An exact three-dimensional (3-D) solution is derived for the steady-state heat conduction equation with the source on an otherwise adiabatic surface and Newtonian cooling on the opposing surface. Dimensionless solutions are provided for maximum and source-averaged thermal spreading resistances. The solution for unit-source contours in a plane perpendicular to the source plane is also included. Maximum thermal spreading resistance plots are provided for several source-to-plate edge length ratios and source aspect ratios (plate maintained square). The Newtonian cooling effects are incorporated via a Biot number. Examples illustrate application of the theory.
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Gordon N. Ellison (2003) studied this question.
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