Showing papers on "Stefan number published in 2000"

Asymptotic results for the Stefan problem with kinetic undercooling

Abstract: We study the behaviour of the one-phase Stefan problem with kinetic undercooling; moving boundary problems governed by the same formulation also arise in the modelling of silicon oxidation and of solvent diffusion in glassy polymers. The one-phase model is carefully derived from a two-phase formulation in the limit of small thermal diffusivity in the solid. A linear kinetic undercooling law is assumed at the moving boundary and the one-phase model is then studied in a number of asymptotic regimes. In particular, results for small and large Stefan number are presented in one dimension and in a paradigm two-dimensional example

Thermal Analysis During Continuous Casting Process Using Effective Heat Capacity Method

Abstract: A numerical analysis has been carried out to investigate the two-phase solidification process in continuous castings. An effective heat capacity method is used for this purpose. The radiation heat transfer at the mold metal interface was taken into account. The results of this method match well with the results obtained by analytical methods. The investigation included the ranges of mold cooling rate Bi 2 , inlet temperature θ 0 , and Peclet number Pe from 0.1-0.5, 1.2-2.0, and 0.1-1.0, respectively. A constant Stefan number Ste of 2.5 was used. It is observed that the solidification process is delayed with the increase of the withdrawal speed and with the increase of the liquid metal inlet temperature. With increased withdrawal speed, the region with temperature gradient moves downward. Steep axial temperature gradient was observed in the cast metal in the mold region.

Two-Dimensional Ablation in Cylindrical Geometry

Abstract: Ablation modeling in cylindrical geometry is a very important problem in the thermal modeling of spacecraft, which has not been dealt with adequately in the literature. In the present work, two-dimensional ablation in cylindrical geometry is considered when the incident heat flux varies axially as well as temporally. A novel idea of using an effective inverse Stefan number, which is analogous to the effective heat of ablation (used in the literature), is proposed to be used as a variable nondimensional latent heat of ablation for ablation modeling, indirectly accounting for various processes involved in ablation. A two-dimensional ablation problem is solved by an alternating direction implicit and adjustable time-step scheme, coupled with boundary immobilization. Quasi-one-dimensional and two-dimensional modeling methods have been compared for two different materials, and the effects of variation of the proposed inverse Stefan number with the incident heat flux and the presence of highly conducting structure bonded to the ablative material have been studied. An optimum modeling method under specific conditions is suggested.

Controlling Phase Interface Motion in Inverse Heat Transfer Problems with Solidification

Abstract: In this paper, an inverse numerical model is presented for solidification problems. It is used to predict the transient boundary conditions, which produce a prescribed interfacial surface motion and heat transfer. The formulation calculates the required boundary temperature to provide a specified velocity of the phase interface during solid-liquid phase transition. A control-volume-based finite element method is employed for the numerical solution of the energy conservation equation. The finite element framework provides a novel alternative to other inverse techniques based on structured grids. The effects of Stefan number and interface velocity on the solidification processes will be investigated. Numerical examples are presented and discussed for one-dimensional and two-dimensional solidification problems. The accuracy and performance of the formulation are assessed by comparisons with analytical solutions. Based on the model's capability of efficiently providing stable and accurate results, it is viewed to be a worthy design tool in practical engineering applications such as thermal energy storage and materials processing, such as casting and extrusion processes.

Heat storage characteristics of latent microcapsules using hot air bubbles by direct contact heat exchange

Abstract: This paper has dealt with the heat storage characteristics of fine microcapsules packed with latent heat storage material in the water layer. The heat storage operation to the latent microcapsules was carried out using hot air bubbles by direct contact heat exchange. The microcapsule consists of n-paraffin as a core latent-heat storage material and melamine resin as a coating substance. The relation of the completion time of latent-heat storage to some parameters was examined experimentally. The non-dimensional correlation equations for the completion time of latent-heat storage process had were derived in terms of the ratio of water layer height to diameter of microcapsule, Reynolds number for air flow, Stefan number and modified Stefan number for absolute humidity of flowing air.

Numerical Solution Of Stefan Problems In Annuli

Abstract: A novel enthalpy formulation is applied to Stefan problems in annuli and is compared with the heat balance integral method (HBIM). Both methods are applied to inward and outward solidification in cylindrical geometry, and the results are combined to give numerical solutions in annuli. It is found that the enthalpy method gives comparable accuracy with the HBIM except for small Stefan number, and is more efficient and flexible.

Transient heat characteristics of water‐saturated porous media with freezing

Abstract: Analytical and experimental investigations were performed to examine the transient heat characteristics of water-saturated porous media with freezing. As a physical model, a two-dimensional vertical cavity was considered. One vertical wall was abruptly cooled below the fusion temperature, the other three walls were thermally insulated. Three different sizes of glass, and iron, alumina, and copper beads were used as the porous media. The cold energy stored in the porous media and the average thickness of the frozen layer were measured in the experiments. Comparisons of the analytical results with the experimental ones were made, and the effects of Darcy number, Stefan number, and modified Prandtl number on the transient heat characteristics were discussed. The dimensionless equations for predicting the averaged frozen layer thickness and the stored cold energy were obtained as a function of various dimensionless parameters.