The water content of soil and its movement within the soil mass are a quite important factors even for a saturated soils.
It becomes furthermore complicated if you go with unsaturated soil, because the changes in moisture content are directly related to and strongly affect the soil suction.
The hydraulic conductivity is also not constant. It varies non nonlinearly as the moisture content. We will also see how to determine our experimentally and we will consider a non-linear variation.
Therefore isothermal soil is an important aspect of the real problem. So what we will do, we will first derive equation for isothermal flow and then move on to non-isothermal flow.