ON APPROXIMATE SOLUTIONS FOR UNSTEADY CONDUCTION IN SLABS WITH UNIFORM HEAT-FLUX

In this paper, the Transversal Method of Lines (TMOL) or Rothe's metho d is employed to obtain analytical expressions of simple form fur the unsteady one-dimensional heat conduction in a slab. Initially: the sla b is maintained at a uniform temperature, and then a uniform heat flux is applied to its surfaces. Implementation of TMOL generates a sequen ce of adjoint ordinary differential equations, where the spatial coord inate Is the only independent variable and the time becomes a paramete r. In spite of the anticipated expectations that the semi-discrete sol utions produced by TMOL would yield accurate temperature responses for short times only, detailed calculations demonstrate the opposite tren d. Surprisingly: the temperature results associated with two equal tim e steps are excellent not only for short times, but during the entire heating period. (C) 1998 Academic Press.