Advanced Computational Methods in Heat Transfer VII
The present paper describes construction of an algorithm for conjugate heat transfer calculations... more The present paper describes construction of an algorithm for conjugate heat transfer calculations in order to find the most suitable form for a heat sink. Applying Volume Averaging theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The example numerical simulations were performed for test sections with isothermal structure as well as with heat conducting Al pin-fins. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at University of California, Los Angeles. The comparison of the drag coefficient as a function of Reynolds number reveals good agreement with already published data, whereas the comparison of the Nusselt number distributions shows much larger discrepancies. Finite conductivity of a solid phase decreases the heat transfer coefficient and the Nusselt number. The influence of conductivity becomes larger with increasing Reynolds number.
ABSTRACT Fractional scaling analysis (FSA) is demonstrated at the system level. The selected exam... more ABSTRACT Fractional scaling analysis (FSA) is demonstrated at the system level. The selected example is depressurization of nuclear reactor primary systems undergoing large- and small-break loss of coolant accidents (LOCA), specifically in two integral test facilities of different sizes and shapes, namely, LOFT and Semiscale. The paper demonstrates (1) the relation between pressure and volume displacement rates in analogy to generalized "effort" and "flow" in interdisciplinary analysis of complex systems and (2) using experimental data that a properly scaled depressurization history applies to both large- and small-break LOCA in two different facilities. FSA, when applied at the system, component, and process levels, serves to synthesize the worldwide wealth of results from analyses and experiments into compact form for efficient storage, transfer, and retrieval of information. The demonstration at the system level shows that during LOCAs the break flow dominates for break sizes between 0.1% and 200% of cold-leg flow cross-sectional area, and that FSA ranks processes quantitatively and thereby objectively in the order of their importance. FSA supersedes the hereunto subjectively implemented phenomena identification and ranking table. FSA readily quantifies scale distortions. FSA reduces significantly the need for and current cost of experiments and analyses.
In this work, we will investigate the performance of the Bi-porous wicks which are intended to ev... more In this work, we will investigate the performance of the Bi-porous wicks which are intended to eventually be used as the substrate in the TGP (Thermal Ground Plane) devices which function like thin heat pipes. In order to more closely simulate the operating conditions in a TGP, tests are conducted with a restrictor plate above the wick. By adding a mono-porous layer at the bottom and a vapor space on the top of the bi-porous wick, respectively vapor removal and liquid supply are meant to be enhanced. Hence the experiments are performed using such wicks. We present our effort improving an electric analogue model for the bi-porous wick based on the similarity between the differential equations governing the two systems. The analog model is initially improved for a disk shaped wick with a restrictor on top. Furthermore, the analogue technique is employed as a tool to investigate the performance of the wick with the vapor restrictor mounted on top; to compare the experimental data achieved in a boiling chamber versus TGP device; and to estimate the required data for the bi-porous evaporator calculations.
Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C, 2009
Developing better heat pipes requires advancement of technology in all aspects of construction. I... more Developing better heat pipes requires advancement of technology in all aspects of construction. In this paper I am investigating the effect of vapor pathways on the performance of biporous wicks in heat pipes. Biporous evaporator wicks, generated by sintering copper particles into semi-uniform clusters, were demonstrated to achieve high flux, heat transfer performance for use in heat pipes by Semenic (2007). The effective thermal conductivity of thick biporous wicks at high heat fluxes was found to be reduced because the region next ...
Volume 2: Heat Transfer Enhancement for Practical Applications; Heat and Mass Transfer in Fire and Combustion; Heat Transfer in Multiphase Systems; Heat and Mass Transfer in Biotechnology, 2013
ABSTRACT Biporous wicks are an effective means for facilitating evaporation in heat pipes used fo... more ABSTRACT Biporous wicks are an effective means for facilitating evaporation in heat pipes used for electronics cooling. They facilitate boiling within the wick by having two distinct size distributions of pores; the smaller pores provide high capillary pressure to pump liquid to the surface while the larger pores maintain high vapor permeability. The wicks investigated in this study were sintered copper biporous material. The authors previously presented a validated statistical model, based on work by Kovalev, which could predict the performance of biporous wicks tested at UCLA with reasonable accuracy [1]. Using this model, the author was able to gain new insight into the effect that the numerical estimate of liquid saturation of the wick has on dry out. The pore size distribution allows the determination of the capillary pressure available inside the wick and the Kovalev model provides the required pressure drop to supply liquid water to the heater surface. This led to a method of predicting dry out by comparing the capillary pressure in the wick to the required pressure drop from the model to estimate when the wick was dried out.When the required pressure drop determined by code exceeds the peak effective capillary pressure provided by the wick, the large pores of the wick are considered to be dry. These values are correlated to the input heat flux to determine what at what input power the wick begins to dry out. While the wick will not fail in this mode, the overall heat transfer coefficient will have peaked. In this work, this method of determining dry out will be validated against wicks tested at UCLA by comparing the input powers at which this dry out phenomenon occurs. Accurate predictions of dry out and the role of the pore size distribution are critical in developing methods to delay dry out of biporous wicks. By comparing the relative dry out points of various wick geometries to each other, augmented wick geometries can be suggested for future work. This modeling tool can lay the foundation for future tailoring of biporous evaporator wicks to specific tasks.
