels. However, cooling the plate under an allowable temperature level decreases the thermal stresses. The mechanical strength of the plate which is heated and loaded mechanically at the same time can be increased by inserting cooling channels in it. The mechanical and thermofluid behavior of a vascularized plate was simulated numerically. The cooling channel configurations that provide the smallest peak temperature and von Mises stress are documented. There is one cooling channel configuration that is the best for the given set of boundary conditions and constraints; however, there is no single configuration that is best for all conditions. (C) 2014 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper documents the effect of thermal expansion on a vascularized plate that is heated and loaded mechanically. Vascular cooling channels embedded in a circular plate provide cooling and mechanical strength. The coolant enters the plate from the center and leaves after it cools the plate to an allowable temperature limit. The mechanical strength of the plate decreases because of the embedded cooling channels. However, cooling the plate under an allowable temperature level decreases the thermal stresses. The mechanical strength of the plate which is heated and loaded mechanically at the same time can be increased by inserting cooling channels in it. The mechanical and thermofluid behavior of a vascularized plate was simulated numerically. The cooling channel configurations that provide the smallest peak temperature and von Mises stress are documented. There is one cooling channel configuration that is the best for the given set of boundary conditions and constraints; however, there is no single configuration that is best for all conditions. (C) 2014 Elsevier Ltd. All rights reserved. |

Cetkin, Erdal Constructal vascularized structures Journal Article OPEN ENGINEERING, 5 (1), pp. 220-228, 2015, ISSN: 2391-5439. @article{ISI:000218406100024, title = {Constructal vascularized structures}, author = {Erdal Cetkin}, doi = {10.1515/eng-2015-0017}, issn = {2391-5439}, year = {2015}, date = {2015-01-01}, journal = {OPEN ENGINEERING}, volume = {5}, number = {1}, pages = {220-228}, abstract = {Smart features such as self-healing and selfcooling require bathing the entire volume with a coolant or/and healing agent. Bathing the entire volume is an example of point to area (or volume) flows. Point to area flows cover all the distributing and collecting kinds of flows, i.e. inhaling and exhaling, mining, river deltas, energy distribution, distribution of products on the landscape and so on. The flow resistances of a point to area flow can be decreased by changing the design with the guidance of the constructal law, which is the law of the design evolution in time. In this paper, how the flow resistances (heat, fluid and stress) can be decreased by using the constructal law is shown with examples. First, the validity of two assumptions is surveyed: using temperature independent Hess-Murray rule and using constant diameter ducts where the duct discharges fluid along its edge. Then, point to area types of flows are explained by illustrating the results of two examples: fluid networks and heating an area. Last, how the structures should be vascularized for cooling and mechanical strength is documented. This paper shows that flow resistances can be decreased by morphing the shape freely without any restrictions or generic algorithms.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Smart features such as self-healing and selfcooling require bathing the entire volume with a coolant or/and healing agent. Bathing the entire volume is an example of point to area (or volume) flows. Point to area flows cover all the distributing and collecting kinds of flows, i.e. inhaling and exhaling, mining, river deltas, energy distribution, distribution of products on the landscape and so on. The flow resistances of a point to area flow can be decreased by changing the design with the guidance of the constructal law, which is the law of the design evolution in time. In this paper, how the flow resistances (heat, fluid and stress) can be decreased by using the constructal law is shown with examples. First, the validity of two assumptions is surveyed: using temperature independent Hess-Murray rule and using constant diameter ducts where the duct discharges fluid along its edge. Then, point to area types of flows are explained by illustrating the results of two examples: fluid networks and heating an area. Last, how the structures should be vascularized for cooling and mechanical strength is documented. This paper shows that flow resistances can be decreased by morphing the shape freely without any restrictions or generic algorithms. |

Cetkin, Erdal INVERTED FINS FOR COOLING OF A NON-UNIFORMLY HEATED DOMAIN Journal Article JOURNAL OF THERMAL ENGINEERING, 1 (1), pp. 1-9, 2015, ISSN: 2148-7847. @article{ISI:000434614600001, title = {INVERTED FINS FOR COOLING OF A NON-UNIFORMLY HEATED DOMAIN}, author = {Erdal Cetkin}, doi = {10.18186/jte.12488}, issn = {2148-7847}, year = {2015}, date = {2015-01-01}, journal = {JOURNAL OF THERMAL ENGINEERING}, volume = {1}, number = {1}, pages = {1-9}, abstract = {This paper shows that the peak temperature of a non-uniformly heated region can be decreased by embedding high-conductivity tree-shaped inserts which is in contact with a heat sink from its stem. The volume fraction of the high-conductivity material is fixed, and so is the volume of the solid region. The length scale of the solid domain is L. Inside there is a cube-shaped region with length scale of 0.1L and heat production 100 times greater than the rest of the domain. The location of this hot spot was varied to uncover how its location affects the peak temperature and the design of inverted fins, i.e. highconductivity tree-shaped inserts. The volume fraction of the high-conductivity tree was varied for number of bifurcation levels of 0, 1 and 2. This showed that increasing the number of the bifurcation levels decreases the peak temperature when the volume fraction decreases. The optimal diameter ratios and optimal bifurcation angles at the each junction level are also documented. Y-shaped trees promise smaller peak temperatures than T-shaped trees. The location of the vascular tree in the z direction also affects the peak temperature when the heat generation is non-uniform. In addition, the peak temperature is minimum when z = 0.65L even though the hot spot is located on z = 0.75L.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper shows that the peak temperature of a non-uniformly heated region can be decreased by embedding high-conductivity tree-shaped inserts which is in contact with a heat sink from its stem. The volume fraction of the high-conductivity material is fixed, and so is the volume of the solid region. The length scale of the solid domain is L. Inside there is a cube-shaped region with length scale of 0.1L and heat production 100 times greater than the rest of the domain. The location of this hot spot was varied to uncover how its location affects the peak temperature and the design of inverted fins, i.e. highconductivity tree-shaped inserts. The volume fraction of the high-conductivity tree was varied for number of bifurcation levels of 0, 1 and 2. This showed that increasing the number of the bifurcation levels decreases the peak temperature when the volume fraction decreases. The optimal diameter ratios and optimal bifurcation angles at the each junction level are also documented. Y-shaped trees promise smaller peak temperatures than T-shaped trees. The location of the vascular tree in the z direction also affects the peak temperature when the heat generation is non-uniform. In addition, the peak temperature is minimum when z = 0.65L even though the hot spot is located on z = 0.75L. |

