A Fast Computational Method for the Optimal Thermal Design of Anisotropic Multilayer Structures with Discrete Heat Sources for Electrified Propulsion Systems

• Analytical method to predict the thermal behavior of multi-source multi-layer compound systems. • Reduction of total component resistance is obtained through optimal apportionment of layer thicknesses. • Anisotropic materials allow limited substrate thickness, but at an expected high cost. • For single-source systems, the objective function reduces to the minimum total resistance of the compound system. • For multi-source systems, the objective function aims at minimizing the peak temperature on top surface. This work investigates the effect of the anisotropy on the heat transfer properties of layered composite materials with discrete heat sources, that are used in the power electronics of hybrid-electric propulsion systems. An analytical method, based on closed-form expressions structured on Fourier expansion series, is proposed for the solution of the Laplace’s steady-state anisotropic heat equation. The physical presence of electrical components is replaced by externally applied power sources. The method provides an accurate prediction of the temperature distribution and of the heat transfer across perfect layer-to-layer adhesion or finite conductance interfaces; its use is therefore encouraged for the optimization of composite substrates. Code verification has been employed on test cases for which the analytical solution was available.