VAT Based Modeling of Plate-Pin Fin Heat Sink and Obtaining Closure From CFD Solution

2011 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Averaging Theory ◽  
Conservation Of Energy ◽  
Pin Fin ◽  
Fast Running ◽  
Volume Averaging Theory

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.

Obtaining Experimental Closure for the VAT-Based Energy Equations Modeling a Heat Sink as a Porous Medium

2011 ◽  
Author(s):  
David J. Geb ◽  
Jonathan Chu ◽  
Feng Zhou ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Internal Heat ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Pin Fin ◽  
Volume Averaging Theory ◽  
The Heat Transfer Coefficient

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 transfer coefficient within a heat sink is explored and results are obtained for air flow through basic pin fin heat sinks. These measurements along with the pressure drop allow for thermal-fluid modeling of a heat sink by closing the Volume Averaging Theory (VAT)-based governing equations, providing an avenue towards optimization. To obtain the heat transfer coefficient the solid phase is subjected to a step change in heat generation rate via induction heating, while the fluid flows through under steady state conditions. The fluid phase temperature response is measured. The heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory with the experimental results. The only information needed is the basic material properties, the flow rate, and the experimental data. The computational procedure alleviates the need for internal solid and fluid phase temperature measurements, which are difficult to make and can disturb the solid-fluid interaction. Moreover, a simple analysis allows us to proceed without knowledge of the heat generation rate, which is difficult to determine precisely. Multiple pin fin heat sink morphologies were selected for this study. Moreover, volume averaging theory scaling arguments allow a single correlation for both the heat transfer coefficient and friction factor that encompass a wide range of pin fin morphologies. It is expected that a precise tool for experimental closure of the VAT-based equations modeling a heat sink as a porous medium will allow for better modeling, and subsequent optimization, of heat sinks.

VAT Based Modeling of Heat Exchanger and Obtaining Closure From CFD Solution

2010 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Conservation Of Energy ◽  
Fast Running ◽  
The Media ◽  
Flow Through ◽  
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 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.

Thermal Optimization of Microchannel Heat Sink With Pin Fin Structures

2003 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Pumping Power ◽  
Heat Transfer Characteristics ◽  
Pin Fin ◽  
Flow And Heat Transfer

In the present work, a novel compact modeling method based on the volume-averaging technique and its application to the analysis of fluid flow and heat transfer in pin fin heat sinks are presented. The pin fin heat sink is modeled as a porous medium. The volume-averaged momentum and energy equations for fluid flow and heat transfer in pin fin heat sinks are obtained using the local volume-averaging method. The permeability, the Ergun constant and the interstitial heat transfer coefficient required to solve these equations are determined experimentally. To validate the compact model proposed in this paper, 20 aluminum pin fin heat sinks having a 101.43 mm × 101.43 mm base size are tested with an inlet velocity ranging from 1 m/s to 5 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. Pressure drop and heat transfer characteristics of pin fin heat sinks obtained from the porous medium approach are compared with experimental results. Upon comparison, the porous medium approach is shown to predict accurately the pressure drop and heat transfer characteristics of pin fin heat sinks. Finally, surface porosities of the pin fin heat sink for which the thermal resistance of the heat sink is minimal are obtained under constraints on pumping power and heat sink size. The optimized pin fin heat sinks are shown to be superior to the optimized straight fin heat sinks in thermal performance by about 50% under the same constraints on pumping power and heat sink size.

Heat Sink Optimization: A Multi-Parameter Optimization Problem

2010 ◽  
Author(s):  
Nicholas Hansen ◽  
Ivan Catton ◽  
Feng Zhou
Keyword(s):  
Heat Sink ◽  
Optimization Problem ◽  
Conjugate Problem ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Conservation Of Energy ◽  
Pin Fin ◽  
S Matrix ◽  
Square Array ◽  
Parameter Problem

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.

scholarly journals Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Feng Zhou ◽  
Nicholas E. Hansen ◽  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Length Scale ◽  
Tube Heat Exchanger ◽  
Volume Averaging Theory

Modeling a fin-and-tube heat exchanger as porous media based on volume averaging theory (VAT), specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts, and the VAT based governing equations can be solved for a wide range of heat exchanger designs. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a representative elementary volume. The present paper describes an effort to model a fin-and-tube heat exchanger based on VAT and obtain closure for the model. Experiment data and correlations for the air side characteristics of fin-and-tube heat exchangers from the published literature were collected and rescaled using the “porous media” length scale suggested by VAT. The results were surprisingly good, collapsing all the data onto a single curve for friction factor and Nusselt number, respectively. It was shown that using the porous media length scale is very beneficial in collapsing complex data yielding simple heat transfer and friction factor correlations and that by proper scaling, closure is a function of the porous media, which further generalizes macroscale porous media equations. The current work is a step closer to our final goal, which is to develop a universal fast running computational tool for multiple-parameter optimization of heat exchangers.

