Classical example of heat conduction modeled by the Fourier’s law of thermal conduction:

fourier_equation

where (including the SI units)

q is the local heat flux density, W·m−2,
k is the material’s conductivity, W·m−1·K−1,
DeltaT is the temperature gradient, K·m−1.

Download code:

heat_conduction_square.zip

More:

https://en.wikipedia.org/wiki/Thermal_conduction