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Showing papers on "Stefan number published in 1983"


Journal ArticleDOI
TL;DR: In this article, it was shown that the flow is confined to a thin layer about the forward hemisphere when the Peclet number is much greater than a known function of the Stefan number.

67 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the effect of nodal point spacing on the occurrence and magnitude of numerical oscillations in the temperature solution and the use of grid point spacing to control these oscillations, and the effect which the range of temperatures over which latent heat is liberated has on the solution.
Abstract: This paper investigates some of the numerical problems involved in simulating heat transfer in porous media in the presence of phase change. Applications of this type of simulation include modeling of certain metal forming processes, of biological tissues and organs during cryosurgery or cyropreservation, and of heat transfer in frozen soils subjected to transient environmental conditions. A two-dimensional finite element model was used in which the latent heat is treated directly as an energy source in the problem formulation. Several parameters addressed in this work are crucial to the successful implementation of numerical methods for nonlinear heat transport with phase change, including: the effect of nodal point spacing on the occurrence and magnitude of numerical oscillations in the temperature solution and the use of grid point spacing to control these oscillations; the limiting element size which should be used in order to insure stable temperature fields; and the effect which the range of temperatures over which latent heat is liberated has on the solution. The results indicate that numerical stability is achieved for combinations of the foregoing parameters which yield small values of the Stefan number.

21 citations


Journal ArticleDOI
TL;DR: In this article, a two-dimensional mathematical model of ingot solidification is developed and a computer procedure is then developed for solving these (half space) problems and this yields results in exact agreement with the analytical solutions.
Abstract: This paper is concerned with the development of methods for investigating moving interface problems that involve more than one space variable. The work was motivated by problems arising from the British Steel Corporation (Scunthorpe) concerning the solidification of killed steel ingots. First we investigate certain two-dimensional analytical solutions, which simulate particular aspects of ingot solidification. These relate to the inward solidification of a liquid half space either when the wall temperature varies with position along the wall or when Newton cooling takes place at the wall with the local heat transfer coefficient a function of wall position. Other approximate analytical approaches (with use of the heat balance integral method and formulation in terms of an integro-differential equation) are discussed briefly and their limited application to two-dimensional problems noted. A computer procedure is then developed for solving these (half space) problems and this yields results in exact agreement with the analytical solutions. In the work special attention is given to obtaining reliable information for small Stefan number $\beta = L/c\_p(T\_F - T_0)$ since this relates to values found in the steel-making process. In the major part of the paper a two-dimensional mathematical model of ingot solidification is developed. Numerical solutions are given for an ingot when the mould surface varies in geometry and in composition. Good agreement is obtained with radio isotope tracer tests performed at the British Steel Corporation (Scunthorpe).

13 citations