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Finite Volume Method Analysis of Heat Transfer in Multi-Block Grid During Solidification
Eliseu Monteiro1 , Regina Almeida2 and Abel Rouboa3
- Engineering Department of University of Tr´ s-os-Montes e Alto Douro, Vila Real a 2 CIDMA/UA - Mathematical Department of University of Tr´ s-os-Montes e Alto Douro, Vila Real a 3 CITAB/UTAD - Department of Mechanical Engineering and Applied Mechanics of University of Pennsylvania, Philadelphia, PA 1,2 Portugal 3 USA
1 CITAB/UTAD

1. Introduction
Solidification of an alloy has many industrial applications, such as foundry technology, crystal growth, coating and purification of materials, welding process, etc. Unlike the classical Stefan problem for pure metals, alloy solidification involves complex heat and mass transport phenomena. For most metal alloys, there could be three regions, namely, solid region, mushy zone (dendrite arms and interdendritic liquid) and liquid region in solidification process. Solidification of binary mixtures does not exhibit a distinct front separating solid and liquid phases. Instead, the solid is formed as a permeable, fluid saturated, crystal-line-like matrix. The structure and extent of this mushy region, depends on numerous factors, such as the specific boundary and initial conditions. During solidification, latent energy is released at the interfaces which separate the phases within the mushy region. The distribution of this energy therefore depends on the specific structure of the multiphase region. Latent energy released during solidification is transferred by conduction in the solid phase, as well as by the combined effects of conduction and convection in the liquid phase. To investigate the heat and mass transfer during the solidification process of an alloy, a few models have been proposed. They can be roughly classified into the continuum model and the volume-averaged model. Based on principles of classical mixture theory, Bennon & Incropera (1987) developed a continuum model for