Unsteady-State Conduction of Heat in Two Dimensions

Unsteady-state heat transfer obeys the PDE:
,
where is the temperature in °C, is the thermal diffusivity in , and , are coordinates with .
The initial and boundary conditions are chosen as follows:
for ,
for or ,
and for or .
This Demonstration plots the temperature profile for various values of the thermal diffusivity and at different instants. The steady-state solution corresponds to the solution of Laplace's equation for the selected boundary conditions.

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