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).