## 2014 |

Toprak, Kasim; Bayazitoglu, Yildiz Interfacial thermal resistance of Cu-SWCNT nanowire in water Journal Article INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 79 , pp. 584-588, 2014, ISSN: 0017-9310. @article{ISI:000343781900056, title = {Interfacial thermal resistance of Cu-SWCNT nanowire in water}, author = {Kasim Toprak and Yildiz Bayazitoglu}, doi = {10.1016/j.ijheatmasstransfer.2014.08.024}, issn = {0017-9310}, year = {2014}, date = {2014-12-01}, journal = {INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, volume = {79}, pages = {584-588}, abstract = {The conduction along the radial direction of CuNW-SWCNT nanocomposite surrounded with water is examined. Due to its simplicity and adaptability, a simple point-charge water model is implemented. Using the Nose-Hoover thermostat, the copper core is kept at a uniform temperature as a heat source, and a circular edge layer of water is kept at a lower temperature as a heat sink in order to impose a radial temperature distribution. The thermal boundary resistance was predicted as 0.1732 x 10(8) m(2) K/W at the interface of CuNW-water, 3.16 x 10(-8) m(2) K/W at the interface of SWCNT-water, and 0.743 x 10(-8) m(2) K/W at the interface of (CuNW-SWCNT)-water. (C) 2014 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The conduction along the radial direction of CuNW-SWCNT nanocomposite surrounded with water is examined. Due to its simplicity and adaptability, a simple point-charge water model is implemented. Using the Nose-Hoover thermostat, the copper core is kept at a uniform temperature as a heat source, and a circular edge layer of water is kept at a lower temperature as a heat sink in order to impose a radial temperature distribution. The thermal boundary resistance was predicted as 0.1732 x 10(8) m(2) K/W at the interface of CuNW-water, 3.16 x 10(-8) m(2) K/W at the interface of SWCNT-water, and 0.743 x 10(-8) m(2) K/W at the interface of (CuNW-SWCNT)-water. (C) 2014 Elsevier Ltd. All rights reserved. |

Cetkin, Erdal Three-dimensional high-conductivity trees for volumetric cooling Journal Article INTERNATIONAL JOURNAL OF ENERGY RESEARCH, 38 (12), pp. 1571-1577, 2014, ISSN: 0363-907X. @article{ISI:000342133500008, title = {Three-dimensional high-conductivity trees for volumetric cooling}, author = {Erdal Cetkin}, doi = {10.1002/er.3176}, issn = {0363-907X}, year = {2014}, date = {2014-10-01}, journal = {INTERNATIONAL JOURNAL OF ENERGY RESEARCH}, volume = {38}, number = {12}, pages = {1571-1577}, abstract = {Here, we show how the cooling performance of a volumetrically heated solid can be increased by embedding high-conductivity tree-shaped designs in it. The volume fraction occupied by the high-conductivity material is fixed. Embedding the high-conductivity material as trees in the solid decreases the maximum temperature more than three times compared with distributing the high-conductivity material uniformly throughout the solid. The maximum temperature decreases as the number of the bifurcation levels and the volume fraction of the highly conductive material increase. The thermal resistance of the cube is the lowest when the diameter ratio of the mother and daughter branches at each pairing junction is 2. Changing from T-shaped to Y-shaped designs and from two-dimensional to three-dimensional designs decrease the maximum and the volume averaged temperatures. The peak temperature is the lowest in three-dimensional and Y-shaped designs. This paper shows that the peak temperature of the heated solid can be decreased by only varying the shape of the high-conductivity tree embedded in it. Copyright (c) 2014 John Wiley & Sons, Ltd.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here, we show how the cooling performance of a volumetrically heated solid can be increased by embedding high-conductivity tree-shaped designs in it. The volume fraction occupied by the high-conductivity material is fixed. Embedding the high-conductivity material as trees in the solid decreases the maximum temperature more than three times compared with distributing the high-conductivity material uniformly throughout the solid. The maximum temperature decreases as the number of the bifurcation levels and the volume fraction of the highly conductive material increase. The thermal resistance of the cube is the lowest when the diameter ratio of the mother and daughter branches at each pairing junction is 2. Changing from T-shaped to Y-shaped designs and from two-dimensional to three-dimensional designs decrease the maximum and the volume averaged temperatures. The peak temperature is the lowest in three-dimensional and Y-shaped designs. This paper shows that the peak temperature of the heated solid can be decreased by only varying the shape of the high-conductivity tree embedded in it. Copyright (c) 2014 John Wiley & Sons, Ltd. |

