Heat Conduction Equation--2-Dimensional -- from Eric Weisstein's World of Physics

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Heat Conduction Equation--2-Dimensional

In two dimensions, the heat conduction equation becomes

where is the heat change, T is the temperature, h is the height of the conductor, and k is the thermal conductivity. Then

where is the density and S is the heat capacity. Equating gives

which is simply a 2-dimensional diffusion equation in T.

Heat Conduction Equation, Heat Conduction Equation--1-Dimensional, Heat Conduction Equation--3-Dimensional