Developments of volume averaging theory (VAT) used to describe transport phenomena in heterogeneous media are applied to optimization of heat dissipation from a heterogeneous media. The media is a porous media representation of a pin fin heat sink (a heterogeneous layer) and the optimization process is accomplished with rigor using the idea of scaled energy transport. The problem is addressed in four steps: 1) determine the parameters needed for optimization from the two temperature VAT equations, 2) use statistical design of experiments (simulating the problem) for the many optimization parameters, 3) perform numerical simulation of the cases that are suggested through the statistical analysis of the optimization parameters, and 4) statistically analyze the numerical results to obtain an optimization response surface. The two applications are enhancement of heat transfer dissipation from a heterogeneous media while minimizing the frictional resistance and minimization of the thermal resistance (a problem of importance to all designers of heat exchangers).

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