Unsteady-State Conduction of Heat in Two Dimensions

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Unsteady-state heat transfer obeys the PDE:

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,

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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Contributed by: Housam Binous (March 2011)
Open content licensed under CC BY-NC-SA


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