Calculation of two-dimensional solidification by orthogonal polynomials

It is noted that even with the powerful computational techniques available today the solution of many multidimensional solidification (and melting) problems of interest to engineering requires considerable effort and computer time. A method is presented to make the solution of such problems easier even with complex boundaries. The method, which involves expressing the temperature as a linear combination of orthonormal polynomials, can be applied to problems in which sensible heat contributions are much smaller than latent heat contributions. The method is verified by application to some solidification problems for which finite-difference computations have been carried out previously. It is noted that the new method reduces the computer time required for solution and, in contrast to the finite-difference method, cases with higher Biot numbers do not require more computer time than those with lower Biot numbers.