J. R. Culham

Optimization of plate fin heat sinks using entropy generation minimization

In this study, an entropy generation minimization, EGM, technique is applied as a unique measure to study the thermodynamic losses caused by heat transfer and pressure drop in cylindrical pin-fin heat sinks. The use of EGM allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general expression for the entropy generation rate is obtained by considering the whole heat sink as a control volume and applying the conservation equations for mass and energy with the entropy balance. Analytical/empirical correlations for heat transfer coefficients and friction factors are used in the optimization model, where the characteristic length is used as the diameter of the pin and reference velocity used in Reynolds number and pressure drop is based on the minimum free area available for the fluid flow. Both in-line and staggered arrangements are studied and their relative performance is compared on the basis of equal overall volume of heat sinks. It is shown that all relevant design parameters for pin-fin heat sinks, including geometric parameters, material properties and flow conditions can be simultaneously optimized.

Thermal Spreading Resistance of Eccentric Heat Sources on Rectangular Flux Channels

A general solution, based on the separation of variables method for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is presented. Solutions are obtained for both isotropic and compound flux channels. The general solution can also be used to model any number of discrete heat sources on a compound or isotropic flux channel using superposition. Several special cases involving single and multiple heat sources are presented. @DOI: 10.1115/1.1568125#

Spreading Resistance of Isoflux Rectangles and Strips on Compound Flux Channels

The general expression for the spreading resistance of an isoe ux, rectangular heat source on a two-layer rectangular e ux channel with convective or conductive cooling at one boundary is presented. The general expression depends on several dimensionless geometric and thermal parameters. Expressions are given for some two- and three-dimensional spreading resistances for two-layer and isotropic e nite and semi-ine nite systems. The effect of heat e ux distribution over strip sources on two-dimensional spreading resistances is discussed. Tabulated values are presented for three e ux distributions, the true isothermal strip, and a related nonisoe ux, nonisothermal problem. For narrow strips, the effect of the e ux distribution becomes relatively small. The dimensionless spreading resistance for an isoe ux square source on an isotropic square e ux tube is discussed, and a correlation equation is reported. The closed-form expression for the dimensionless spreading resistance for an isoe ux rectangular source on an isotropic half-space is given.

Analytical forced convection modeling of plate fin heat sinks

An analytical model is presented that predicts the average heat transfer rate for forced convection air cooled plate fin heat sinks for use in the design and selection of heat sinks for electronics applications. Using a composite solution based on the limiting cases of fully-developed and developing flow between isothermal parallel plates, the average Nusselt number can be calculated as a function of the heat sink geometry and fluid velocity. The resulting model is applicable for the full range of Reynolds number, 0.1<Re/sub b/*<100, and accurately predicts the experimental results to within an RMS difference of 2.1%.

Analytical modeling of spreading resistance in flux tubes, half spaces, and compound disks

A review of previously published models and solutions pertinent to the issue of modeling thermal resistances of diamond on copper heat sink systems is presented. The many particular solutions are shown to be special cases of the comprehensive model developed for a circular heat source in perfect thermal contact with the top surface of a compound disk which consists of two isotropic layers in perfect thermal contact. The bottom surface of the compound disk is subjected to a convective or contact cooling condition. Whenever possible simple models and correlation equations are presented for ease of computation. Bounds are presented for estimating the overall thermal resistance of several important cases.

Thermal Spreading Resistance in Compound and Orthotropic Systems

Ar eview of thermal spreading resistances in compound and orthotropic systems is presented. Solutions for thermal spreading resistances in compound systems are reported. Solutions are reported for both cylindrical and rectangular systems, variable flux distributions, and edge cooling. Transformations of the governing equations and boundary conditions for orthotropic systems are discussed, and new solutions are obtained for rectangular flux channels and circular flux tubes. Nomenclature Ab = baseplate area, m 2 Am, An, Amn, Bn =F ourier coefficients As = heat source area, m 2 a, b

Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes

The characteristics of fully-developed, laminar, pressure-driven, incompressible flow in rough circular microchannels are studied. A novel analytical model is developed that predicts the increase in pressure drop due to wall roughness in microtubes. The wall roughness is assumed to posses a Gaussian isotropic distribution. The present model is compared with experimental data, collected by other researchers and good agreement is observed.

Modeling thermal contact resistance: A scale analysis approach

A compact analytical model is developed for predicting thermal contact resistance (TCR) of nonconforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach is taken by employing the scale analysis method. It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable for an applicable range of contact pressure

Review of Thermal Conductance Models for Joints Incorporating Enhancement Materials

A comprehensive review of analytical and empirical models for calculating the thermal conductance across mechanically formed joints is presented. A historical perspective of modeling procedures for a range of interface cone gurations is presented, including barecontacting surfaces for conforming rough surfaces aswell as interfacial surfaces augmented with enhancement materials such as greases, metallic foils, polymeric compliant materials, e lms, and coatings. Given the wide range of interface materials available and their associated thermophysical and surface properties, the models presented provide an effective procedure for determining the signie cance of these properties in the prediction of contact, gap, and overall joint conductance.

FLUID FLOW AND HEAT TRANSFER IN POWER-LAW FLUIDS ACROSS CIRCULAR CYLINDERS - ANALYTICAL STUDY

An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausen method is used to solve the momentum integral equation whereas the energy integral equation is solved for both isothermal and isoflux boundary conditions. A fourth-order velocity profile in the hydrodynamic boundary layer and a third-order temperature profile in the thermal boundary layer are used to solve both integral equations. Closed form expressions are obtained for the drag and heat transfer coefficients that can be used for a wide range of the power-law index, and generalized Reynolds and Prandtl numbers. It is found that pseudoplastic fluids offer less skin friction and higher heat transfer coefficients than dilatant fluids. As a result, the drag coefficients decrease and the heat transfer increases with the decrease in power-law index. Comparison of the analytical models with available experimental/numerical data proves the applicability of the integral approach for power-law fluids. DOI: 10.1115/1.2241747