Ozgumus, Turkuler; Mobedi, Moghtada; Ozkol, Unver DETERMINATION OF KOZENY CONSTANT BASED ON POROSITY AND PORE TO THROAT SIZE RATIO IN POROUS MEDIUM WITH RECTANGULAR RODS Journal Article ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS, 8 (2), pp. 308-318, 2014, ISSN: 1994-2060. @article{ISI:000337224100010, title = {DETERMINATION OF KOZENY CONSTANT BASED ON POROSITY AND PORE TO THROAT SIZE RATIO IN POROUS MEDIUM WITH RECTANGULAR RODS}, author = {Turkuler Ozgumus and Moghtada Mobedi and Unver Ozkol}, doi = {10.1080/19942060.2014.11015516}, issn = {1994-2060}, year = {2014}, date = {2014-06-01}, journal = {ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS}, volume = {8}, number = {2}, pages = {308-318}, abstract = {Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and Navier-Stokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and Navier-Stokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios. |

Atalay, Selcuk; Barisik, Murat; Beskok, Ali; Qian, Shizhi Surface Charge of a Nanoparticle Interacting with a Flat Substrate Journal Article JOURNAL OF PHYSICAL CHEMISTRY C, 118 (20), pp. 10927-10935, 2014, ISSN: 1932-7447. @article{ISI:000336509400046, title = {Surface Charge of a Nanoparticle Interacting with a Flat Substrate}, author = {Selcuk Atalay and Murat Barisik and Ali Beskok and Shizhi Qian}, doi = {10.1021/jp5023554}, issn = {1932-7447}, year = {2014}, date = {2014-05-01}, journal = {JOURNAL OF PHYSICAL CHEMISTRY C}, volume = {118}, number = {20}, pages = {10927-10935}, abstract = {Electrostatic interactions between two charged dielectric objects highly depend on their surface charge. Most existing studies assume constant surface charge densities between the two interacting objects regardless of the separation distance between them. The surface charge of a spherical silica nanoparticle interacting with a flat silica plate is investigated numerically as a function of the separation distance normalized with the electrical double layer thickness (kappa h), pH, and background salt concentration. The numerical model employs Poisson-Nernst-Planck equations for ionic mass transport and considers surface charge regulation in the presence of multiple ionic species. Relatively weak interactions between the nanoparticle and the plate are observed for kappa h >> 1, resulting in uniform surface charge densities. Because of curvature, the surface charge density of the nanoparticle is higher than that of the plate. Strong interactions are observed for kappa h <= 1, leading to spatially nonuniform surface charge densities on the nanoparticle and the plate. This effect increases with decreased separation distance (kappa h). Enhanced proton concentration in the gap between the particle and the plate leads to reduced surface charge densities on the two objects.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Electrostatic interactions between two charged dielectric objects highly depend on their surface charge. Most existing studies assume constant surface charge densities between the two interacting objects regardless of the separation distance between them. The surface charge of a spherical silica nanoparticle interacting with a flat silica plate is investigated numerically as a function of the separation distance normalized with the electrical double layer thickness (kappa h), pH, and background salt concentration. The numerical model employs Poisson-Nernst-Planck equations for ionic mass transport and considers surface charge regulation in the presence of multiple ionic species. Relatively weak interactions between the nanoparticle and the plate are observed for kappa h >> 1, resulting in uniform surface charge densities. Because of curvature, the surface charge density of the nanoparticle is higher than that of the plate. Strong interactions are observed for kappa h <= 1, leading to spatially nonuniform surface charge densities on the nanoparticle and the plate. This effect increases with decreased separation distance (kappa h). Enhanced proton concentration in the gap between the particle and the plate leads to reduced surface charge densities on the two objects. |

