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## Solving heat equation for heat-pulse in a point on the surface

 Quote by rollingstein What confuses me is how come the OP's original equation does not have a diffusion term at all? Shouldn't k, Cp and density always occur in combination (i.e. Diffusivity) in the solutions of the heat equation?
Two reasons. First of all, in the OP's relationship, κ (kappa) is the thermal diffusivity, not, as he stated, the thermal conductivity k. Secondly, the term involving Q is not quite right. The units don't properly give temperature. I'm too lazy to look up what the correct expression for what this term should be, but, at the very least, there should be a k (thermal conductivity) in the denominator (if U has units of temperature and Q has units of energy). I'm guessing that the denominator should be a constant times $kt\sqrt{\kappa t})$. This would give the correct units for temperature.

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 Quote by Jbari You are correct, I ment κ to be thermal diffusivity (= K/(ρ*Cp)) but I defined it incorrectly in my explanation as thermal conductivity.. And to return to the problem: the thermal diffusivities are NOT equal, but I would still like to find an analytical solution (if possible of course). Any suggestions on how/where to find it (maybe in literature, but my search has been fruitless untill now).
Try "Conduction of Heat in Solids" [H. S. Carslaw, J. C. Jaeger] . Another possibility is to solve it yourself. Of course, there won't be a nice similarity solution like the one you have given.

 Quote by Chestermiller Try "Conduction of Heat in Solids" [H. S. Carslaw, J. C. Jaeger] . Another possibility is to solve it yourself. Of course, there won't be a nice similarity solution like the one you have given.
+1 for that book. If it is documented anywhere it is in there.

I'll add a possibility of trying to take help from one of the Symbolic solvers like Maxima / Mathematica etc. after you frame the problem.

 Tags heat equation, pde, semi-infinite solid