Solution of the 2D Heat Equation Using the Method of Lines

Consider the unsteady-state heat conduction problem defined by
,
where is the temperature, is the thermal diffusivity, is the time, and and are the spatial coordinates.
This Demonstration solves this partial differential equation–a two-dimensional heat equation–using the method of lines in the domain , subject to the following Dirichlet boundary conditions (BC) and initial condition (IC):
BC 1: , where and ,
BC 2: , where and ,
BC 3: , where and ,
BC 4: , where and ,
IC: , where and .
The Demonstration gives a contour plot of the temperature for user-set values of and .

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