Question

Under what conditions does the general form of the heat conduction equation become a linear partial differential?

Answer 1

The General Heat Conduction equation is given by,

k is the thermal conductivity, T is temperature is Rate of heat generation. is density and is Heat capacity at constant pressure.

Now for a homogenous and isentropic media, there will be no changes in thermal conductivity, This gives,

This here is a linear partial differential equation. Therefore the heat conduction equation becomes a linear partial differential equation when the material is homogenous and isentropic.