Equivalent thermal conductivity for compact heat sink models based on the Churchill and Chu correlation

In this study an asymptotic technique is presented for calculating the equivalent thermal conductivity of a compact heat sink model. The method uses the known Nusselt number correlation given by Churchill and Chu (1975) for both laminar and turbulent regimes. This correlation is valid for airflow over a vertical flat plate and is applicable over the entire range of Rayleigh and Prandtl numbers. The resulting asymptotic solution presented here is applicable for overall heat transfer coefficients ranging from 0 to 100,000 Wm^-2K^-1. The closed-form analytical solution is compared to an iterative numerical solution and found to exhibit a very small error over a wide range of flow conditions. Being practically equivalent to the numerical solution, the asymptotic correlation obviates the need for guesswork and iteration in a compact heat sink simulation. It enables the implementation of a self-contained numerical scheme that does not require user intervention.