Minimum thermal resistance of a convectively cooled orthotropic plate with a uniform heat flux

摘要

The solution to the effective thermal resistance of a convectively cooled plate with a uniform heat flux was minimized with respect to the aspect ratio a. The resulting optimization equation, a transcendental equation in a, was solved iterativelyusing a hybrid Newton-Raphson/bisection numerical algorithm. The accuracy of the results was verified by comparing selected eases with published results. The minimization solution was presented graphically for several values of the vertical-to-horizontalconductivity ratio, Biot number, and the full range of the nondimensional width of the applied heat flux region. The optimum value of the plate aspect ratio was found to be a relatively strong function of both Biot number and the vertical-to-horizontalconductivity ratio. Furthermore, insight into the problem was gained by investigating limiting eases of the solution.