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Showing papers on "Stefan number published in 2011"


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this paper, a variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite grid when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent.
Abstract: In this paper, variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite egion when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent. The Result is compared with result obtained by exact method (when thermal conductivity and specific heat in two regions are temperature independent) and semi analytical method (When thermal conductivity and specific heat are temperature dependent) and are in good agreement. We obtain the solution in the form of continuous functions. The method performs extremely well in terms of efficiency and simplicity and effective for solving the moving boundary problem.

22 citations


Journal ArticleDOI
TL;DR: In this paper, the phase change material (PCM) freezing process is used for recovery and storage of the cryogenic gas cold energy, and numerical study has been conducted on this two-dimensional transient freezing problem by using the Solidification and Melting model in the Computational Fluid Dynamics (CFD) code FLUENT.

18 citations


Journal ArticleDOI
TL;DR: The results show that the solidified materials with larger Stefan number grow slower than those with relatively smaller Stefan number and the impact of oscillating mold temperature boundary on the growth of shell thickness is particularly significant at earlier stages of the process and more pronounced for smaller Stefan numbers.

5 citations


Journal ArticleDOI
TL;DR: In this article, an analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented.
Abstract: Ablation is the most common approach for thermal management for reentry of the spacecraft to the atmosphere. An analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented in this paper. The problem is divided into five stages and the temperature distributions in both layers in the five stages are obtained using an integral approximate method. The locations of ablation interface, thermal penetration depth, and ablation rate are obtained and the effects of Stefan number, subcooling parameter, thickness of the ablative material, and ratio of thermal diffusivities between two materials are investigated.

3 citations


01 Jun 2011
TL;DR: In this paper, a physical model is developed to analyze the thermal performance of packed bed-PCM latent heat thermal energy storage system and the results obtained are used for the thermal behavior of both charging and discharging modes.
Abstract: Packed bed-PCM latent heat thermal energy storage system is presented in this study. The packed bed cylindrical column is filled with spherical capsules of PCM (paraffin wax) that used for solar water heating application. In this study, the physical model is developed to use for analyzing the thermal performance of packed bed-PCM latent heat thermal energy storage. The model depends on energy balance equation that can be applicable only to the sensible heat storage materials and can be converted to enthalpy equation that can be applicable to the PCM storage bed. The governing equations are numerically solved using simple explicit and first order finite difference technique. The results obtained are used for the thermal behavior of both charging and discharging modes. The effects of mass flow rate and inlet heat transfer fluid temperature (Stefan number) on the thermal performance of the PCM capsules of different radii are investigated. The melt/solid fraction distribution of the bed as function of time and axial position during charging and discharging modes is investigated. The results show that higher inlet heat fluid temperature and higher mass flow rate of heat transfer fluid indicates shorter time for complete charging processes. The complete solidification time is too longer compared to the melting time. This is due to the very low heat transfer coefficient during solidification. The charging and discharging rate are significantly higher for the PCM capsule of smaller radius compared those of lager radius. The phase transition temperature range reduces the complete melting time; a difference of 31.7% is observed for the case when the PCM has melting in the temperature range as compared to that for a PCM with at fixed temperature.

3 citations


Journal ArticleDOI
TL;DR: In this article, the phase change solidification thickness and temperature distribution in the solid region with second-order accuracy solutions were compared with those with first-order accurate solutions for different Stefan numbers.
Abstract: The analytical solutions to solidification characteristics of a phase change material in the plate capsule of a cool storage system are presented. The influence of the Stefan number (the ratio of sensible heat to latent heat of a cool storage material) on phase change solidification thickness and temperature distribution in the solid region is analyzed. The phase change solidification thickness and temperature distribution in the solid region with second-order accuracy solutions are compared with those with first-order accuracy solutions for different Stefan numbers. It is found that the difference in temperature distribution in the solid region between second-order accuracy solutions and first-order accuracy solutions is very small as the Stefan number is small (i.e., Ste ≤ 0.1). In addition, the results present that the difference in phase change solidification thickness between second-order accuracy solutions and first-order accuracy solutions is small as the Stefan number is small (i.e., Ste ≤ 0.1). T...

3 citations


Journal Article
TL;DR: In this article, a lattice Boltzmann model under local thermal non-equilibrium conditions based on double temperature equations is developed for simulation of melting governed by heat conduction of phase change materials in metal foams.
Abstract: A lattice Boltzmann model under local thermal non-equilibrium conditions based on double temperature equations is developed for simulation of melting governed by heat conduction of phase change materials in metal foams.Nonlinear phase change aspects are tackled by an enthalpy based method.The numerical simulation results show the non-equilibrium effect can not be neglected when the porous metal foam is with low porosity density,when the thermal conduction difference between the fluid and the porous metal foam is significant,and when the Stefan number of phase change material is relative small.

1 citations


Proceedings Article
23 Sep 2011
TL;DR: In this article, a finite difference approach to spherical and cylindrical phase change problem with periodic boundary condition is established by using an invariant-space-grid method, and the effects of the Stefan number, the amplitude and frequency of periodically oscillating surface temperature on the motion of the moving interface and the temperature distribution are analyzed.
Abstract: A finite difference approach to spherical and cylindrical phase change problem with periodic boundary condition is established by using an invariant-space-grid method The motion of the moving interface and the temperature field are simulated numerically Also the effects of the Stefan number, the amplitude and frequency of the periodically oscillating surface temperature on the motion of the moving interface and the temperature distribution are analyzed Numerical experiments show that, for given amplitude and frequency, the Stefan number strongly influences the temperature distribution and the evolution of the moving interface, while the effect of the oscillating boundary temperature on the evolution of the moving interface is more pronounced when the phase change domain is small and diminishes as the domain grows And comparing with spherical phase change, cylindrical phase change is influenced more strongly by the Stefan number

01 Jan 2011
TL;DR: In this article, the authors investigated the dynamic response of a solid phase formed during unidirectional solidification below a cooling top wall of a square cavity filled with distilled water and subjected to time- varying heating temperatures at its bottom wall.
Abstract: In this work, we investigate the dynamic response of a solid phase formed during unidirectional solidification below a cooling top wall of a square cavity filled with distilled water and subjected to time- varying heating temperatures at its bottom wall. Assuming a quasi- steady state condition, we have formulated a one-dimensional model that predicts the average thickness of the forming solid phase. While non-dimensionalizing the model equations, three important non-di- mensional parameters are identified, namely the Biot number based on the solid phase thickness at steady state, the Stefan number based on the temperature difference between the cooling upper wall and the liquid temperatures, and the Stefan number based on the heating bottom wall and the liquid temperatures. A perturbation solution of the quasi-steady state formulation has been developed for small amplitude temperature variations on the heating bottom wall. The perturbation solution has been extensively tested against a full two-dimensional numerical solution that uses boundary-tracking techniques for tracing the solid-liquid interface, and good general agreements have been confirmed. The solid phase thickness variation with the time and its phase delays have been expressed as a function of the non-dimen- sional angular frequency of the heating bottom temperature and the above-mentioned three non-dimensional parameters. The implications of this study and its potential for employment in education and practical engineering have been also addressed.