Analysis of Multidimensional Conduction Phase Change Via the Enthalpy Model

[+] Author and Article Information
N. Shamsundar, E. M. Sparrow

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota

J. Heat Transfer 97(3), 333-340 (Aug 01, 1975) (8 pages) doi:10.1115/1.3450375 History: Received January 26, 1975; Online August 11, 2010


The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

Copyright © 1975 by ASME
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