Abstract: By managing the heat conduction problem in solids the thermal conductivity is usually taken as a constant,but in reality varying thermal conductivity reveals in every heat transfer process, Therefore, in the present paper,we wish to consider it to vary with the space coordinate according to a linear and an ex ponential law; basing on this proposal we have been able to set up six secottd order heat conduction differential equations, By the way,for the case of variable density, specific heat as well as thermal conductivity, we have been successful to deduce other similar six heat transfer differential equations.