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 .