Constructal design of X-shaped conductive pathways for cooling a heat-generating body

This paper applies constructal design to discover the configuration that facilitates the access of the heat that flows through X-shaped pathways of high-conductivity material embedded within a square-shaped heat-generating medium of low-conductivity to cooling this finite-size volume. The objective is to minimize the maximal excess of temperature of the whole system, i.e. the hot spots, independent of where they are located. The total volume and the volume of the material of high thermal conductivity are fixed, but the lengths can vary. It was found numerically that the performance of X-shaped pathways is approximately the same as that the one calculated for a simpler I-shaped blade (i.e. a single pathway of high thermal conductivity material beginning in the heat sink and ending of such a way that there is spacing between the tip of the pathway and the insulated wall) for small values of the high thermal conductivity material and area fraction. However, the X-shaped conductive pathway configuration performs approximately 51% better when compared to l-shaped pathway configuration for larger values of the high-conductivity material and area fraction.