Topic
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, a unified approach is adopted that allows simultaneous treatment of the problem in plane, cylindrical, and spherical geometries for three different types of boundary condition and a general recurrence formula is derived for the determination of the series solutions up to any desired order of the Stefan number.
Abstract: The method of strained coordinates is applied to the inward solidification problem. Constant thermal properties are assumed throughout the analysis for the liquid, which is initially at the fusion temperature. A unified approach is adopted that allows the simultaneous treatment of the problem in plane, cylindrical, and spherical geometries for three different types of boundary condition. A general recurrence formula is derived for the determination of the series solutions up to any desired order of the Stefan number. A comparison is made with numerical and regular perturbation solutions in the plane case to illustrate the usefulness and the validity of the method.
35 citations
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TL;DR: In this article, a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analyzed and the results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect.
34 citations
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TL;DR: In this article, the freezing of a supercooled droplet is modelled by a mixed boundary condition on the outer surface of the droplet, and a novel asymptotic solution is developed for a small Stefan number and an arbitrary Biot number.
Abstract: The freezing of a supercooled droplet occurs in two steps: recalescence, that is, a rapid return to thermodynamic equilibrium at the freezing temperature leading to a liquid–solid mixture and a longer stage of complete freezing. The second freezing step can be modelled by the one-phase Stefan problem for an inward solidification of a sphere, assuming the droplet to be spherical. A convective heat transfer with the ambient immiscible fluid is modelled by a mixed boundary condition on the outer surface of the droplet. This condition depends on the Biot number (ratio of the heat transfer resistances inside the droplet and at its surface). A novel asymptotic solution is developed for a small Stefan number and an arbitrary Biot number. Applying the method of matched asymptotic expansions, uniformly valid solutions are obtained for the temperature profile and freezing front evolution in the whole stage of complete freezing. For an infinite Biot number, that is, for a fixed temperature at the droplet outer boundary, known solutions are recovered. In parallel, numerical results are obtained for an arbitrary Stefan number using a finite-difference scheme based on the enthalpy method. The asymptotic and numerical solutions are in good agreement.
34 citations
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TL;DR: In this paper, a three-zone model is developed to predict the freezing process in fine-grained, porous media under phase-transition conditions, where a freezing zone, characterized by a wide temperature range of phase transitions, is formed.
34 citations
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TL;DR: In this article, the combined integral method (CIM) is used to solve the Stefan problem, which reduces the standard problem, consisting of a PDE defined over a domain specified by ODE, to the solution of one or two algebraic equations.
34 citations