| Abstract: | A transformation well-known for a long time is used to transform the differential equation for heat conduction for temperature dependent material values into a differential equation written in a more simplified form. It is investigated how the initial and boundary conditions are transformed and in which cases the problem with variable material values can be solved by applying the solutions known for constant material values. For constant thermal diffusivity, this reduction is possible for boundary conditions of the first and second kind without limitation, for conditions of the third kind only in some cases. The results of different methods of calculation are compared in an example calculation. The series solution with transformation lies generally much closer to the numerically calculated temperature than the solution without transformation. The computing times for the series solution with transformation are reduced by a factor of 100. If the first minutes of the heating period are disregarded, the first term constitutes an excellent approximation. The computing time for the finite-difference method with transformation is 20% lower than without transformation. |
