Stefan number

About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.

Solid/liquid phase change heat transfer in porous media (Effects of fins on the solidification process)

Abstract: Numerical calculations on the solidification process in a porous medium surrounded by a finned surface were performed using a simple quasi-steady model as well as an accurate finite-difference method, and their results were compared with experimental data. Calculations for the case without fins were also performed for comparison. In addition, the effects of important parameters appearing the governing equations on the solidification process were systematically examined using the finite-difference method. As a result, the finite-difference solutions were in excellent agreement with the experimental ones over a wide range of conditions. The quasi-steady model gives fairly accurate solutions for the case without fins, but the solutions were not sufficiently accurate for the case with fins, especially under conditions for which the solidification rate was large. Among parameters appearing in the governing equations, both the porosity of the porous medium and the ratio of the thermal conductivity of the porous particles to that of ice did not largely affect the solidification process and the fin effectiveness. They were largely affected by changes in the Stefan number and the aspect ratio of the considered region.

The Effect of Uniform Rotation on Convective Instability of a Mushy Layer During Binary Alloys Solidification

Abstract: The linear stability analysis of interstitial liquid within the mushy layer relative to a steady basic state is performed in order to incorporate the effect of uniform rotation on the onset of convective instability whose existence was found by Anderson and Worster (1996). The full set of non–dimensional governing equations for the temperature field, the local solid fraction and the fluid velocity are reduced asymptotically. In particular, the limit of small dimensionless mushy layer thickness, the limit of small differences between the initial and eutectic compositions of the liquid and the limit of large Stefan number are considered. The square root of Taylor number is assumed to be of the order unity. These simplifying assumptions involved in our analysis lead to a much simplified model which can essentially be solved analytically.

Generalized Lame-Clapeyron Solution for a One-Phase Source Stefan Problem

Abstract: In this paper we obtain a generalized Lam� e-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.

Heat and fluid flow processes during the coating of a moving surface

Abstract: In this paper, a theoretical study is presented for the problem of coating a flat moving surface with a small Prandtl number melt, exemplified by a liquid metal or a liquid crystal. From the heat and fluid flow standpoint, the process is modeled as one of forced convection in the melt (induced by both the motion of the surface and the velocity of the melt as it is deposited on the surface) coupled with conduction in the solidifying coating layer. The effect of the main parameters of the problem, such as the ratio of the melt deposition velocity to the surface velocity, the Stefan number, the Prandtl number, and the ratios of the main properties of the solid and liquid phases on the thickness of the resulting coating layer and the heat transfer to the moving surface, are determined. An important assumption adopted in this study is that the moving surface is isothermal. The parametric domain of validity of this assumption is defined.