| Abstract: | In this paper, the time–space method (TSM) for multidimensional melting and solidification problems is proposed. In the proposed TSM, the timewise co-ordinate is incorporated into one of the spatial co-ordinates, thereby transforming the usual transient 2-D (or 3-D) problems into steady 3D (or 4-D) boundary-value problems. Since time integration is not necessary, the TSM has a feature that eliminates the so-called numerical instability which has been a great concern in the principal numerical methodologies in the past. That is, no error propagation in the timewise direction occurs in the TSM calculation. The TSM is applicable to almost all transient heat transfer and flow problems. The computer running time will be reduced to only 1/100th–1/1000th of the existing schemes for 2-D or 3-D problems. The sample calculations are presented for a 2-D melting problem in a square cavity and the validity of the present method is examined. |
