Computer Methods in Applied Mechanics and Engineering 104 (1993) 19-30 North-Holland CMA 328 Finite element analysis for convective heat diffusion with phase change Daichao Sheng, Kennet B. Axclsson and Sven Knutsson Department of Civil Engineering, Luled Universi.ry of Technology, S-95187, Luled, ,Sweden Received 14 Octnber 199t Revised manuscript received 18 May 1992 Whereas phase-change problems associated with heat conduction L - been well ~*udiedduring the last three decades, very little attention has been paid to phase changes taking place in convective heat diffusion. Numerical methods dealing with conventional phase change problems do not directly work in cases where a fluid is concerned. In this paper, an enthalpy method is extended to solve phase-change problems associated with fluids. By using the concept enthalpy, the governing equations are first reformulated into a single quasi-linear partial differential equation that implicitly takes into account the condition of phase change. This equation together with appropriate initial and boundary conditions are then decomposed into two sets of equations respectively representing a convection and a diffusion problem. The decomposition is accomplished in such a way that no phase contradiction occurs between the two separate problems. The convection problem is solved by the method of step by step characteristics and the diffusion problem by a Galerkin finite element method. Numerical examples demonstrate that the numerical method produces reasonable results. l. Introduction Numerous attempts have been made to search numerical methods solving phase change problems during the last three decades and, indeed, effective techniques have been developed for handling difficulties such as moving boundaries and non-linearity [1-5]~ However, almost all of the methods are limited to phase changes taking place in stationary media and only heat conduction is considered. Recent concern for e.g. freezing of channel flow under low temperature and ice forming processes in arctic rivers, calls for attemion to phase change problems associated with convective heat diffusion. Consider a fluid flowing through a channel which risks freezing. The possibdity of freezing depends not only on the rate of heat diffusion and latent heat due to phase change, but also on the velocity of the fluid. The faster the fluid is flowing, the longer distance it can flow before freezing, For a very high velocity, diffasian may even be of less importance. This can be seen more clearly by considering the heat conservation equation Correspondence to: Daichao Sheng, Department of Civil Engineer~,,~, Lule~ University of Technology, S-95187~ Lule~, Sweden~ Telephone: 092091877, Telex: 80447 LUHS, Telefax: 0920 91913, Ernail: daico@anl.luth.se. 0045-7825/93/$06.00 (~) 1993 Elsevier Science Publishers B.V. All rights reserved