(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello, I am trying to simulate the heat diffusion from a laser beam striking a sample. My model/concept is very simple in that it assumes the temperature distribution will be a radially symetric sphere (i.e T=T(r,t)).

I would like to plot a temperature profile evolving through time as a function of position from the initial contact of the laser beam. I am not making a 2D/3D map of the temperature distribution but simply a position vs T plot evolve through time.

My question is that can I use the solution for the heat diffusion equation in 1D cartesian coordinates to simulate the temperature distribution from the initial point of contact or would I have to use the spherical heat diffusion equation. The reason is that the solution for 1d cartesian is readily available while in spherical coordinates obtaining the solution is a bit more difficult.

2. Relevant equations

Heat Diffusion Equations

Cartesian

dT/dt=a(d^2/dx^2), where a represents thermal diffusivity

Spherical

1/r^2(d(r^2dT/dr)dr)=1/a(dT/dt), since no dependence on theta or phi

3. The attempt at a solution

I am currently simulating the heat diffusion using the solution from the 1d cartesian coordinate heat diffusion equation but I am not sure if this is entirely correct. Also, I would imagine that my temperature profiles would be the same as long as a set my position axis to be centered at the origin (point of contact of laser beam).

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Heating Simulation

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