Thermal Resistance Approach: An Engineering Tool for Improvement of Conductive Constructal Configurations

In the last decade, various conductive networks for cooling heat generating bodies have been proposed, analyzed, and optimized. Nevertheless, many of these studies have not been based on an analytical or mathematical formulation of the effective parameters. In this trend, a new geometry is assumed and analyzed (by analytical or numerical methods) hoping to decrease the total thermal resistance of the system. Therefore, the objective of the present paper is to illustrate how to analyze a conductive cooling network and improve it using the analytical procedures based on the general formulation of thermal resistance. As an example, the conventional rectangular elemental volumes with I shaped conductive link is modified to V shaped and pencil shaped designs and optimized analytically. Moreover, general expressions for optimum local thickness and thermal resistance of the links with variable cross section in an arbitrary network are provided. It is shown that improvements up to 50% can be achieved easily by simple geometrical changes if the designer is equipped with a profound knowledge of the important governing parameters.