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Showing papers on "Stefan number published in 2009"


Journal ArticleDOI
TL;DR: In this paper, the phase change phenomena of PCM inside the capsules are analyzed by using enthalpy method, and the results obtained are used for the thermal performance analysis of both charging and discharging processes.

291 citations


Journal ArticleDOI
TL;DR: In this paper, the melting of a spherical or cylindrical nanoparticle is modelled as a Stefan problem by including the effects of surface tension through the Gibbs-Thomson condition, and the resulting equations are studied analytically in the limit of small time and large Stefan number.

44 citations


Journal ArticleDOI
TL;DR: In this paper, the process of melting a small spherical particle is treated by setting up a two-phase Stefan problem and surface tension is included through the Gibbs-Thomson condition, which is to decrease the melting temperature as the particle radius decreases.
Abstract: The process of melting a small spherical particle is treated by setting up a two-phase Stefan problem. Surface tension is included through the Gibbs-Thomson condition, the effect of which is to decrease the melting temperature as the particle radius decreases. Analytical results are derived via a small-time expansion and also through large Stefan number asymptotics. Numerical solutions are computed with a front-fixing scheme, and these results suggest that the model exhibits finite-time blow-up, in the sense that both the interface speed and the temperature gradient in the solid phase (at the interface) will become unbounded at some time before complete melting. The near blow-up behaviour appears to be similar to that encountered in the ill-posed problem of melting a superheated solid (without surface tension), and may help explain the onset of abrupt melting observed in some experiments with nanoscaled particles.

40 citations


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this article, the heat transfer behavior of phase change material fluid (PCM) under laminar flow conditions in circular tubes and internally longitudinal finned tubes was studied, and an effective specific heat technique was used to model the phase change process.
Abstract: The heat transfer behavior of phase change material fluid (PCM) under laminar flow conditions in circular tubes and internally longitudinal finned tubes was studied. An effective specific heat technique was used to model the phase change process. Heat transfer results for a smooth circular tube with PCM fluid were obtained under hydrodynamically and thermally fully developed conditions. Results for the finned tube were obtained using the H2 and T boundary conditions. It was determined that the Nusselt number was strongly dependent on the Stefan number, fin thermal conductivity value, and height of the fins.

31 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical model of the volumetric change rate for the phase change processes of hexadecane within a cylindrical container was presented and a special experimental device was designed and constructed to verify the numerical model.
Abstract: The solid-to-liquid phase change material can be used to convert the thermal energy of low quality into mechanical energy. Its volumetric change rate has a great effect on the converting efficiency. The mathematical model of the volumetric change rate for the phase change processes of hexadecane within a cylindrical container was presented. A special experimental device was designed and constructed to verify the numerical model. The results at different Stefan numbers of the experiments matched well with those from the numerical simulations. The influences of Stefan number, Biot number and radius of cylinder on the volumetric change rate were studied and analyzed. The results showed that the volumetric change rate depends on the mass fraction of liquid phase and the difference between liquid and solid density of the materials. All the factors affecting the phase change rate will influence the volumetric change rate. The volumetric expansion rate is less than theoretical value under an external pressure. While a high-pressure situation is taken into consideration, the numerical model should also be modified by adding a function calculating density varying with pressure to ensure that the model operates properly. The power output can be enhanced by reducing the total time of melting. It can also be improved when the phase change material is partly melted at a volumetric expansion rate less than 100% of the total value. Copyright © 2008 John Wiley & Sons, Ltd.

22 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present results of solid-liquid phase change driven by volumetric energy generation (VEG) in a vertical cylinder, and show excellent agreement between a quasi-static, approximate analytical solution valid for Stefan numbers less than one, and a computational model solved using the computational fluid dynamics code FLUENT®.
Abstract: This paper presents results of solid–liquid phase change, driven by volumetric energy generation (VEG), in a vertical cylinder. We show excellent agreement between a quasi-static, approximate analytical solution valid for Stefan numbers less than one, and a computational model solved using the computational fluid dynamics code FLUENT®. A computational study also shows the effect that the VEG has on both the mushy zone thickness and convection in the melt during phase change.

