## Partial Differential Equations- Two-Dimensional Heat Equation

^{Posted at Sat, 11 Sep 2010 16:10:06 GMT}

using separation of variables to ?nd the temperature distribution of rectangular and circular plates in the transient state.

Suppose that for a thin rectangular plate which occupies the plane region 0 ? x ? a, 0 ? y ? b, the top and bottom faces are insulated, and that its four edges are held at zero temperature. If the plate has the initial temperature function u(x, y, 0) = f(x, y), then in the transient state its temperature function u(x, y, t) is the solution of the following initial boundary value problem

We shall ?nd the solution of (36.1)

Suppose that for a thin rectangular plate which occupies the plane region 0 ? x ? a, 0 ? y ? b, the top and bottom faces are insulated, and that its four edges are held at zero temperature. If the plate has the initial temperature function u(x, y, 0) = f(x, y), then in the transient state its temperature function u(x, y, t) is the solution of the following initial boundary value problem

We shall ?nd the solution of (36.1)