ABSTRACT

This paper deals with the elaborated numerical analysis of some examples which elucidate the most important features of the computer program prepared for the proposed formulation of the heat transfer with phase change presented in our previous paper. In particular, attention was concentrated on the treatment of the phase change effect. The special features of the computer program discussed herein are connected with determination of the best temporal scheme, which is the crucial matter in the calculation of the temperature gradient at the phase change interface. In this context, interesting results are obtained in simulation of the 2-dimensional infinite media, necessarily being of finite size in the finite element method formulation. Two examples of considerable importance for engineering practice in cold climate regions are discussed in detail and compared with published results.

INTRODUCTION

Our previous paper, “Fixed Finite Element Model of Heat Transfer with Phase Change — Part I: Theoretical Formulation and Numerical Algorithm,” presented the detailed formulation of the heat transfer problem with special emphasis on the phase change effect. The formulation was based on the first law of conservation of energy for continua with discontinuous thermal properties given in integral form. This approach in a natural way resulted in the spatial discretization by means of the finite element method which was obtained via the Galerkin-Bubnow approach for variational functions. The explicit derivation required for the description of the phase change effect was presented. Then, the numerical simulation of the curvilinear phase change front intersecting the original finite element in arbitrary fashion was shown, employing the computer flow chart. The temporal modelling of the transient thermal phenomenon was supported by the concept of the incremental decomposition procedure applied with respect to all thermal quantities, together with Euler backward method utilised for the discretization of the temperature rate.

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