Showing papers on "Stefan number published in 1990"
TL;DR: In this paper, the Coupled Integral Equation approach for solving phase change problems of semi-infinite medium is extended to develop an approximate analytic solution for melting or solidification in a slab of finite thickness subjected to a time-varying prescribed temperature at one surface and a constant prescribed temperature on the other.
Abstract: The recently advanced Coupled Integral Equation approach for solving phase-change problems of semi-infinite medium is extended to develop an approximate analytic solution for melting or solidification in a slab of finite thickness subjected to a time-varying prescribed temperature at one surface and a constant prescribed temperature at the other. The accuracy of the analytic expressions obtained in this manner is examined by comparing the present results to those reported in the literature. The influence of physical parameters such as the Stefan number and the applied surface temperature on the interface position and boundary heat fluxes is examined.
19 citations
TL;DR: In this paper, the problem of inward solidification of a liquid in cylindrical and spherical geometries is considered and the results are compared with a numerical solution, obtained by using the enthalpy method, for various values of the Stefan number.
17 citations
TL;DR: In this paper, the influence of the Prandtl number on buoyancy-induced transport phenomena was investigated through two-dimensional steady-state computations for flow in a square enclosure at two different vertical wall temperatures, both with and without solidification.
14 citations
TL;DR: In this paper, the authors studied the effect of high Rayleigh number convection and the convection-conduction interaction across the freezing front on the time-dependent solidification in an enclosed liquid cooled from the side.
13 citations
01 Jun 1990
TL;DR: In this article, the authors performed fundamental heat transfer experiments on the melting of a phase change medium in a spherical shell and found that the energy transfer associated with melting was substantially higher than that predicted by the conduction model.
Abstract: Fundamental heat transfer experiments were performed on the melting of a phase change medium in a spherical shell. Free expansion of the medium into a void space within the sphere was permitted. A step function temperature jump on the outer shell wall was imposed and the timewise evolution of the melting process and the position of the solid-liquid interface was photographically recorded. Numerical integration of the interface position data yielded information about the melted mass and the energy of melting. It was found that the rate of melting and the heat transfer were significantly affected by the movement of the solid medium to the base of the sphere due to gravity. The energy transfer associated with melting was substantially higher than that predicted by the conduction model. Furthermore, the radio of the measured values of sensible energy in the liquid melt to the energy of melting were nearly proportional to the Stefan number. The experimental results are in agreement with a theory set forth in an earlier paper.
9 citations
TL;DR: In this paper, a 600g cylindrical charge of nepheline (85.8 wt.%)-sodium disilicate (14.2 wt.) contained in a platinum crucible was brought to its solidus temperature, 768°C.
5 citations
TL;DR: The results of an experimental study of melting of a free solid in a cylinder heated by external forced convection have been presented in this article, where the average wall Stefan number and Archimedes number have been varied between 0.026 to 0.053 and 8.76×106 to 3.34×108 respectively.
2 citations
TL;DR: In this paper, the phase-change material rotating with a constant speed is put into a wall which is kept at a constant temperature higher than the melting point of the phase change material.
Abstract: The contact melting problem of a phase-change matrial is studied theoretically. The phase-change material rotating with a constant speed is put a wall which is kept at a constant temperature higher than the melting point of the phase-change material. The problem is governed by four parameters, the Stefan number, the Prandtl number, the ratio of the centrifugal force to the externally applied force, and the ratio of the viscous dissipation to the externally applied heat. The fluid motion and the heat transfer in the narrow gap between the solid and the wall is examined by obtaining an approximate solution expanded in the form of the power series of the Stefan number with the precision up to the first order. It is found from order of magnitude analysis that the melting is caused by the heat transfer from the heated wall rather than the heat generation due to the viscous dissipation, that is, the latter is not important from a point of view of the heat transfer. However, since the attractive force due to the rotation easily exceeds the externally applied force in many practical cases, the effect of the convection on the melting speed is not always found to be negligible, and it causes the liquid-solid interface to be flatter.
2 citations
TL;DR: In this article, it was shown that the initial dynamic behavior of the free boundary velocity (i.e., the convexity of free boundary) is determined by the Stefan number of the system.
1 citations
04 Apr 1990
TL;DR: In this article, a regular perturbation to this solution was constructed for a downward growing axisymmetric dendrite, based on the smallness of a buoyancy parameter G, to examine the effects of buoyant flow on the solidification.
Abstract: : In solidification, when the process is limited by diffusion of released latent heat or solute, often the two-phase interface forms finger-like shapes called dendrites, whose tips are nearly paraboloidal in form. For a pure material solidifying into an undercooled melt, if surface energy and gravity are negligible, a well-known solution due to Ivantsov (1947) describes the steady growth with a paraboloidal interface. We construct a regular perturbation to this solution for a downward growing axisymmetric dendrite, based on the smallness of a buoyancy parameter G, to examine the effects of buoyant flow on the solidification. The analytic solution predicts that generally the buoyancy enhances growth and changes the shape of the interface, giving a sharper tip and wider base. These effects depend strongly on the Prandtl number, and also on the Stefan number (undercooling). The results compare will with the experiments of Huang and Glicksman (1981) up to G 5000, but over predict convective effects for higher G.