Temperature is an important quantity to know for the understanding of the system. Material properties such as density, thermal conductivity, viscosity, and specific heat depend on temperature, and very high or low temperature can bring unexpected changes in the system. In solid, the heat equation can be used to obtain the temperature distribution inside the material with given geometries.
For steady-state and static case, the heat equation can be written as
where Fourier’s law of conduction is applied.
Applying boundary conditions gives a solution for the temperature distribution.