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Stefan number
About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.
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TL;DR: In this article, the one phase Stefan problem is discussed using the Goodman HBI method and an explicit numerical method including modified boundary immobilization scheme, which is obtained using the variable space step method based on variable domain.
Abstract: The one phase Stefan problem is discussed using the Goodman HBI method and an explicit numerical method including modified boundary immobilization scheme. The main advantage of the HBI method lie in the remarkable association of simplicity, flexibility and acceptable accuracy which an error less than 2.5% in predicting the moving front location for Stefan number less than unity which covers most usual isothermal phase change material. An accurate explicit numerical model to track the moving front in Stefan-like problems is provided. The scheme is obtained using the variable space step method based on variable domain. The method is developed using central difference approximations to replace spatial and temporal derivatives. Furthermore, iterative procedure, in numerical calculation, is avoided by introducing simple assumptions. The numerical results show that the accuracy of the method has been considerably improved without additional computational cost.
21 citations
TL;DR: In this paper, the behavior of the one-phase Stefan problem with nonlinear kinetic undercooling is studied and a method similar to the Boltzmann-Matano method for determining nonlinear diffusivities is described.
Abstract: The behaviour of the one-phase Stefan problem with nonlinear kinetic undercooling is studied. This system is physically relevant in a number of contexts, in particular as the sharp-interface (fast-reaction) limit of a variety of reaction-diffusion systems. The similarities and differences with the linear kinetic condition (studied by Evans and King) are highlighted for both one- and two-dimensional problems. Asymptotic results (both in time and in the Stefan number) are obtained for the power-law form of the kinetic condition. Significantly, the one-dimensional growth behaviour of the moving boundary is seen to be relatively insensitive to the precise form of the nonlinear kinetic condition, and this in effect has hindered its experimental determination in applications such as silicon oxidation. By contrast, the two-dimensional development of the moving boundary around a mask edge depends strongly on the form of the kinetic condition and consequently a method, similar to the Boltzmann-Matano method for determining nonlinear diffusivities, is described to determine the kinetic undercooling relation from experiment
21 citations
TL;DR: In this article, the authors present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature, where the thermal and physical properties of the melt and solid are assumed to be identical.
21 citations
TL;DR: It is shown that improving the porous thermal conductivity not only leads to an increase in the rate of heat transfer but also augments the fluid flow inside the cavity and opens up an avenue for further application-based studies.
21 citations
TL;DR: In this paper, the authors investigate the thermal, hydrodynamic and entropy generation behavior of nano-encapsulated phase change materials (NEPCM) in a porous medium and demonstrate that the rates of heat transfer and the average Bejan number are maximum and the generated entropy is minimum when the fusion temperature of the nano-capsules is Tfu ǫ = 0.5.
21 citations