Pham, An Truong; Barisik, Murat; Kim, Bohung Molecular Dynamics Simulations of Kapitza Length for Argon-Silicon and Water-Silicon Interfaces Journal Article INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING, 15 (2), pp. 323-329, 2014, ISSN: 2234-7593. @article{ISI:000331786500017, title = {Molecular Dynamics Simulations of Kapitza Length for Argon-Silicon and Water-Silicon Interfaces}, author = {An Truong Pham and Murat Barisik and Bohung Kim}, doi = {10.1007/s12541-014-0341-x}, issn = {2234-7593}, year = {2014}, date = {2014-02-01}, journal = {INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING}, volume = {15}, number = {2}, pages = {323-329}, abstract = {A comprehensive understanding of heat conduction between two parallel solid walls separated by liquid remains incomplete in nanometer scale. In addition, the solid/liquid interfacial thermal resistance has been an important technical issue in thermal/fluid engineering such as micro electro-mechanical systems and nano electro-mechanical systems with liquid inside. Therefore, further advancements in nanoscale physics require an advanced understanding of momentum and energy transport at solid/liquid interfaces. This study employs three-dimensional molecular dynamics (MD) simulations to investigate the thermal resistance at solid/liquid interfaces. Heat conduction between two parallel silicon walls separated by a thin film of liquid water is considered. The density distribution of liquid water is discussed with the simulation results to further understanding of the dynamic properties of water near solid surfaces. Meanwhile, temperature profiles appear discontinuous between liquid and solid temperatures due to the dissimilarity of thermal transport properties of the two materials, which validates thermal resistance (or Kapitza length) at solid/liquid interfaces. MD results also investigate the temperature dependence of the Kapitza length, demonstrating that the Kaptiza lengths fluctuate around an average value and are independent of the wall temperature at solid/liquid interfaces. Our study provides useful information for the design of thermal management or heat dissipation devices across silicon/water and silicon/argon interfaces in nanoscale.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A comprehensive understanding of heat conduction between two parallel solid walls separated by liquid remains incomplete in nanometer scale. In addition, the solid/liquid interfacial thermal resistance has been an important technical issue in thermal/fluid engineering such as micro electro-mechanical systems and nano electro-mechanical systems with liquid inside. Therefore, further advancements in nanoscale physics require an advanced understanding of momentum and energy transport at solid/liquid interfaces. This study employs three-dimensional molecular dynamics (MD) simulations to investigate the thermal resistance at solid/liquid interfaces. Heat conduction between two parallel silicon walls separated by a thin film of liquid water is considered. The density distribution of liquid water is discussed with the simulation results to further understanding of the dynamic properties of water near solid surfaces. Meanwhile, temperature profiles appear discontinuous between liquid and solid temperatures due to the dissimilarity of thermal transport properties of the two materials, which validates thermal resistance (or Kapitza length) at solid/liquid interfaces. MD results also investigate the temperature dependence of the Kapitza length, demonstrating that the Kaptiza lengths fluctuate around an average value and are independent of the wall temperature at solid/liquid interfaces. Our study provides useful information for the design of thermal management or heat dissipation devices across silicon/water and silicon/argon interfaces in nanoscale. |

Cetkin, Erdal EMERGENCE OF TAPERED DUCTS IN VASCULAR DESIGNS WITH LAMINAR AND TURBULENT FLOWS Journal Article JOURNAL OF POROUS MEDIA, 17 (8), pp. 715-722, 2014, ISSN: 1091-028X. @article{ISI:000342967400005, title = {EMERGENCE OF TAPERED DUCTS IN VASCULAR DESIGNS WITH LAMINAR AND TURBULENT FLOWS}, author = {Erdal Cetkin}, doi = {10.1615/JPorMedia.v17.i8.50}, issn = {1091-028X}, year = {2014}, date = {2014-01-01}, journal = {JOURNAL OF POROUS MEDIA}, volume = {17}, number = {8}, pages = {715-722}, abstract = {Here we show that tapered ducts emerge in volumetrically bathed porous materials to decrease the resistance to the flow in laminar and turbulent flow regimes. The fluid enters the volume from one point and it is distributed to the entire volume. After bathing the volume, it is collected and leaves the volume from another point, i.e., two trees matched canopy to canopy. This paper shows that the flow architecture (i.e., design of the void spaces in a porous material) should be changed to obtain the minimum resistance to the flow as its size increases. Tapering the ducts decreases the order of the transition size, i.e., the size for changing from one construct to another to obtain the minimum pressure drop. The decrease in the pressure drop is 16% and 38% with the tapered ducts when the flow is laminar and turbulent, respectively. In addition, the volume ratios and the shape of the tapered ducts are documented. There is no design existing in nature with diameters of constant size in order to distribute and/or collect heat, fluid, and/or stress such as bones, rivers, veins, and tree branches. The emergence of the tapered ducts in designed porous materials is natural.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here we show that tapered ducts emerge in volumetrically bathed porous materials to decrease the resistance to the flow in laminar and turbulent flow regimes. The fluid enters the volume from one point and it is distributed to the entire volume. After bathing the volume, it is collected and leaves the volume from another point, i.e., two trees matched canopy to canopy. This paper shows that the flow architecture (i.e., design of the void spaces in a porous material) should be changed to obtain the minimum resistance to the flow as its size increases. Tapering the ducts decreases the order of the transition size, i.e., the size for changing from one construct to another to obtain the minimum pressure drop. The decrease in the pressure drop is 16% and 38% with the tapered ducts when the flow is laminar and turbulent, respectively. In addition, the volume ratios and the shape of the tapered ducts are documented. There is no design existing in nature with diameters of constant size in order to distribute and/or collect heat, fluid, and/or stress such as bones, rivers, veins, and tree branches. The emergence of the tapered ducts in designed porous materials is natural. |

