Topology optimization for the conduction cooling of a heat-generating volume with orthotropic material

Abstract

In this paper the two dimensional numerical topology optimization of a high conductive conduit material, distributed within a heat-generating material, is investigated with regards to the effect of orthotropic materials. Specifically, materials with orthotropic thermal conductivities (different primary and secondary principal thermal conductivities).Two cases are considered in this study, namely the optimal distribution of an isotropic conduit material within an orthotropic heat generating material; and the optimal distribution of an orthotropic conduit material within an isotropic heat-generating material. A finite volume method (FVM) code, coupled with the method of moving asymptotes (MMA); the solid isotropic with material penalization (SIMP) scheme; and the discrete adjoint method, was used to find the optimal distribution of the high conductive conduit material within the heat generating material.For the optimal distribution of an isotropic conduit material within an orthotropic heat-generating material is was found that a heat-generating material angle 10°⩽θ0⩽60° is preferred, for a higher thermal performance, and a heat-generating material angle θ0<10° and θ0>60° should be avoided.For the optimal distribution of an orthotropic conduit material within an isotropic heat-generating material is was found that an optimal conduit material angle exists giving the best thermal performance (lowest τmax). It was found that the optimal conduit material angle remains the same for different conductivity ratios and different heat-generating material angles. It was also found that the optimal conduit material angle directly corresponds to the domain aspect ratio, θ1,opt=tan-1(2H/L), with a minimum improvement of 3% and a maximum improvement of 50% of the thermal performance when using an orthotropic conduit material over that of an isotropic conduit material. A 50% improvement of the thermal performance effectively translates to either double the allowable heat generation or half the peak operating temperature of the isotropic heat-generating material.