Compact Thermal Representations for Several Fundamental Shapes in Natural Convection

In this article, general canonical forms for the effective thermal conductivities of compact heat sink models are derived using perturbation tools. The resulting approximations apply to a large number of fundamental heat sink shapes used in natural convection applications. The effective thermal conductivity is a property that can be assigned to the porous block (i.e., volume of fluid) above the heat sink base that was once occupied by the fins. The increased thermal conductivity of the fluid entering the porous block produces a reduced thermal resistance that matches that of the original heat sink. The use of a compact representation is accompanied by substantial computational savings that promote faster optimization and communication between simulation analysts and design engineers. The generalized approximations for the effective thermal conductivity presented here are numerically verified.