Journal of Thermal Science and Engineering Applications, 2011
Résumé/Abstract A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. ... more Résumé/Abstract A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was discovered originally in use with a device consisting of a metal tube charged with the patented inorganic aqueous solution (IAS), which is evaporated when the tube is evacuated before use. According to the patent, this evaporation leaves a thin film that allows the tube to carry high heat flux loads with low temperature drop across the tube in a solid state mode. However, various experiments with these tubes have produced ...
2010 14th International Heat Transfer Conference, Volume 5, 2010
Investigation of bi-porous wicks has yielded an effective method for increasing surface heat tran... more Investigation of bi-porous wicks has yielded an effective method for increasing surface heat transfer when the heat flux is high. It was further found that addition of a mono-porous layer on the heated surface significantly reduced the heated wall surface temperature. These bi-layer wicks were designed for use in 3× 5 heat spreading devices called Thermal Ground Planes (TGP) in order to transfer heat from a 1 cm source. In this work we will investigate the performance of a biporous wick with a monoporous layer in various test set-ups to show ...
A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was di... more A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was discovered originally in use with a device consisting of a metal tube charged with the patented inorganic aqueous solution (IAS) which is evaporated when the tube is evacuated before use. According to the patent, this evaporation leaves a thin film which allows the tube to carry high heat flux loads with low temperature drop across the tube in a solid state mode. However, various experiments with these tubes have produced inconsistent results and ...
ABSTRACT A plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some p... more ABSTRACT A plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some pin fins planted between the flow channels. Just as the other kinds of heat sinks, it is a hierarchical multilevel device with many parameters required for its description. Volume Averaging Theory (VAT) is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the plate-pin fin (porous media) morphology and to describe the hierarchical nature of the heat sink. Closure for the upper level is obtained using VAT to describe the lower level. At the lower level, the media is described by a representative elementary volume (REV). Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV. The terms in the closure expressions are complex and relating experimental data to the closure terms resulting from VAT is difficult. In this work, we model the plate-pin fin heat sink based on Volume Averaging Theory and use CFD to obtain detailed solutions of flow through an element of PPFHS and use these results to evaluate the closure terms needed for a fast running VAT based code. The VAT based code can then be used to solve the heat transfer characteristics of the higher level heat sink. The objective is to show how plate-pin fin heat sinks can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort.
ABSTRACT VAT is used to rigorously cast the point-wise conservation of energy, momentum and mass ... more ABSTRACT VAT is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of heat exchanger channel morphology. At the lower level, the media is described by a representative elementary volume (REV). Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV. The terms in the closure expressions are complex and relating experimental data to the closure terms resulting from Volume Averaging Theory (VAT) is difficult. In this work we use CFD to obtain detailed solutions to flow through an element of a heat exchanger and use these results to evaluate the closure terms needed for a fast running VAT based code. The VAT based code can then be used to solve the heat transfer characteristics of the higher level heat exchanger. A comparison is then made of the CFD closure and experimental data rescaled by VAT scaling. The objective is to show how heat exchangers can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort.
ABSTRACT Experimentally determining internal heat transfer coefficients in porous structures has ... more ABSTRACT Experimentally determining internal heat transfer coefficients in porous structures has been a challenge in the design of heat exchangers. In this study, a novel combined experimental and computational method for determining the internal heat ...
ABSTRACT The plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some... more ABSTRACT The plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some pin fins planted between the flow channels. In this paper, a numerical investigation was performed to compare the thermal and hydraulic performances of the PPFHSs and PFHS. PPFHSs with five forms of pin cross-section profiles (square, circular, elliptic, NACA 0050, and dropform) were numerically simulated. The influence of pin fin cross-section profile on the flow and heat transfer characteristics was presented by means of Nusselt number and pressure drop. It is found that the Nu number of a PPFHS is at least 35% higher than that of a PFHS used to construct the PPFHS at the same Reynolds number. Planting circular and square pins into the flow channel of heat sinks enhances the heat transfer at the expense of high pressure loss. Using the streamline shaped pins, not only the pressure drop of the compound heat sinks could be decreased considerably, the heat transfer enhancement also makes a step forward. The present numerical simulation provides original information of the influence of different pin-fin cross-section profiles on the thermal and hydraulic performance of the new type compound heat sink, which is helpful in the design of heat sinks.
