Unsteady-State Conduction of Heat in Two Dimensions

Unsteady-state heat transfer obeys the PDE:

,

where is the temperature in °C, is the thermal diffusivity in , and , are coordinates with .

The initial and boundary conditions are chosen as follows:

for ,

for or ,

and for or .

This Demonstration plots the temperature profile for various values of the thermal diffusivity and at different instants. The steady-state solution corresponds to the solution of Laplace's equation for the selected boundary conditions.