Compact Thermal Representations for Several Fundamental Shapes in Forced Convection

In the cooling of electronic packages, the task of simulating large arrays of heat sinks is often accomplished by the use of compact models. These simpler models attempt to capture the thermal and flow resistance characteristics of a representative heat sink while ignoring secondary detail. In the porous block model, an equivalent thermal conductivity is assigned to the fluid that enters the ‘porous’ space above the heat sink base that was once occupied by the fins. This artificially enhanced thermal conductivity enables the porous block of fluid to exhibit the same thermal resistance as that of the original heat sink. Due to the three-dimensional distribution of the thermal resistance in space, temperature maps associated with the resulting model provide better agreement with detailed numerical simulations than is possible with other models based on two-dimensional flat plate or thin sheet approximations. In this paper, we present closed-form expressions for the equivalent thermal conductivity associated with a large number of heat sink shapes in a forced convection environment.