Example and Code

For an example let us consider a 1x1 square of sheet metal.

Here we use the heat equation, initial condition and boundary conditions to solve and plot on mathematica.

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Our equation:

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Let us ignore the thermal diffusivity constant for now, setting it equal to one

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First let's use an initial condition of zero, meaning the whole plate just starts at temperature zero with no fluctuation:

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Now the boundary conditions:

 

Let us start simple with three sides insulated meaning

                                                                       for x=0 and y=0, 1 values.

 

The right side will be at heated at 2 degrees after the initial condition.:

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