Showing papers on "Stefan number published in 1998"

Convection‐based model for a PCM vertical storage unit

Abstract: This paper presents a two-dimensional axi-symmetrical model for the formulation of the problem of fusion of PCM around a vertical cylinder in the presence of natural convection. The basic equations of mass, momentum and energy were formulated in terms of the vorticity and the stream function. The numerical predictions were compared with available experimental results indicating good agreement. Additional results show the effects of the geometrical and operational parameters on the solid–liquid interface, stream function, energy stored and melt mass fraction. The model was extended to produce charts and correlations for the mean heat transfer rate, total solidification (or fusion) time in terms of the geometrical parameter, the modified Rayleigh number and the Stefan number. These charts and correlations are helpful in engineering design of PCM storage units. © 1998 John Wiley & Sons, Ltd.

Numerical solution of the effect of vibration on melting of unfixed rectangular phase-change material under variable-gravity environment

Abstract: This article presents a numerical method for simulating the melting process in a cavity in the presence of wall vibration. An enthalpy method is employed to solve the governing equations associated with melting of an unfixed solid phase-change material (PCM) in a low gravitational environment. In this method, the problem is solved in one domain. The PCM, initially at its melting temperature, is placed inside a rectangular enclosure. The enclosure walls are then exposed to a uniform temperature under a specified amplitude and frequency of vibration. Melting begins from all sides, and owing to natural convection, the PCM would not retain its initial shape. The governing equations are discretized by using a control-volume-based finite difference method and are solved together with the solid PCM's equation of motion. The results are presented in the form of a parametric study of the effects of aspect ratio, Stefan number, Strouhal number, and dimensionless frequency or period of vibration, on the melt thickne...

Effect of convective heat transfer on thawing of frozen soil

Abstract: Most analyses of the thawing of frozen soil are based on purely conductive heat transfer, a very good assumption in most cases, but vertical and horizontal water flows occur frequently in permafrost regions. The effect of vertical water movement on the rate of thaw and the thermal regime of the soil is quantified. An exact similarity solution only occurs when the vertical water velocity is proportional to the rate of thaw. This solution indicates that seepage flows (the magnitude of the water velocity is near that of the rate of thaw) have little effect upon the thaw process. Approximate solutions are also given for the case of constant water velocity, using the heat balance integral and quasi-steady methods; they agree with the exact solution if the Stefan number is not too large. Thaw can be greatly accelerated or retarded if the water velocity (Peclet number) is large. The effect upon thawing for the case of horizontal water flow is less than that for the same magnitude of vertical flow.

The Effect of Uniform Rotation on Convective Instability of a Mushy Layer During Binary Alloys Solidification

Abstract: The linear stability analysis of interstitial liquid within the mushy layer relative to a steady basic state is performed in order to incorporate the effect of uniform rotation on the onset of convective instability whose existence was found by Anderson and Worster (1996). The full set of non–dimensional governing equations for the temperature field, the local solid fraction and the fluid velocity are reduced asymptotically. In particular, the limit of small dimensionless mushy layer thickness, the limit of small differences between the initial and eutectic compositions of the liquid and the limit of large Stefan number are considered. The square root of Taylor number is assumed to be of the order unity. These simplifying assumptions involved in our analysis lead to a much simplified model which can essentially be solved analytically.

Estimating the last point to solidify in a casting

Abstract: An approximate method for predicting the last point to solidify in a casting is presented. On defining a time-averaged temperature field, an approximate method for predicting the last point to solidify is defined by the solutions of two steady-state Poisson equations. The method is demonstrated by solving a number of one- and two-dimensional problems. For moderate values of Stefan number ( St < 2) predictions for the last point to solidify are in close agreement with predictions obtained from analytical and complete transient numerical solutions.

A Comprehensive Analysis of the Conduction-Dominated Transient Contact Melting on an Isothermal Surface

Abstract: This paper focuses on the development of a comprehensive analytical model for the conduction-dominated transient contact melting occurring on an isothermal surface, in which emphasis is placed on the treatment of an arbitrary strength of the external force. For a small Stefan number, the proposed model agrees reasonably not only with the exact solution for non-contact melting but also with the existing numerical data for close-contact melting. Normalization of the model equations with reference to the steady solution makes it possible to pick up a single consolidated parameterG by which the constrained melting processes can be effectively classified into three regimes: non-contact, intermediate and close-contact. Taking advantage of the approximate analytical solution available for close-contact melting, the value of demareation between the regimes of intermediate and close-contact melting is found to beG=103. It is also revealed for the first time that in the intermediate regime the contact melting system approaches the steady state passing through a damped oscillation.

Augmentation of heat transport in laminar falling film of ice crystals

Abstract: A fmite volume numerical code has been developed to nwnerically approximate the rate of ice crystal growth in a laminar falling film flowing down a cooled vertical plate. The governing energy equation contains the phase energy as the source termoEnhancement of heat transfer due to suspended ice crystals is accounted for in the use of effective values of thermal conductivity, viscosity, thermal diffusivity, and specific heat as function of volumetric concentration of ice crystals in the falling film, Nusselt numbers, overall heat transfer coefficients between the fluid and cooled plate, and ice crystal growth rate were calculated for different film thicknesses with and without axial diffusion. Nusselt number and ice crystal growth rate were found to be dependent on Stefan number and film thickness. Axial diffusion effects were found to be negligible for larger film thickness (large flowrate). Enhancement of heat transfer was noticed for the case of two phase flow with ice crystals.