Multivariable optimization of pyramidal compound substrates for cooling of power-electronics in modern hybrid and electric propulsion systems

We present a method for the optimization of the thermal cooling of heat sources mounted on top of layered composites and pyramidal substrates, that are widely used in the power electronics of hybrid-electric propulsion systems. The analytical solution of the Laplace's heat equation is approximated via Fourier expansion series and it is coupled to the Influence Coefficient Method (ICM) to provide a functional of the overall thermal stress to minimize. A multivariable optimization method is derived by coupling the equations for the heat transfer with the Sequential Least-Square Quadratic Programming (SLSQP), or the Bounded Limited-Memory BFGS (L-BFGS-B) algorithm. Code validation is performed against three-dimensional simulations and experimental data available from the literature. It is shown that an optimal component relocation and apportionment of the overall thickness of the multilayer substrate promotes a sensible reduction of the thermal stress.