## 2013 |

Toprak, K; Bayazitoglu, Y Numerical modeling of a CNT-Cu coaxial nanowire in a vacuum to determine the thermal conductivity Journal Article INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 61 , pp. 172-175, 2013, ISSN: 0017-9310. @article{ISI:000318260200018, title = {Numerical modeling of a CNT-Cu coaxial nanowire in a vacuum to determine the thermal conductivity}, author = {K Toprak and Y Bayazitoglu}, doi = {10.1016/j.ijheatmasstransfer.2013.01.082}, issn = {0017-9310}, year = {2013}, date = {2013-06-01}, journal = {INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, volume = {61}, pages = {172-175}, abstract = {A molecular dynamics simulation is created to predict the thermal conductivity of a (7,7) single wall carbon nanotube filled with a copper nanowire for lengths ranging from 9.957 nm to 63.091 nm. In the simulations, a temperature difference is created using Nose-Hoover thermostats at the two ends with 320 K and 280 K. The thermal conductivity of the carbon nanotube-copper nanowire nanostructure is calculated to be 24% higher than that of a corresponding pure single wall carbon nanotube and estimated to be 40% lower than that of a pure copper nanowire. (C) 2013 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A molecular dynamics simulation is created to predict the thermal conductivity of a (7,7) single wall carbon nanotube filled with a copper nanowire for lengths ranging from 9.957 nm to 63.091 nm. In the simulations, a temperature difference is created using Nose-Hoover thermostats at the two ends with 320 K and 280 K. The thermal conductivity of the carbon nanotube-copper nanowire nanostructure is calculated to be 24% higher than that of a corresponding pure single wall carbon nanotube and estimated to be 40% lower than that of a pure copper nanowire. (C) 2013 Elsevier Ltd. All rights reserved. |

Ozgumus, Turkuler; Mobedi, Moghtada; Ozkol, Unver; Nakayama, Akira Thermal Dispersion in Porous Media-A Review on the Experimental Studies for Packed Beds Journal Article APPLIED MECHANICS REVIEWS, 65 (3), 2013, ISSN: 0003-6900. @article{ISI:000329612200001, title = {Thermal Dispersion in Porous Media-A Review on the Experimental Studies for Packed Beds}, author = {Turkuler Ozgumus and Moghtada Mobedi and Unver Ozkol and Akira Nakayama}, doi = {10.1115/1.4024351}, issn = {0003-6900}, year = {2013}, date = {2013-05-01}, journal = {APPLIED MECHANICS REVIEWS}, volume = {65}, number = {3}, abstract = {Thermal dispersion is an important topic in the convective heat transfer in porous media. In order to determine the heat transfer in a packed bed, the effective thermal conductivity including both stagnant and dispersion thermal conductivities should be known. Several theoretical and experimental studies have been performed on the determination of the effective thermal conductivity. The aim of this study is to review the experimental studies done on the determination of the effective thermal conductivity of the packed beds. In this study, firstly brief information on the definition of the thermal dispersion is presented and then the reported experimental studies on the determination of the effective thermal conductivity are summarized and compared. The reported experimental methods are classified into three groups: (1) heat addition/removal at the lateral boundaries, (2) heat addition at the inlet/outlet boundary, (3) heat addition inside the bed. For each performed study, the experimental details, methods, obtained results, and suggested correlations for the determination of the effective thermal conductivity are presented. The similarities and differences between experimental methods and reported studies are shown by tables. Comparison of the correlations for the effective thermal conductivity is made by using figures and the results of the studies are discussed.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Thermal dispersion is an important topic in the convective heat transfer in porous media. In order to determine the heat transfer in a packed bed, the effective thermal conductivity including both stagnant and dispersion thermal conductivities should be known. Several theoretical and experimental studies have been performed on the determination of the effective thermal conductivity. The aim of this study is to review the experimental studies done on the determination of the effective thermal conductivity of the packed beds. In this study, firstly brief information on the definition of the thermal dispersion is presented and then the reported experimental studies on the determination of the effective thermal conductivity are summarized and compared. The reported experimental methods are classified into three groups: (1) heat addition/removal at the lateral boundaries, (2) heat addition at the inlet/outlet boundary, (3) heat addition inside the bed. For each performed study, the experimental details, methods, obtained results, and suggested correlations for the determination of the effective thermal conductivity are presented. The similarities and differences between experimental methods and reported studies are shown by tables. Comparison of the correlations for the effective thermal conductivity is made by using figures and the results of the studies are discussed. |

