Calculation of conjugate heat transfer in a heat sink using Volume Averaging Technique (VAT) (original) (raw)
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Numerical technique for modeling conjugate heat transfer in an electronic device heat sink
International Journal of Heat and Mass Transfer, 2003
A fast running computational algorithm based on the volume averaging technique (VAT) is developed to simulate conjugate heat transfer process in an electronic device heat sink. The goal is to improve computational capability in the area of heat exchangers and to help eliminate some of empiricism that leads to overly constrained designs with resulting economic penalties.
Numerical investigation of chip cooling using volume averaging technique (VAT)
Advanced Computational Methods in Heat Transfer VII
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.
Modeling of conjugate heat transfer using Galerkin approach
An algorithm for simulation of conjugate heat transfer in an electronic chip heat sink is described. Applying Volume Averaging Theory (VAT) to a system of transport equations, a heat exchanger structure is modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, is accomplished with drag and heat transfer coefficients taken from the available literature and inserted into a computer code. The system of partial differential equations is solved using the Galerkin method to decompose the temperature field into a series of eigenfunctions. An example calculation is performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions follow the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at University of California, Los Angeles. A comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows good agreement with finite volume method results as well as with experimental data. The calculated temperature fields reveal the local heat flow distribution and enable optimization of the surface geometry.
APPLICATION OF GALERKIN METHOD TO CONJUGATE HEAT TRANSFER CALCULATION
Numerical Heat Transfer, Part B: Fundamentals, 2003
A fast-running computational algorithm based on the volume averaging technique (VAT) is developed and solutions are obtained using the Galerkin method (GM). The goal is to extend applicability of the GM to the area of heat exchangers in order to provide a reliable benchmark for numerical calculations of conjugate heat transfer problems. Using the VAT, the computational algorithm is fast-running, but still able to present a detailed picture of temperature fields in air flow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient C d and Nusselt number Nu were compared with finite-volume method (FVM) results and with experimental data to verify the computational model. The comparison shows good agreement. The present results demonstrate that the selected Galerkin approach is capable to perform heat exchanger calculations where the thermal conductivity of the solid structure has to be taken into account.
Application of Fourier-Galerkin Method to Volume Averaging Theory Based Model of Heat Sinks
Volume 8C: Heat Transfer and Thermal Engineering, 2013
Efficient analysis of heat sink performance is a crucial step in the optimization process of such devices. Accurate analysis of these complex geometric systems with CFD and FEM methods requires fine meshes which imply significant computational time. In this study, Volume Averaging Theory (VAT) is rigorously applied to obtain a geometrically simplified but physically accurate model for any periodic heat sink geometry. The governing equations are averaged over a Representative Averaging Volume (REV) to obtain a set of integro-differential equations. Some information about lower level phenomena is lost in every averaging process and a closure scheme is required to model these behaviors. Experimental data for friction factor and Nusselt number in an REV is used to close the set of PDEs. This mathematical process replaces the complex geometry of the heat sink with a fictitious continuous medium and smoothens the quantities of interest throughout the system. These system features allow the use of a global Fourier-Galerkin method to efficiently solve the resulting equations and accurately predict the performance of the system. The effectiveness of the method is proven by applying it to model thermal behavior for laminar flow over an aircooled pin-fin heat sink and a water-cooled micro-channel heat sink. The convergence in the Nusselt number in the case of constant heat flux is found to be quadratic with respect to the number of basis functions. The accuracy of the method is validated by comparing the numerical results obtained to existing experimental data. The maximum difference between the predicted Nusselt number and the experimental measurements is found to be only 4% for both cases.
Multiphase Science and Technology, 2013
Air-and water-cooled heat sinks are still the most common heat rejection devices in electronics, making their geometric optimization a key issue in thermal management. Because of the complex geometry, the use of finite-difference, finite-volume, or finite-element methods for the solution of the governing equations becomes computationally expensive. In this work, volume averaging theory is applied to a general heat sink with periodic geometry to obtain a physically accurate, but geometrically simplified, system model. The governing energy and momentum equations are averaged over a representative elementary volume, and the result is a set of integro-partial differential equations. Closure coefficients are introduced, and their values are obtained from data available in the literature. The result of this process is a system of closed partial differential equations, defined on a simple geometry, which can be solved to obtain average velocities and temperatures in the system. The intrinsic smoothness of the solution and the simplified geometry allow the use of a modified Fourier-Galerkin Method for efficient solutions to the set of differential equations. Modified Fourier series are chosen as the basis functions because they satisfy the boundary conditions a priori and lead to a sparse system of linear equations for the coefficients. The validity of the method is tested by applying it to model the hydraulic and thermal behavior of an air-cooled pin-fin and a water-cooled micro-channel heat sink. The convergence was found to be O(N −3.443 ), while the runtime was ∼0.25 s for N = 56. The numerical results were validated against the experimental results, and the agreement was excellent with an average error of ∼4% and a maximum error of ∼5%.
