Constructal Design of Y-Shaped Conductive Pathways for Cooling a Heat-Generating Body

Abstract

This paper applies constructal design to obtain numerically the configuration that facilitates the access of the heat that flows through Y-shaped pathways of a 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. Results show that there is no universal optimal geometry for the Y-shaped pathways for every value of high conductivity investigated here. For small values of high thermal conductivity material the best shape presented a well defined format of Y. However, for larger values of high thermal conductivity the best geometry tends to a V-shaped (i.e., the length of stem is suppressed and the bifurcated branches penetrates deeply the heat-generating body towards the superior corners). A comparison between the Y-shaped pathway configuration with a simpler I-shaped blade and with X-shaped configuration was also performed. For constant values of area fraction occupied with a high-conductivity material and the ratio between the high thermal conductivity material and low conductivity of the heat-generating body (φ = 0.1 and = 100) the Y-shaped pathways performed 46% and 13% better when compared to I-shaped and X-shaped pathway configuration, respectively. The best thermal performance is obtained when the highest temperatures (hot spots) are better distributed in the temperature field, i.e., according to the constructal principle of optimal distribution of imperfections.