Cetkin, E; Lorente, S; Bejan, A Constructal paddle design with ``fingers'' Journal Article JOURNAL OF APPLIED PHYSICS, 113 (19), 2013, ISSN: 0021-8979. @article{ISI:000319295200065, title = {Constructal paddle design with ``fingers''}, author = {E Cetkin and S Lorente and A Bejan}, doi = {10.1063/1.4804961}, issn = {0021-8979}, year = {2013}, date = {2013-05-01}, journal = {JOURNAL OF APPLIED PHYSICS}, volume = {113}, number = {19}, abstract = {Here, we show how the performance of a paddle that pushes a fluid can be increased by making parallel slits through it. The slit spacing is varied to see its effect on the drag force and the maximum stress in the paddle. The effect of water speed and paddle dimensions is documented. Designs with one or more slits are investigated. The drag force is maximum when the slit spacing matches the boundary layer thickness of the flow through the slit. Furthermore, the drag force is greater when the slit spacing is nonuniform: larger in the central slits than in the peripheral slits. The paddle with slits of one size performs almost as well as the best design with nonuniform spacings. The paddle design with slits achieves the same drag force and maximum stress with less material compared with a paddle without slits. (C) 2013 AIP Publishing LLC.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here, we show how the performance of a paddle that pushes a fluid can be increased by making parallel slits through it. The slit spacing is varied to see its effect on the drag force and the maximum stress in the paddle. The effect of water speed and paddle dimensions is documented. Designs with one or more slits are investigated. The drag force is maximum when the slit spacing matches the boundary layer thickness of the flow through the slit. Furthermore, the drag force is greater when the slit spacing is nonuniform: larger in the central slits than in the peripheral slits. The paddle with slits of one size performs almost as well as the best design with nonuniform spacings. The paddle design with slits achieves the same drag force and maximum stress with less material compared with a paddle without slits. (C) 2013 AIP Publishing LLC. |

## 2012 |

Barisik, Murat; Beskok, Ali Surface-gas interaction effects on nanoscale gas flows Journal Article MICROFLUIDICS AND NANOFLUIDICS, 13 (5), pp. 789-798, 2012, ISSN: 1613-4982. @article{ISI:000310640900009, title = {Surface-gas interaction effects on nanoscale gas flows}, author = {Murat Barisik and Ali Beskok}, doi = {10.1007/s10404-012-1000-0}, issn = {1613-4982}, year = {2012}, date = {2012-11-01}, journal = {MICROFLUIDICS AND NANOFLUIDICS}, volume = {13}, number = {5}, pages = {789-798}, abstract = {Molecular dynamics (MD) method is used to simulate shear driven argon gas flows in the early transition and free molecular flow regimes to investigate surface effects as a function of the surface-gas potential strength ratio (epsilon(wf)/epsilon(ff)). Results show a bulk flow region and a near wall region that extends three molecular diameters away from the surfaces. Within the near wall region the velocity, density, and shear stress distributions exhibit deviations from the kinetic theory predictions. Increased epsilon(wf)/epsilon(ff) results in increased gas density, leading toward monolayer adsorption on surfaces. The near wall velocity profile shows reduced gas slip, and eventually velocity stick with increased epsilon(wf)/epsilon(ff). Using MD predicted shear stress values and kinetic theory, tangential momentum accommodation coefficients (TMAC) are calculated as a function of epsilon(wf)/epsilon(ff), and TMAC values are shown to be independent of the Knudsen number. Presence of this near wall region breaks down the dynamic similarity between rarefied and nanoscale gas flows.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Molecular dynamics (MD) method is used to simulate shear driven argon gas flows in the early transition and free molecular flow regimes to investigate surface effects as a function of the surface-gas potential strength ratio (epsilon(wf)/epsilon(ff)). Results show a bulk flow region and a near wall region that extends three molecular diameters away from the surfaces. Within the near wall region the velocity, density, and shear stress distributions exhibit deviations from the kinetic theory predictions. Increased epsilon(wf)/epsilon(ff) results in increased gas density, leading toward monolayer adsorption on surfaces. The near wall velocity profile shows reduced gas slip, and eventually velocity stick with increased epsilon(wf)/epsilon(ff). Using MD predicted shear stress values and kinetic theory, tangential momentum accommodation coefficients (TMAC) are calculated as a function of epsilon(wf)/epsilon(ff), and TMAC values are shown to be independent of the Knudsen number. Presence of this near wall region breaks down the dynamic similarity between rarefied and nanoscale gas flows. |

Cetkin, E; Lorente, S; Bejan, A Vascularization for cooling a plate heated by a randomly moving source Journal Article JOURNAL OF APPLIED PHYSICS, 112 (8), 2012, ISSN: 0021-8979. @article{ISI:000310597500155, title = {Vascularization for cooling a plate heated by a randomly moving source}, author = {E Cetkin and S Lorente and A Bejan}, doi = {10.1063/1.4759290}, issn = {0021-8979}, year = {2012}, date = {2012-10-01}, journal = {JOURNAL OF APPLIED PHYSICS}, volume = {112}, number = {8}, abstract = {Here, we show that a plate heated by a moving beam can be cooled effectively by fluid that flows through a vasculature of channels embedded in the plate. The vascular designs studied are radial, grid and hybrid (radial + grid). The peak temperature of the plate changes with the path and direction of the moving beam. The strength, size and speed of the beam vary. The peak temperature increases as the beam strength and size increase and as the speed of the beam decreases. The grid and hybrid designs are robust because of loops present in the flow structure. The pressure difference that drives the fluid flow varied. The channel diameter ratios that provide greatest flow access are reported. The cooling performance of the multiscale grid structures is less sensitive to the changes in beam path than the cooling performance of the other structures studied. The effect of adding a vascular structure to the design is dramatic. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4759290]}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here, we show that a plate heated by a moving beam can be cooled effectively by fluid that flows through a vasculature of channels embedded in the plate. The vascular designs studied are radial, grid and hybrid (radial + grid). The peak temperature of the plate changes with the path and direction of the moving beam. The strength, size and speed of the beam vary. The peak temperature increases as the beam strength and size increase and as the speed of the beam decreases. The grid and hybrid designs are robust because of loops present in the flow structure. The pressure difference that drives the fluid flow varied. The channel diameter ratios that provide greatest flow access are reported. The cooling performance of the multiscale grid structures is less sensitive to the changes in beam path than the cooling performance of the other structures studied. The effect of adding a vascular structure to the design is dramatic. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4759290] |

