Write a MATLAB script for the 1D heat equation

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Job Description

I need a simple (but WELL notated / explained) MATLAB script that will give a solution for the 1D heat equation WITH latent heat.

1) I want the script to solve for T(t) and ...
2) ask for the value of each parameter needed for the input (T(initial), thermal conductivity, specific heat, latent heat, etc), ...
3) ask for the latent heat a) value and b) range (for instance, the latent heat of 220 J/kg may be released linearly between 990 K and 1100 K).
3) ask for the value of the time step and ...
4) ask the number of iterations the user wants

(i.e. 100 year time steps, 1000 iterations = solutions of T(t) for 100,000 years.)

I've attached a picture of the heat equation, but you can use any 1D version you're familiar with ...

If you can write a 2D and 3D version as well, I will add another $10.

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