Steady-State Temperature Distribution in Conducting Square

Laplace's differential equation in two dimensions, (((∂^2) T(x,y))/(∂(x^2)))+(((∂^2)T(x,y))/(∂(y^2)))=0, with T(x,y) representing a stationary temperature field, is solved in a square region. Uniform and controllable boundary conditions along the edges (excepting the corners) are considered, in a temperature range of -300 °C to 300 °C.  The resulting isotherms are plotted.

THINGS TO TRY

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DETAILS

Snapshot 1: borders at 0 ºC

Snapshot 2: left border at 150 ºC and right border at -150 ºC; top and bottom are kept at 0 ºC

Snapshot 3: borders held at 150 ºC

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Contributed by: Hernan Vivas

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