Lorente, S; Cetkin, E; Bello-Ochende, T; Meyer, J P; Bejan, A The constructal-law physics of why swimmers must spread their fingers and toes Journal Article JOURNAL OF THEORETICAL BIOLOGY, 308 , pp. 141-146, 2012, ISSN: 0022-5193. @article{ISI:000307030100015, title = {The constructal-law physics of why swimmers must spread their fingers and toes}, author = {S Lorente and E Cetkin and T Bello-Ochende and J P Meyer and A Bejan}, doi = {10.1016/j.jtbi.2012.05.033}, issn = {0022-5193}, year = {2012}, date = {2012-09-01}, journal = {JOURNAL OF THEORETICAL BIOLOGY}, volume = {308}, pages = {141-146}, abstract = {Here we show theoretically that swimming animals and athletes gain an advantage in force and speed by spreading their fingers and toes optimally. The larger force means larger body mass lifted and greater speed, in accord with the constructal theory of all animal locomotion. The spacing between fingers must be twice the thickness of the boundary layer around one finger. This theoretical prediction is confirmed by computational fluid dynamics simulations of flow across two and four cylinders of diameter D. The optimal spacing is in the range 0.2D-0.4D, and decreases slightly as the Reynolds number (Re) increases from 20 to 100. For example, the total force exerted by two optimally spaced cylinders exceeds by 53% the total force of two cylinders with no spacing when Re=20. These design features hold for both time-dependent and steady-state flows. (C) 2012 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Here we show theoretically that swimming animals and athletes gain an advantage in force and speed by spreading their fingers and toes optimally. The larger force means larger body mass lifted and greater speed, in accord with the constructal theory of all animal locomotion. The spacing between fingers must be twice the thickness of the boundary layer around one finger. This theoretical prediction is confirmed by computational fluid dynamics simulations of flow across two and four cylinders of diameter D. The optimal spacing is in the range 0.2D-0.4D, and decreases slightly as the Reynolds number (Re) increases from 20 to 100. For example, the total force exerted by two optimally spaced cylinders exceeds by 53% the total force of two cylinders with no spacing when Re=20. These design features hold for both time-dependent and steady-state flows. (C) 2012 Elsevier Ltd. All rights reserved. |

Shi, Ziyuan; Barisik, Murat; Beskok, Ali Molecular dynamics modeling of thermal resistance at argon-graphite and argon-silver interfaces Journal Article INTERNATIONAL JOURNAL OF THERMAL SCIENCES, 59 , pp. 29-37, 2012, ISSN: 1290-0729. @article{ISI:000306765700005, title = {Molecular dynamics modeling of thermal resistance at argon-graphite and argon-silver interfaces}, author = {Ziyuan Shi and Murat Barisik and Ali Beskok}, doi = {10.1016/j.ijthermalsci.2012.04.009}, issn = {1290-0729}, year = {2012}, date = {2012-09-01}, journal = {INTERNATIONAL JOURNAL OF THERMAL SCIENCES}, volume = {59}, pages = {29-37}, abstract = {Heat conduction between two parallel solid walls separated by liquid argon is investigated using three-dimensional molecular dynamics (MD) simulations. Liquid argon molecules confined in silver and graphite nano-channels are examined separately. Heat flux and temperature distribution within the nano-channels are calculated by maintaining a fixed temperature difference between the two solid surfaces. Temperature profiles are linear sufficiently away from the walls, and heat transfer in liquid argon obeys the Fourier law. Temperature jump due to the interface thermal resistance (i.e., Kapitza length) is characterized as a function of the wall temperature. MD results enabled development of a phenomenological model for the Kapitza length, which is utilized as the coefficient of a Navier-type temperature jump boundary condition using continuum heat conduction equation. Analytical solution of this model results in successful predictions of temperature distribution in liquid argon confined in silver and graphite nano-channels as thin as 7 nm and 3.57 nm, respectively. (C) 2012 Elsevier Masson SAS. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Heat conduction between two parallel solid walls separated by liquid argon is investigated using three-dimensional molecular dynamics (MD) simulations. Liquid argon molecules confined in silver and graphite nano-channels are examined separately. Heat flux and temperature distribution within the nano-channels are calculated by maintaining a fixed temperature difference between the two solid surfaces. Temperature profiles are linear sufficiently away from the walls, and heat transfer in liquid argon obeys the Fourier law. Temperature jump due to the interface thermal resistance (i.e., Kapitza length) is characterized as a function of the wall temperature. MD results enabled development of a phenomenological model for the Kapitza length, which is utilized as the coefficient of a Navier-type temperature jump boundary condition using continuum heat conduction equation. Analytical solution of this model results in successful predictions of temperature distribution in liquid argon confined in silver and graphite nano-channels as thin as 7 nm and 3.57 nm, respectively. (C) 2012 Elsevier Masson SAS. All rights reserved. |

