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

fourier_equation

where (including the SI units)

\overrightarrow{q} is the local heat flux density, W·m−2
\big.k\big. is the material’s conductivity, W·m−1·K−1,
\big.\nabla T\big. is the temperature gradient, K·m−1.

heat_conduction_square
Download Code:

heat_conduction_square.zip

More:

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