The heat conduction problem with temperature-dependent material properties (Q1116744)

The heat conduction problem in a semi-infinite region with temperature- dependent material properties is investigated. The problem is linearized by dividing the complete temperature range into a finite number of subintervals. These subintervals are chosen small enough so that the material functions can be considered constant. The resulting problem resembles that of a composite material, except that the interfaces between elements are unknown functions to be solved. It also resembles the Stefan problem of a multi-phase or a polymorphous material. A similarity solution is found and determined. The existence and uniqueness of the solution is thoroughly examined and proved. Finally, when the material functions are temperature independent, the known solution is recovered.