## 2010 |

Mobedi, Moghtada; Ozkol, Uenver; Sunden, Bengt Visualization of diffusion and convection heat transport in a square cavity with natural convection Journal Article INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 53 (1-3), pp. 99-109, 2010, ISSN: 0017-9310. @article{ISI:000272877900012, title = {Visualization of diffusion and convection heat transport in a square cavity with natural convection}, author = {Moghtada Mobedi and Uenver Ozkol and Bengt Sunden}, doi = {10.1016/j.ijheatmasstransfer.2009.09.048}, issn = {0017-9310}, year = {2010}, date = {2010-01-01}, journal = {INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, volume = {53}, number = {1-3}, pages = {99-109}, abstract = {In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, Omega(t). The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s(p) = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity. maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented. (C) 2009 Elsevier Ltd. All rights reserved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, Omega(t). The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s(p) = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity. maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented. (C) 2009 Elsevier Ltd. All rights reserved. |

## Project Title | ## Director of the Project | ## Start Date | ## Funds |

Jeotermal enerji araştırma-geliştirme, test ve eğitim Merkezi | Prof. Dr. Zafer İLKEN | 2002 | DPT |

Biyoteknoloji ve Biyomühendislik Araştırma Merkezi | Prof. Dr. Barış ÖZERDEM (Proje Eş Yürütücü) | 2007 | DPT |

Adsorpsiyonlu Isı Pompası | Doç. Dr. M. Mobedi | 2006 | DPT |

Evaluation Of Geothermal Developments In Turkey From The Clean Energy Point Of View. Case Studies: Balcova District Heating System-Izmir And Kizildere Geothermal Power Plant-Denizli | Prof. Dr. Gülden Gökçen | 2005 | TÜBİTAK |

Jet Akışlarındaki Kararsızlıkların Kontrolü İle Isı Transferinin Arttırılması | Yrd.Doç.Dr. Ünver Özkol | 2008 | TÜBİTAK |

İYTE Kampüs Alanındaki Rüzgar Enerjisi Potansiyelinin Ölçülmesi | Prof. Dr. Barış ÖZERDEM | 2000 | İYTE-BAP |

Alüminyum Köpük Malzeme ile İmal Edilmiş Hava Tipi Güneş Kollektörlerinin Analizi | Prof.Dr. Zafer İLKEN | 2001 | İYTE-BAP |

Jeotermal Enerjide Kullanılan Kuyu İçi Eşanjör Performanslarının Artırılması | Prof.Dr. Zafer İLKEN | 2001 | İYTE-BAP |

Endüstriyel Ürün Tasarımının , Üretiminin ve Mühendisliğinin ( CAD/CAM/CAE) Profesyonel Amaçlı Bir Hizmet Sektörü Olarak İnternet Ortamında Gerçekleştirilmesine Yönelik İnteraktif Bir Stüdyo Modeli : E- Stüdyo | Prof. Dr. Barış ÖZERDEM (Ortak Yürütücü) | 2000 | İYTE-BAP |

Rüzgar Türbinlerinde Verim Arttırmaya ve Veri Toplamaya Yönelik Bir Bilgisayar Kontrol Sistemi Geliştirilmesi | Prof. Dr. Barış ÖZERDEM | 2005 | İYTE-BAP |

Sinüsoidal ve “Offset Strip” tipindeki ısı değiştirici kanallarda akışın görüntülenmesi ve CDF ile karşılaştırılması | Yrd.Doç.Dr. Ünver Özkol | 2008 | İYTE-BAP |

Kamu Binalarında Enerji Verimliliği: İyte İdari Bina’nın Enerji Performansının Belirlenmesi | Prof. Dr. Gülden Gökçen | 2005 | İYTE-BAP |

Tarımsal Ürünlerin Kurutulmasında Kurutma Parametrelerinin Belirlenmesi | Prof. Dr. Gülden Gökçen | 2006 | İYTE-BAP |

Moleküler Seviyede Nano-Ölçek Gaz Akışlarının İncelenmesi | Yrd. Doç. Dr. Murat Barışık | 2015 | Marie Skłodowska-Curie COFUND |

Adsorpsiyon Yatak Isı Pompası Kullanılarak Buzdolabı Verimliliğinin Artırılması | Yrd. Doç. Dr. Murat Barışık | 2015 | SANTEZ Projesi |

Momentum Flux, Phase Doppler Anemonetry and High Speed Imaging Analysis of GDI injector under flash boiling conditions | Yrd. Doç. Dr. Alvero Diez Rodriguez | 2014 | TÜBİTAK |

Biodiesel Spray Investigation in a Constant Volume Combustion Chamber | Yrd. Doç. Dr. Alvero Diez Rodriguez | 2013 | TÜBİTAK |

Türkiye’nin Farklı İklim Koşullarında Isıl Konfor Sıcaklıklarına Bağlı Olarak Konutların Enerji Performanslarının Değerlendirilmesi | Prof. Dr. Gülden Gökçen | 2012 | TTMD |

Konutlarda Enerji Performansı Standard Değerlendirme Metodu (KEP-SDM) | Prof. Dr. Gülden Gökçen | 2010 | TMMOB |