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This is a basic heat transfer problem, the equation is visible in the attached file. It is done with Comsol 5.1, wish you can open it.

BR
Lasse

Hi Lasse

for some replies I prefer to answer this way, to be more in line with the professors trying to learn physics to their students:

Copy of my answer on the "private side" of the Forum, and of general interest to those wanting to learn HT

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Hi

You have got a nice introductory to HT problem there.

What you need to do is to:
1) define and sketch out your heat fluxes and sources
2) check the general equation you have and identify which variables remain i.e. which value has "u" ? (it's written in the text)
3) you should do some analytical estimations you have two variables of interest, one is "alpha" the "heat diffusivity", units (m^2/s), in fact its the multiplier of the second order derivative of T alpha = k/rho/Cp it indicates the speed of the flow of heat, driven by the heat gradient dT/dx. The seconds is the value rho*Cp it gives you an estimate of the total energy storage capacity of the volume (do not forget the depth here. This should give you a good estimate of the time scale you are talking about, for how long should you simulate ? With the sketch of 1) you should be able to have a first rough hand sketch of the temperature profile with time.
4) you should analyze the geometrical dimensions: you have a 3D problem, but clearly it has symmetries such that it reduces to a 1D problem

Once this is done you should be able to rapidly set this model up in COMSOL even with only the "math-physics" module, but even quicker in HT if available.

A few advices for the modeling:
a) decide of you go for 1,2 or 3D, I would suggest start simple 1D is the simplest, but perhaps less intuitive visually.
b) turn on the plot while solving and select for all steps taken by the solver, this helps the debugging
c) check your mesh, start coarser, then refine once the model seem to behave correctly, ideally you should consider a non linear distributed mesh but that is a final refinement step. Reminder: the objective of the mesh resolve de dependent variable "T" AND its first spatial derivative dT/dx correctly.
d) explain why you might get "negative" temperature differences for the first time step(s), if you plot the temperature, versus time, over a 1D cut line in the middle of your slab. (hint play also with the COMSOL Plot "Quality" and default "refinement" settings
e) propose a faster converging time step than the default linear "range()" stepping and justify why ;)
d) use the Global Parameter section extensively, with UNITS! to calculate alpha, rho*CP and the time and spatial diffusion constants.
e) as final verification: calculate the total fluxes and check that the energy conservation is respected (hint use the Derived Variables and plot the tables results)

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Have fun COMSOLing
Ivar