Fractal model for evaluating heat transfer of high temperature porous corundum shell in vacuum investment casting

• Main Authors: WAN Xin, XU Cheng-hai, FENG Wen-gang
• Format: Article
• Language: English
• Published: Foundry Journal Agency 2006-02-01
• Series: China Foundry
• Subjects: porous corundum shell; fractal; thermal conductivity; vacuum investment casting
• Online Access: http://www.foundryworld.com/uploadfile/20093450454737.pdf

Under vacuum, heat transfer in porous corundum shell of investment casting depends on the characteristics of the solid materials and the spatial arrangement of solids and pores. In this study, we present a modified fractal approach to model the pore structure of corundum shell and to describe its influence on the thermal conductivity. We assumed that there is no heat convection in the shell. A sectioned view of porous corundum shell was studied and used to describe the geometric structure and to calculate the fractal dimension d. Based on the fractal dimension d, we obtained the relationship between volumetric solid content and pore arrangement in different measure scales. A heat transfer model was thus established using a network of resistors in which we applied an equivalent approach to calculate the effective thermal conductivity of real porous corundum shell that include the effects of heat conduction and heat radiation of solid. From the obtained results we discuss these effects on the effective thermal conductivity including the scale of measurement, the structure of pore and the temperature. At last these results were compared with other empirical model, which computed by assuming even porosity in which effect of pore structure was not being considered. Though the thermal conductivity calculated essentially in agreement with that obtained from empirical model, model used in this study is more close to the real heat transfer process.