15 citations


Journal ArticleDOI
TL;DR: In this paper, the authors numerically explored melting of a pure substance with the thermal conductivity of the solid phase, assumed to be anisotropic, using the standard one-phase Gobin-Le Quere melting benchmark.
Abstract: This paper numerically explores melting of a pure substance with the thermal conductivity of the solid phase, assumed to be anisotropic A two-phase test case for such situations is deduced from the standard one-phase Gobin–Le Quere melting benchmark The solution is presented for Prandtl number 0·02, Stefan number 0·01 and Rayleigh number 2·5 × 104 which are specific for metals Three cases are compared in terms of the terminal interface boundary position and average liquid fraction as a function of time for isotropic case and two distinctly oriented principal directions of the thermal conductivity tensor The calculations have been performed by using the one-domain enthalpy formulation with artificial melting interval and the recently developed explicit local radial basis function collocation method (LRBFCM) which belongs to the entirely new generation of meshless methods The results are not sensitive to the increased thermal conductivity of the solid phase in the direction parallel with the he

9 citations


Journal ArticleDOI
TL;DR: In this paper, an improvement is introduced to the conservation element and solution element (CE/SE) phase change scheme presented previously, which addresses a well-known weakness in numerical simulations of the enthalpy method when the Stefan number (the ratio of sensible to latent heat) is small (less than 0.1).
Abstract: An improvement is introduced to the conservation element and solution element (CE/SE) phase-change scheme presented previously. The improvement addresses a well-known weakness in numerical simulations of the enthalpy method when the Stefan number (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.

7 citations


Journal ArticleDOI
TL;DR: In this article, two-dimensional axisymmetric Navier-Stokes and energy equations are solved using the finite volume method to predict the time required for a steel sphere to melt in a melt pool of the same material.
Abstract: Blown-powder laser cladding finds its application in manufacturing industries to improve the surface properties of metallic mechanical parts. In the blown-powder laser-cladding process the powder particles go into the superheated melt pool formed by melting ofthe powder and become the integral part of the substrate coating upon solidification as the laser beam moves away. In the present study, two-dimensional axisymmetric Navier-Stokes and energy equations are solved using the finite volume method to predict the time required for a steel sphere to melt in a melt pool of the same material. The effect of forced convection, characterized by a Reynolds number, and superheat of the melt pool, characterized by a Stefan number, have been studied in detail for a Prandtl number of 0.13. The effect of buoyancy is neglected for the present investigation. It is found that the effect of forced convection on melting time reduction is more pronounced for the low Stefan number case. The rate of melting of the sphere with time under different conditions is also presented. Finally, the heat transfer characteristic is presented by the correlation of a Nusselt number with a Reynolds number and a Stefan number for a Prandtl number of 0.13. The decrease in size of the particle and its change in shape have been presented along with the evolving velocity and temperature field around the particle.

4 citations


Journal ArticleDOI
TL;DR: In this article, the authors model the extent of reduction in the active area due to freezing, assuming that the freezing point decreases linearly with solute concentration, conditions for freezing to occur have been derived and the ineffective fraction of catalyst pellet is found to be the same irrespective of the mode of freezing.
Abstract: Spatial variations in the concentration of a reactive solute in solution are often encountered in a catalyst particle, and this leads to variation in the freezing point of the solution. Depending on the operating temperature, this can result in freezing of the solvent oil a portion of catalyst, rendering that part of the active area ineffective Freezing call occur by formation of a sharp front or it mush that separates the solid and fluid phases. In this paper, we model the extent of reduction in the active area due to freezing. Assuming that the freezing point decreases linearly with solute concentration, conditions for freezing to occur have been derived. At steady state, the ineffective fraction of catalyst pellet is found to be the same irrespective of the mode of freezing. Progress of freezing is determined by both the heat of reaction and the latent heat of fusion Unlike in freezing of alloys where the latter plays a dominant role, the exothermicity of the reaction has a significant effect on freezing in the presence of chemical reactions. A dimensionless group analogous to the Stefan number could be defined to capture the combined effect of both of these.

Journal Article
Ling Feng1
TL;DR: In this article, the convergence properties of the refined heat balance integral solution for the one-phase melting problem were investigated, and it was proved that, for an equally spaced subdivision of n-1 and a piecewise linear polynomial selected as the approximate temperouture profile, when the Stefan number β≥1, the refined Heat Balance integral solution of this problem converges formally to the exact solution, and the convergence rate is O(n-1).
Abstract: The convergence properties of the refined heat balance integral solution for the one-phase melting problem are investigated.It is proved that,for an equally spaced subdivision of n-1 and a piecewise linear polynomial selected as the approximate temperouture profile,when the Stefan number β≥1,the refined heat balance integral solution of this problem converges formally to the exact solution,and the convergence rate is O(n-1).