Showing papers on "Stefan number published in 1994"

The solidification of buoyancy-driven flow in a flexible-walled channel. Part 1. Constant-volume release

Abstract: The solidification of hot fluid flowing in a thin buoyancy-driven layer between cold solid boundaries is analysed in a series of two papers. As an approximation to flow in a crack in a weakly elastic solid or to free-surface flow beneath a thin solidified crust, the boundaries are considered to be flexible and to exert negligible resistance to lateral deformation. The resultant equations of continuity and motion reduce to a kinematic-wave equation with a loss term corresponding to the accumulation of solidified material at the boundaries. The Stefan problem for the solidification is coupled back to the flow through the advection of heat by the fluid, which competes with lateral heat loss by conduction to the solid. Heat and mass conservation are used to derive boundary conditions at the propagating nose of the flow. In this paper the two-dimensional flow produced by a line release of a given volume of fluid is investigated. It is shown that at short times the flow solidifies completely only near the point of release where the flow is thinnest, at later times complete solidification also occurs near the nose of the flow where the cooling rates are greatest and, eventually, the flow is completely solidified along its depth. Some transient melting of the boundaries can also occur if the fluid is initially above its solidification temperature. The dimensionless equations are parameterized only in terms of a Stefan number S and a dimensionless solidification temperature Θ. Asymptotic solutions for the flow at short times and near the source are derived by perturbation series and similarity arguments. The general evolution of the flow is calculated numerically, and the scaled time to final solidification, the length and the thickness of the solidified product are determined as functions of S and Θ. The theoretical solutions provide simple models of the release of a pulse of magma into a fissure in the Earth's lithosphere or of lava flow on the flanks of a volcano after a brief eruption. Other geological events are better modelled as flows fed by a continual supply of hot fluid. The solidification of such flows will be investigated in Part 2.

Solid/liquid phase change heat transfer in porous media (Effects of fins on the solidification process)

Abstract: Numerical calculations on the solidification process in a porous medium surrounded by a finned surface were performed using a simple quasi-steady model as well as an accurate finite-difference method, and their results were compared with experimental data. Calculations for the case without fins were also performed for comparison. In addition, the effects of important parameters appearing the governing equations on the solidification process were systematically examined using the finite-difference method. As a result, the finite-difference solutions were in excellent agreement with the experimental ones over a wide range of conditions. The quasi-steady model gives fairly accurate solutions for the case without fins, but the solutions were not sufficiently accurate for the case with fins, especially under conditions for which the solidification rate was large. Among parameters appearing in the governing equations, both the porosity of the porous medium and the ratio of the thermal conductivity of the porous particles to that of ice did not largely affect the solidification process and the fin effectiveness. They were largely affected by changes in the Stefan number and the aspect ratio of the considered region.

Numerical analysis of freeze coating on a two-dimensional moving plate

Abstract: The process of freeze coating of a polymeric melt onto a two-dimensional flat plate moving continuously in the axial direction is simulated, taking into account the limited heat capacity of the plate, the spatial variation of the plate temperature, and the heat convected from the melt to the freeze coat. To identify the controlling parameters in the process, the system of equations governing the plate temperature and the shape and the temperature of the freeze coat is transformed into dimensionless coordinates. Numerical methods have been used to solve the resulting mathematical model. The history of the spatial variation of the shape of the freeze coat is presented in graphs. The parameters controlling the shape of the freeze coat are identified, and it has been found that the plate-coat diffusivity ratio, a convective heat transfer parameter, Peclet number, Stefan number, and the fusion temperature of the molten fluid are the parameters that control the growth and decay of the freeze-coat layer. The effect of these parameters and the boundary conditions on the behavior of the freeze-coat process is discussed.

Conduction-Controlled Phase-Change Energy Storage With Radiative Heat Addition

Abstract: Thermal energy storage in a phase-change material due to latent heat of fusion caused by conduction-controlled melting during radiative heat injection is considered. It is solved employing variational, integral, and quasi-steady methods. They yield closed-form solutions which are functions of the Stefan number, St, and the surrounding temperature. The results for the design parameters for the storage system obtained from these methods exhibit insignificant variation and are unaffected by the surrounding temperature, [theta][sub a], for St<0.1. The second law efficiency for this storage is devised. It is insensitive to changes in St and the heat absorption depth, [eta][sub m], for [theta][sub a][<=]1.2.

A Theoretical Model for Multiphase Flow with Solidified Particles : Physical Signification of Constitutive Equations and Evaluation of Latent Heat Effect

Abstract: Constitutive equations regarding the drift flux model for a multiphase flow consisting of molten material and its solidified particles were thermodynamically derived under a condition of local quasiequilibrium. The basic equations, including the conservation equations and the constitutive equations for the multiphase flow, were expressed in dimensionless forms. The theory developed here confirmed that the temperature fields closely depended on the Lagrangian derivative of the solid fraction accompanying the latent heat effect, and was characterized by the Stefan number. It was also suggested that the simplified basic equations corresponding to the phase equilibrium diagram were useful in the analysis of multiphase flow with solid-liquid phase change.