Geometrical evaluation of T-shaped high conductive pathway with thermal contact resistance for cooling of heat-generating medium

The present work employs Constructal Design to numerically evaluate the geometrical configuration which facilitates the heat transfer through a T-shaped conductive pathway and heat-generating volumetric medium with low thermal conductivity. It is inserted a third material placed between the conductive pathway and the heat-generating medium which acts as thermal contact resistance. The objective function is to minimize the maximum excess of temperature over the entire system (materials with high and low thermal conductivity and thermal contact resistance), i.e., reduce the hot spots of a system with uniform heat generation. The total volume is fixed, however the volume of the high thermal conductivity material as well as the amount of the material that represents the thermal contact resistance can vary. Considering all possible geometries the configuration was optimized by varying the lengths and widths of the two branches forming the “T'', keeping fixed the aspect ratio of the area of the conductive material with respect to the total area of the body. For the three times optimized geometry, the presence of thermal contact resistance changed the optimal length and width ratios in nearly 16% and 12% in comparison with optimal ratios achieved for the case with perfect thermal contact.