Numerical Heat Transfer, Part A, 36:449±472, 1999 Copyright Q 1999 Taylor & Francis 1040±7782 r 99 $12.00 H .00 SEMI-IMPLICIT FEM ANALYSIS OF NATURAL CONVECTION IN FREEZING WATER J. Banaszek and Y. Jaluria Department of Mechanical and Aerospace Engineering, Rutgers Uni versity, New Brunswick,New Jersey08903, USA T. A. Kowalewski and M. Rebow IPPT PAN, Polish Academy of Sciences,00-049 Warsaw, Poland, and Warsaw Uni versityof Technology, Institute of Heat Engineering, Nowowiejska 25, 00-665 Warsaw, Poland ( ) A semi-implicit finite element method FEM is presented for the two-dimensional computer simulation of solid-liquid phase change controlled by natural con v ection and conduction. () The algorithm is based on a combination of 1 a projection method to uncouple velocity () calculations from pressure calculations for incompressible fluid flow, 2 the backward Euler and explicit Adams-Bashforth schemes to effecti v ely integrate diffusion and ad v ection in () time, and 3 an enthalpy-porosity approach to account for the latent heat effect on a fixed finite element grid. Credibility of th e obtained numerical predictions is in v esti- gated through computation al model verification and v alidation procedures. Commonly used benchm ark problems are employed to v erify the algorithm accuracy and performance. The natural con v ecti on of freezing pure water is studied experimentally through the use of sophisticated full-field acquisition experimental techniques. The measured v elocity and temperature fields are compared with the pertinent calculations. The range of congruity of the experimental and numerical results is thoroughly studied, and potential reasons of some disparity in a local structure of the natural con v ection flow and in the interface shape are discussed. INTRODUCTION s . The cost-effectiveness of finite element method FEM calculations continues to be significant in the computer simulation of coupled fluid flow and heat transfer problems. It is commonly known that the finite difference method is superior in terms of computer storage and CPU time requirements when compared with FEM analysis. This results from a less sparse form of FEM matrices, due to the use of irregular grids and high-order polynomial interpolations of the unknown field Received 24 September 1998; accepted 27 April 1999. The authors acknowledge the support in part by the U.S.-Polish Commission of the Fullbright Foundation and by the Polish State Committee for Scientific Research, Grant No. 3 T09C 002 12. Address correspondence to Jerzy Banaszek, Institute of Heat Engineering, Warsaw University of Technology, 25 NowowiejskaStr., 00-665 Warsaw, Poland. E-mail: banaszek@itc.pw.edu.pl 449