ABSTRACT In the present study, air-side turbulent heat transfer and friction characteristics of f... more ABSTRACT In the present study, air-side turbulent heat transfer and friction characteristics of fin-and-tube heat exchangers with a large number of tube rows and large diameter of tubes are investigated numerically. Finite Volume Method based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based Shear-Stress-Transport (SST) model was used to predict the turbulent flow and heat transfer through the fin-and-tube heat exchanger coil. The effects of parameters such as Reynolds number, the number of tube rows, tube diameter, tube pitches and fin pitch are examined. In the end, correlations for the Nusselt number and friction factor which applicable to fin-and-tube heat exchangers with large number of large-diameter tube rows are proposed.
ABSTRACT In this paper, a consistant model is developed to describe transport phenomena in a pin ... more ABSTRACT In this paper, a consistant model is developed to describe transport phenomena in a pin fin heat sink that take into account the scales and other characteristics of the medium morphology. The specific geometry of the heat sink is accounted for in such a way that the details of the original structure are replaced by their averaged counterparts. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. These terms are closed experimentally from available data for pin fin morphology. The resulting equation set is relatively simple and is descretized using the finite difference method. Such computational algorithm is fast running, but still able to present a detailed picture of themperature fields in the airflow as well as in the solid structure of the heat sink. The calculated friction factor and thermal resistance are compared with experimental data to verify the porous model and validate the numerical code. The results calculated by the code agrees with the experimental data quite well, which offers possibility for multiple parameter optimization using Design of Experiment (DOE) to achieve high cooling capabilities.
Advanced Computational Methods in Heat Transfer VII
The present paper describes construction of an algorithm for conjugate heat transfer calculations... more The present paper describes construction of an algorithm for conjugate heat transfer calculations in order to find the most suitable form for a heat sink. Applying Volume Averaging theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The example numerical simulations were performed for test sections with isothermal structure as well as with heat conducting Al pin-fins. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at University of California, Los Angeles. The comparison of the drag coefficient as a function of Reynolds number reveals good agreement with already published data, whereas the comparison of the Nusselt number distributions shows much larger discrepancies. Finite conductivity of a solid phase decreases the heat transfer coefficient and the Nusselt number. The influence of conductivity becomes larger with increasing Reynolds number.
ABSTRACT Fractional scaling analysis (FSA) is demonstrated at the system level. The selected exam... more ABSTRACT Fractional scaling analysis (FSA) is demonstrated at the system level. The selected example is depressurization of nuclear reactor primary systems undergoing large- and small-break loss of coolant accidents (LOCA), specifically in two integral test facilities of different sizes and shapes, namely, LOFT and Semiscale. The paper demonstrates (1) the relation between pressure and volume displacement rates in analogy to generalized "effort" and "flow" in interdisciplinary analysis of complex systems and (2) using experimental data that a properly scaled depressurization history applies to both large- and small-break LOCA in two different facilities. FSA, when applied at the system, component, and process levels, serves to synthesize the worldwide wealth of results from analyses and experiments into compact form for efficient storage, transfer, and retrieval of information. The demonstration at the system level shows that during LOCAs the break flow dominates for break sizes between 0.1% and 200% of cold-leg flow cross-sectional area, and that FSA ranks processes quantitatively and thereby objectively in the order of their importance. FSA supersedes the hereunto subjectively implemented phenomena identification and ranking table. FSA readily quantifies scale distortions. FSA reduces significantly the need for and current cost of experiments and analyses.
In this work, we will investigate the performance of the Bi-porous wicks which are intended to ev... more In this work, we will investigate the performance of the Bi-porous wicks which are intended to eventually be used as the substrate in the TGP (Thermal Ground Plane) devices which function like thin heat pipes. In order to more closely simulate the operating conditions in a TGP, tests are conducted with a restrictor plate above the wick. By adding a mono-porous layer at the bottom and a vapor space on the top of the bi-porous wick, respectively vapor removal and liquid supply are meant to be enhanced. Hence the experiments are performed using such wicks. We present our effort improving an electric analogue model for the bi-porous wick based on the similarity between the differential equations governing the two systems. The analog model is initially improved for a disk shaped wick with a restrictor on top. Furthermore, the analogue technique is employed as a tool to investigate the performance of the wick with the vapor restrictor mounted on top; to compare the experimental data achieved in a boiling chamber versus TGP device; and to estimate the required data for the bi-porous evaporator calculations.
Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C, 2009
Developing better heat pipes requires advancement of technology in all aspects of construction. I... more Developing better heat pipes requires advancement of technology in all aspects of construction. In this paper I am investigating the effect of vapor pathways on the performance of biporous wicks in heat pipes. Biporous evaporator wicks, generated by sintering copper particles into semi-uniform clusters, were demonstrated to achieve high flux, heat transfer performance for use in heat pipes by Semenic (2007). The effective thermal conductivity of thick biporous wicks at high heat fluxes was found to be reduced because the region next ...
Volume 2: Heat Transfer Enhancement for Practical Applications; Heat and Mass Transfer in Fire and Combustion; Heat Transfer in Multiphase Systems; Heat and Mass Transfer in Biotechnology, 2013
ABSTRACT Biporous wicks are an effective means for facilitating evaporation in heat pipes used fo... more ABSTRACT Biporous wicks are an effective means for facilitating evaporation in heat pipes used for electronics cooling. They facilitate boiling within the wick by having two distinct size distributions of pores; the smaller pores provide high capillary pressure to pump liquid to the surface while the larger pores maintain high vapor permeability. The wicks investigated in this study were sintered copper biporous material. The authors previously presented a validated statistical model, based on work by Kovalev, which could predict the performance of biporous wicks tested at UCLA with reasonable accuracy [1]. Using this model, the author was able to gain new insight into the effect that the numerical estimate of liquid saturation of the wick has on dry out. The pore size distribution allows the determination of the capillary pressure available inside the wick and the Kovalev model provides the required pressure drop to supply liquid water to the heater surface. This led to a method of predicting dry out by comparing the capillary pressure in the wick to the required pressure drop from the model to estimate when the wick was dried out.When the required pressure drop determined by code exceeds the peak effective capillary pressure provided by the wick, the large pores of the wick are considered to be dry. These values are correlated to the input heat flux to determine what at what input power the wick begins to dry out. While the wick will not fail in this mode, the overall heat transfer coefficient will have peaked. In this work, this method of determining dry out will be validated against wicks tested at UCLA by comparing the input powers at which this dry out phenomenon occurs. Accurate predictions of dry out and the role of the pore size distribution are critical in developing methods to delay dry out of biporous wicks. By comparing the relative dry out points of various wick geometries to each other, augmented wick geometries can be suggested for future work. This modeling tool can lay the foundation for future tailoring of biporous evaporator wicks to specific tasks.
Journal of Thermal Science and Engineering Applications, 2011
Résumé/Abstract A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. ... more Résumé/Abstract A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was discovered originally in use with a device consisting of a metal tube charged with the patented inorganic aqueous solution (IAS), which is evaporated when the tube is evacuated before use. According to the patent, this evaporation leaves a thin film that allows the tube to carry high heat flux loads with low temperature drop across the tube in a solid state mode. However, various experiments with these tubes have produced ...
2010 14th International Heat Transfer Conference, Volume 5, 2010
Investigation of bi-porous wicks has yielded an effective method for increasing surface heat tran... more Investigation of bi-porous wicks has yielded an effective method for increasing surface heat transfer when the heat flux is high. It was further found that addition of a mono-porous layer on the heated surface significantly reduced the heated wall surface temperature. These bi-layer wicks were designed for use in 3× 5 heat spreading devices called Thermal Ground Planes (TGP) in order to transfer heat from a 1 cm source. In this work we will investigate the performance of a biporous wick with a monoporous layer in various test set-ups to show ...
A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was di... more A novel fluid for use as a working fluid in a heat pipe has been tested at UCLA. The fluid was discovered originally in use with a device consisting of a metal tube charged with the patented inorganic aqueous solution (IAS) which is evaporated when the tube is evacuated before use. According to the patent, this evaporation leaves a thin film which allows the tube to carry high heat flux loads with low temperature drop across the tube in a solid state mode. However, various experiments with these tubes have produced inconsistent results and ...
ABSTRACT A plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some p... more ABSTRACT A plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some pin fins planted between the flow channels. Just as the other kinds of heat sinks, it is a hierarchical multilevel device with many parameters required for its description. Volume Averaging Theory (VAT) is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the plate-pin fin (porous media) morphology and to describe the hierarchical nature of the heat sink. Closure for the upper level is obtained using VAT to describe the lower level. At the lower level, the media is described by a representative elementary volume (REV). Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV. The terms in the closure expressions are complex and relating experimental data to the closure terms resulting from VAT is difficult. In this work, we model the plate-pin fin heat sink based on Volume Averaging Theory and use CFD to obtain detailed solutions of flow through an element of PPFHS and use these results to evaluate the closure terms needed for a fast running VAT based code. The VAT based code can then be used to solve the heat transfer characteristics of the higher level heat sink. The objective is to show how plate-pin fin heat sinks can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort.
