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Abstract
Solidification in an enclosed space is investigated, considering conduction in the mold wall. This gives rise to a conjugate, transient problem, with the flow in the liquid driven by thermal buoyancy. An enthalpy formulation is used for the energy equation, with a porous medium approximation for the region undergoing phase change. The governing equations are solved using primitive variables in the physical space. The control volume approach is employed to discretize the equations. The numerical simulation of the phase change process is discussed in detail. The mold is subjected to different thermal conditions at the outer surface, and the effect of these on the shape of the solid-liquid interface, rate of solid formation, and rate of heat transfer quantified. Streamlines, isotherms, and velocity profiles are also obtained. The conditions under which natural convection in the melt can be neglected are investigated. The effects of important design parameters such as the mold material and width, aspect ratio of the cavity, and heat removal rate from the mold are considered in detail. A comparison is made of the important characteristics between the conjugate and nonconjugate cases. The differences in the numerical simulation of these two cases are investigated. Of particular interest are the temperature distributions that arise in the liquid, solid, and mold. It is shown that conjugate transport must be included for a realistic simulation of practical problems.