TEMPERATURE-TRANSFORMING MODEL FOR BINARY SOLID-LIQUID PHASE-CHANGE PROBLEMS PART I.pdfVIP

TEMPERATURE-TRANSFORMING MODEL FOR BINARY SOLID -LIQUID PHASE-CHANGE PROBLEMS PART I: MATHEMATICAL MODELING AND NUMERICAL METHODOLOGY Xin Zeng and Amir Faghri DepartmentofMechanicaland Materials Engineering, Wright State University, Dayton, Ohio, USA The objective of this work is /Q devewp a new kmperature-tronsforming model for the treaJment of binary solid-liquid phase-change problems. The essentiDJ feature of the proposed model is the separation of the coupled effects of temperature and concentralwn on the latem heat evolution in the energy equation. ThaJ is, the lasen: heal evo/alion due /Q temperature variation is accounted for by thedefinuion ofan effective heal coejJicienl, while latent heat evolution owing to the concentrationvariation is accountedlOT by a source term. The main advantages of this model indude direct treasmem ofthe coupling relations among temperature, concentration, and liquid fraction, and the improvement ofnumerical SlDbiJity by the definitWn of the effective heal coefficient. INTRODUCTION Heat and mass transfer and fluid flow phenomena associated with solid-liquid phase-change systems have attracted much attention during recent years because of their practical importance [1-4]. The typical applications include casting and welding processes of metal and alloy materials, crystal growth techniques in material processing, solar energy storage systems for energy industries, and food freezing and thawing control. The release or absorption of thermal energy in a system undergoing phase change can take place either at a distinct phase-change temperature, as in most pure substances, or over a temperature/concentration range, which is the case for most mixtures. In fact, the former class of problems is generally referred to as isothermal phase-change problems, and can be readily characterized by a moving interface. The latter class is referred to as mushy-region phase-change problems. The range of temperature and concentration in which the solid an