On approximate solutions for unsteady conduction in slabs with uniform heat flux (Q1287156)

An unsteady one-dimensional initial boundary value problem of heat conduction in a slab subjected to iso-heat flux is investigated especially from a numerical point of view. The transversal method of lines (TMOL) or Rothe's method is employed to obtain effective numerical solutions of this problem. The time-derivative in the parabolic partial differential equation (PDE) is discretized with a standard first order time accurate finite difference formulation, so the original PDE is therefore replaced by an adjoint ordinary differential equation. This method is compared with traditional approximate techniques -- Fourier series and Laplace transform solution. Several examples using TMOL are included.