ABSTRACT VAT is used to rigorously cast the point-wise conservation of energy, momentum and mass ... more ABSTRACT VAT is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of heat exchanger channel morphology. At the lower level, the media is described by a representative elementary volume (REV). Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV. The terms in the closure expressions are complex and relating experimental data to the closure terms resulting from Volume Averaging Theory (VAT) is difficult. In this work we use CFD to obtain detailed solutions to flow through an element of a heat exchanger and use these results to evaluate the closure terms needed for a fast running VAT based code. The VAT based code can then be used to solve the heat transfer characteristics of the higher level heat exchanger. A comparison is then made of the CFD closure and experimental data rescaled by VAT scaling. The objective is to show how heat exchangers can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort.
ABSTRACT Experimentally determining internal heat transfer coefficients in porous structures has ... more ABSTRACT Experimentally determining internal heat transfer coefficients in porous structures has been a challenge in the design of heat exchangers. In this study, a novel combined experimental and computational method for determining the internal heat ...
ABSTRACT The plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some... more ABSTRACT The plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some pin fins planted between the flow channels. In this paper, a numerical investigation was performed to compare the thermal and hydraulic performances of the PPFHSs and PFHS. PPFHSs with five forms of pin cross-section profiles (square, circular, elliptic, NACA 0050, and dropform) were numerically simulated. The influence of pin fin cross-section profile on the flow and heat transfer characteristics was presented by means of Nusselt number and pressure drop. It is found that the Nu number of a PPFHS is at least 35% higher than that of a PFHS used to construct the PPFHS at the same Reynolds number. Planting circular and square pins into the flow channel of heat sinks enhances the heat transfer at the expense of high pressure loss. Using the streamline shaped pins, not only the pressure drop of the compound heat sinks could be decreased considerably, the heat transfer enhancement also makes a step forward. The present numerical simulation provides original information of the influence of different pin-fin cross-section profiles on the thermal and hydraulic performance of the new type compound heat sink, which is helpful in the design of heat sinks.
ABSTRACT In the present study, air-side turbulent heat transfer and friction characteristics of f... more ABSTRACT In the present study, air-side turbulent heat transfer and friction characteristics of fin-and-tube heat exchangers with a large number of tube rows and large diameter of tubes are investigated numerically. Finite Volume Method based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based Shear-Stress-Transport (SST) model was used to predict the turbulent flow and heat transfer through the fin-and-tube heat exchanger coil. The effects of parameters such as Reynolds number, the number of tube rows, tube diameter, tube pitches and fin pitch are examined. In the end, correlations for the Nusselt number and friction factor which applicable to fin-and-tube heat exchangers with large number of large-diameter tube rows are proposed.
ABSTRACT In this paper, a consistant model is developed to describe transport phenomena in a pin ... more ABSTRACT In this paper, a consistant model is developed to describe transport phenomena in a pin fin heat sink that take into account the scales and other characteristics of the medium morphology. The specific geometry of the heat sink is accounted for in such a way that the details of the original structure are replaced by their averaged counterparts. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. These terms are closed experimentally from available data for pin fin morphology. The resulting equation set is relatively simple and is descretized using the finite difference method. Such computational algorithm is fast running, but still able to present a detailed picture of themperature fields in the airflow as well as in the solid structure of the heat sink. The calculated friction factor and thermal resistance are compared with experimental data to verify the porous model and validate the numerical code. The results calculated by the code agrees with the experimental data quite well, which offers possibility for multiple parameter optimization using Design of Experiment (DOE) to achieve high cooling capabilities.
ABSTRACT Earlier efforts to optimize a simple pin fin heat sink only considered in line or rotate... more ABSTRACT Earlier efforts to optimize a simple pin fin heat sink only considered in line or rotated square configurations, a six or seven parameter problem. In this work, a staggered non-square array, two pitch dimensions, with non-circular pin cross-section are added to the heat sink description. The effects of optimizing fin eccentricity and pitch have both been shown to enhance the convective heat transfer as well as to increase the required pumping power thereby contributing to the performance. To optimize, the full conjugate problem must be solved. Volume averaging theory (VAT) is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the channel morphology. With a VAT based model, multiple heat sinks can be analyzed quickly while being able to change all dimensions. Using commercial software, S-Matrix Corporation’s DOE Fusion, a multi-parameter pin fin heat sink is optimized.
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