COMPUTATIONAL HEAT TRANSFER ANALYSIS OF ELECTRONIC EQUIPMENT
IAEME, 2019
The Research area of engineering of the electronic system cooling is having wide application nowadays. Therefore, in the present work, Aluminum is chosen as the material for the heat sink. In the present work effect of various shapes of cross sections of fins on the mother board is studied keeping the inlet air velocity, temperature of the ambient and the heat generation constant. The optimized shape of cross section is done to analyzing the effects of velocity and inlet air temperature, keeping the other parameters constant. The results are compared and optimum operational condition of that sink is found out. The optimized shape is proceeded to find a suitable sectional area which gives a minimum temperature.
THERMAL ANALYSIS OF A HEAT SINK FOR ELECTRONICS COOLING
Heat transfer is a discipline of thermal engineering that concern the generation, use, conversion and exchange of thermal energy, heat between physical systems. Heat transfer is classified in to various mechanisms such as heat conduction, convection, thermal radiation & transfer of energy by phase change. Most of the electronic equipment are low power and produce negligible amount of heat in their operation. Some devices, such as power transistors, CPU's, & power diodes produce a significant amount of heat. so sufficient measures are need to be taken so as to prolong their working life and reliability. Here, we deal with the design of a heat sink of Aluminum alloy for cooling of a PCB of dimension 233.3×160 with FPGA, fine pitch BGA package, which dissipates 19.5 watts of heat energy. The whole mode of heat transfer is carried out through forced convection with help of a cooling fan of specific velocity. Heat sinks are passive components that cool a device by dissipating heat into surrounding air. We need to introduce discontinuities in the fin surface to break up the boundary layer. This can be accomplished by cross cutting an extruded 'Al' heat sink to create a segmented fin. Heat sinks have a wide range of applications mainly in micro processors, BGA's, PCB's, Airplanes, Satellites, Space vehicles & missiles.
Effect of heat sink design on the thermal characteristic in computational fluid dynamics analysis
The thermal management in the electronic device or system using the heat sink is important to ensure the device or system operating under the allowable temperature. The present study aims to investigate the thermal characteristic (i.e., temperature distribution) of the various heat sink designs via computational fluid dynamics (CFD) analysis. The electronic cooling process of the heat sink is carried out via CFD software. The temperature distribution of the various heat sink designs (i.e., plate fin, circular pin fin and rectangular fin) was analyzed and compared. The CFD analysis revealed the plate fin heat sink has lowest temperature distribution on the fin region. High temperature distribution was observed on the pin fin heat sink. The non-uniform temperature distribution was attributed by the direction of inlet airflow, whereas the low temperature was found in the region that close to the inlet airflow. Thus, the research findings indicated the design of heat sink significantly affects the temperature distribution during the electronic cooling process.
An Analysis for Optimization of Heat Transfer for Various Heat Sink Cross-section and Length
2011
An analytical simulation model is presented in this study to predicting and optimizing the thermal performance, maximum thermal dissipation and the least material cost in electrical devices. According to general derivation, the longitudinal fin arrays on a heat sink can have either square, rectangular, equilaterally triangular, or cylindrical cross-section. It is observed that actual convection flow velocity through fins is usually unknown to designers. By input of the Biot number Bi, heat transfer coefficient ratio, H and the shape parameter, the heat transfer equation which is expressed in implicit form can be solved by iterative method to calculate the optimum fin length and fin thickness. Optimization of heat- sink designs and typical parametric behaviors are discussed based on the sample simulation results. Also the thermal resistance of a heat sink can be obtained to illustrate the cooling performance under various design conditions. Key word: Analytical Model, thermal Perform...