Calculation of stationary heat flow through a hole in a flat wall

Stationary heat flow through a hole in a thermally insulated diaphragm is examined on the basis of the Laplace equation in the plane domain. Integral equations (similar to those of elasticity theory) are used to determine the width of the hole for the case of a thin diaphragm. These equations are solved explicitly for the case of a symmetrically positioned diaphragm. Approximate solutions are obtained for the case of a small hole in a nonsymmetrical diaphragm, and also for a thick diaphragm using conformal mapping.