Laser Heating & Mathematica Problem

[TaBaC]

Hi
the problem i am dealing with is that we want to heat samples up with a laser in our lab. For estimating the required laser power, as you know better than me, the main loss will be the heat diffusion in the material.

My heat equation is in the following:

$\frac{du(x,y,z,t)}{dt}$ - $\nabla^2u(x,y,z,t)$ - f(x) =0

where f(x) is the temperature increase by the laser beam (in unit time) in the middle of the plane. i think it should be a step function. 0 outside the beam and constant inside the beam.

do you think what i have here is correct ?

how can i solve it in mathematica ?

do have you have any book/reference for this problem ?

i think this is a well solved problem but i cannot find any thing on the net.

 

[Future Bruno]

Yes, what you have presented is correct. To solve this problem in Mathematica, you will need to use the NDSolve command. You can find a tutorial for this on the Wolfram website: https://reference.wolfram.com/language/tutorial/SolvingPDEs.htmlTo find some books or references, a good place to start would be the Wolfram Library Archive. It contains a comprehensive collection of books and other resources related to Mathematica: https://library.wolfram.com/You may also be able to find some books related to your specific problem by searching for 'heat equation' or 'heat diffusion'. Good luck!