Generalized Correlations for Predicting Optimal Spacing of Decaying Heat Sources in a Conducting Medium

Abstract

This paper presents a numerical study for predicting the optimal spacing (OS) of decaying heat sources/sinks in a conducting medium. The optimal configuration that minimizes the overall thermal resistance between the cylinder array and surrounding medium is tracked using interpolation technique. Consequently, the dimensionless OS obtained is of the order of 0.442th power of the Fourier number (Fo) defined as a function of the decaying time constant, which differs from the 0.5th value reported in previous study. In addition, the overall thermal resistance is shown to be highly dependent on the dimensionless spacing and Fo, while the OS also depends on the array type of the cylinders. Based on the extensive numerical study, closed-form correlations are proposed for predicting the OS of decaying heat sources/sinks in both quadratic and hexagonal arrangements. These results can be widely utilized for optimally positioning heat sources/sinks with two dimensional configurations.