Laser Heating & Mathematica Problem

1. Jan 23, 2012

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.

Last edited: Jan 23, 2012