Thermal Conduction :

[ssThermalConduction] Summary Here we shall learn how to deal with a time dependent# timedependent parabolic problem. We shall also show how to treat an axisymmetric problem and show also how to deal with a nonlinear problem.

How air cools a plate

We seek the temperature distribution in a plate \((0,Lx)\times(0,Ly)\times(0,Lz)\) of rectangular cross section \(\Omega=(0,6)\times(0,1)\); the plate is surrounded by air at temperature \(u_e\) and initially at temperature \(u=u_0+\frac x L u_1\). In the plane perpendicular to the plate at \(z=Lz/2\), the temperature varies little with the coordinate \(z\); as a first approximation the problem is 2D.
We must solve the temperature equation in \(\Omega\) in a time interval (0,T).