M. M. Yovanovich

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.

Laminar forced convection heat transfer in the combined entry region of non-circular ducts

A new model for predicting Nusselt numbers in the combined entrance region of non-circular ducts and channels is developed. This model predicts both local and average Nusselt numbers and is valid for both isothermal and isoflux boundary conditions. The model is developed using the asymptotic results for convection from a flat plate, thermally developing flows in non-circular ducts, and fully developed flow in non-circular ducts. Through the use of a novel characteristic length scale, the square root of cross-sectional area, the effect of duct shape on Nusselt number is minimized. Comparisons are made with several existing models for the circular tube and parallel plate channel and with numerical data for several non-circular ducts

Review of Elastic and Plastic Contact Conductance Models: Comparison with Experiment

More than 450 thermal contact conductance data points obtained from isotropic conforming rough surfaces for five different materials; nickel, stainless steel, two zirconium alloys, and aluminum have been compared with the existing elastic and plastic models. For the first time data have been reduced to a dimensionless form assuming both elastic as well as plastic deformation. Normally, data were compared with either the elastic model or the plastic model assuming a type of deformation a priori. The relative merits of different models and the surface factors influencing the mode of deformation are still not clear. Hence, the aim of the present work was to compare most of the models available in the literature with themselves as well as with isotropic data. Comparison showed that generally smoother surfaces deform elastically, and rougher ones plastically. However, there are some data sets that compare well with both the elastic as well as the plastic models.

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.

Modeling friction factors in non-circular ducts for developing laminar flow

Solutions to hydro dynamically developing flow in circular and non-circular ducts are examined. It is shown that the apparent friction factor based upon the square root of the crosssectional area is a weak function of the shape of the geometry provided an appropriate aspect ratio is defined. A general model which is valid for many duct configurations is developed by combining the developing flow and fully developed flow asymptotes. The new model is simpler than other general models and provides equal or better accuracy. Finally, it is shown that the solution for the elliptic duct geometry may be used to compute accurately, results for 8 singly-connected ducts and 2 doubly-connected ducts, respectively, with an accuracy of ±12 percent.

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.

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.