Compact Modeling of Fluid Flow and Heat Transfer in Pin Fin Heat Sinks

2004 ◽  
Vol 126 (3) ◽  
pp. 342-350 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim ◽  
Alfonso Ortega
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Pumping Power ◽  
Pin Fin ◽  
Flow And Heat Transfer

In this work, a novel compact modeling method based on the volume-averaging technique is presented. Its application to the analysis of fluid flow and heat transfer in pin fin heat sinks are further analyzed. The pin fin heat sink is modeled as a porous medium. The volume-averaged momentum and energy equations for fluid flow and heat transfer in pin fin heat sinks are obtained by using the local volume-averaging method. The permeability, the Ergun constant, and the interstitial heat transfer coefficient required to solve these equations are determined experimentally and correlations for them are presented. To validate the compact model proposed in this paper, 20 aluminum pin fin heat sinks having a 101.43 mm×101.43 mm base size are tested with an inlet velocity ranging from 1 m/s to 5 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. Pressure drop and heat transfer characteristics of pin fin heat sinks obtained from the porous medium approach are compared with experimental results. Upon comparison, the porous medium approach is shown to predict accurately the pressure drop and heat transfer characteristics of pin fin heat sinks. Finally, for minimal thermal resistance, the optimum surface porosities of the pin fin heat sink are obtained under constraints on pumping power and heat sink size. The optimized pin fin heat sinks are shown to be superior to the optimized straight fin heat sinks in thermal performance by about 50% under the same constraints on pumping power and heat sink size.

Hierarchical Modeling and Closure Evaluation for Fin-and-Tube Heat Exchangers Using 3-D Numerical Simulation

2012 ◽  
Author(s):  
Feng Zhou ◽  
David Geb ◽  
George DeMoulin ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Cfd Modeling ◽  
Original Structure ◽  
Tube Heat Exchanger ◽  
Wide Range ◽  
Volume Averaging Theory

A plain fin-and-tube heat exchanger was modeled based on Volume Averaging Theory (VAT) and the closure for the model was evaluated using CFD. Modeling a fin-and-tube heat exchanger as porous media based on VAT, specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts and the VAT based governing equations can be efficiently solved for a wide range of parameters. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a Representative Elementary Volume (REV). The terms in the closure expressions are complex and sometimes relating experimental data to the closure terms is difficult. In this work we use CFD to obtain detailed solutions of flow and heat transfer through an element of a fin-and-tube heat exchanger and use these results to evaluate the closure terms needed for a fast running VAT based code, which can then be used to solve the heat transfer characteristics of a higher level heat exchanger. The objective is to show how heat sinks can be modeled as a porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort to obtain closure for a VAT based model.

Pin-Fin Heat Sink With Horizontal Base and Blocked Edges

2008 ◽  
Author(s):  
D. Sahray ◽  
H. Shmueli ◽  
N. Segal ◽  
G. Ziskind ◽  
R. Letan
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Contact Resistance ◽  
Cross Section ◽  
Heat Input ◽  
Heat Sink ◽  
Numerical Study ◽  
Heat Sinks ◽  
Transfer Enhancement ◽  
Pin Fin

In the present work, horizontal-base pin fin heat sinks exposed to free convection in air are studied. They are made of aluminum, and there is no contact resistance between the base and the fins. For the same base dimensions the fin height and pitch vary. The fins have a constant square cross-section. The edges of the sink are blocked: the surrounding insulation is flush with the fin tips. The effect of fin height and pitch on the performance of the sink is studied experimentally and numerically. In the experiments, the heat sinks are heated using foil electrical heaters. The heat input is set, and temperatures of the base and fins are measured. In the corresponding numerical study, the sinks and their environment are modeled using the Fluent 6 software. The results show that heat transfer enhancement due to the fins is not monotonic. The differences between sparsely and densely populated sinks are analyzed for various fin heights. Also assessed are effects of the blocked edges as compared to the previously studied cases where the sink edges were exposed to the surroundings.

Compact Modeling of Fluid Flow and Heat Transfer in Straight Fin Heat Sinks

2004 ◽  
Vol 126 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Heat Sink ◽  
Volume Averaging ◽  
Thermal Design ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Flow And Heat Transfer

In the present work, a compact modeling method based on a volume-averaging technique is presented. Its application to an analysis of fluid flow and heat transfer in straight fin heat sinks is then analyzed. In this study, the straight fin heat sink is modeled as a porous medium through which fluid flows. The volume-averaged momentum and energy equations for developing flow in these heat sinks are obtained using the local volume-averaging method. The permeability and the interstitial heat transfer coefficient required to solve these equations are determined analytically from forced convective flow between infinite parallel plates. To validate the compact model proposed in this paper, three aluminum straight fin heat sinks having a base size of 101.43mm×101.43mm are tested with an inlet velocity ranging from 0.5 m/s to 2 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. The resulting pressure drop across the heat sink and the temperature distribution at its bottom are then measured and are compared with those obtained through the porous medium approach. Upon comparison, the porous medium approach is shown to accurately predict the pressure drop and heat transfer characteristics of straight fin heat sinks. In addition, evidence indicates that the entrance effect should be considered in the thermal design of heat sinks when Re Dh/L>∼O10.

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