Abstract
The melting process of a solid contained in a rectangular enclosure is investigated by an unsteady two-dimensional analysis of induced natural-convection heat transfer in the liquid region via the Boussinesq model. The mathematical model represented by the system of governing partial differential equations, as well as the initial and boundary conditions for the field variables, is transformed into an equivalent variational form by using the adjoint variational formulations. The weighted function finite element method was used to descretize the resulting variational principles into a system of algebraic equations suitable for numerical calculations. Numerical results obtained by a computer program designed for this purpose, i. e., values of the Rayleigh numbers in the range of 1O7-1O8, showed good agreement with experimental and other numerical data available for such problems.
