Rectangular thermal doublers of uniform thickness

Abstract

An infinite series solution is developed for the steady temperature field in a thin, rectangular region exposed to a piecewise continuous heat flux and losing energy from exposed surfaces either by linearized radiation or true convection. The geometry and environmental conditions approximate a spacecraft application in which a finlike plate (thermal doubler) is used to enhance the radiating area of an energy-dissipating electronic component mounted in an equipment bay. A numerical example, based on typical spacecraft power and environmental conditions, is used to show how the closed-form solution may be used to investigate geometrical influences. Both direct (i.e., specified thickness, unknown temperature) and design (i.e., specified temperature, unknown thickness) problems are examined to show how temperature and doubler thickness depend on the shape of the heated area (''footprint), the shape of the doubler, and the location of the footprint within the doubler boundaries. The numerical results indicate that the two-dimensional solution for a case with double symmetry is bounded by the one-dimensional solutions for a circular footprint/circular doubler and a simple Cartesian geometry. The present formulation will be useful both for the trade studies leading to a preliminary design and as an exact solution for calibrating nodal models.