An efficient new method has been developed to incorporate the effects of heat transfer in a liquid pool into models of heat conduction with solidification. The procedure has been added into the commercial package Abaqus  as a user-defined subroutine (UMATHT). Computational results of fluid flow and heat transfer in a liquid domain can be characterized by the heat flux crossing the boundary representing the solidification front, or liquidus temperature. This superheat flux can be incorporated into an uncoupled transient simulation of heat transfer phenomena in the mushy and solid regions by enhancing latent heat. The new method has been validated and compared to semianalytical solutions and two other numerical methods on simple test problems: two-dimensional, steady-state ledge formation in cryolite in aluminum extraction cells, and shell thinning in continuous casting of steel. Its real power, however, is for multiphysics simulations involving complex phenomena, such as solidification stress analysis with nonlinear constitutive equations. Including the superheat flux from a thermal-fluid flow simulation of the liquid pool into the latent heat provides a very efficient and robust method for incorporating the effects of fluid flow in the liquid pool into thermal-stress problems, especially for transient problems.
Bibliographical noteFunding Information:
Received 23 March 2010; accepted 12 May 2010. The authors would like to thank the Continuous Casting Consortium at the University of Illinois, Urbana-Champaign, the National Science Foundation for Grant DMI 05-28668, and the National Center for Supercomputing Applications (NSCA) for computational and software resources. Address correspondence to Seid Koric, National Centre For Supercomputing Applications, University of Illinois at Urbana-Champaign, Mail Code 257, 1205 West Clark Street, Urbana, IL 61801, USA. E-mail: email@example.com
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