[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).