Showing papers on "Stefan number published in 1992"

Oscillatory convection in solidifying pure metals

Abstract: A two-dimensional numerical study that models solidification of a pure metal in a horizontal crucible by using a finite-volume-enthalpy method has been carried out. The primary goals of the investigation are to assess the influence of phase change on the known transition to time-periodic convection and to predict the critical parameters associated with this phenomenon. Numerical simulations reveal the influence of the dimensionless solidification temperature Ts, on the critical value of the Grashof number Grcrit. The influence is found to be directly related to an effective aspect ratio of the liquid part of the cavity. When Ts is increased, it is found that oscillatory convection takes place at a higher Grashof number and with slightly higher frequency. However, varying the Stefan number Ste has small influence on the critical parameters. The critical value of Gr for the onset of the oscillation is determined by carrying out a series of time-dependant calculations.

Heat transfer analysis of thermal energy storage using phase change materials

Abstract: An analytical study is described of a freezing/melting phenomenon of a phase change material encapsulated in a pipe with the heat transfer fluid flowing in the annulus of a concentric pipe. The moving front problem is solved numerically using the boundary immobilization technique. Parameters such as the Stefan number, the Fourier number and the diameter ratio of the two concentric pipes to obtain sufficiently large heat transfer rates to make the system suitable for thermal energy storage are examined.

Modelling of dendritic solidification using finite element method

Abstract: Computer based numerical modelling of solidification is being increasingly used in an effort to develop and improve casting processes, a long term goal of this work being the prediction of microstructural features such as grain shape, size, and dendrite arm spacings throughout a casting. In a numerical heat flow model this can be achieved only through the inclusion of the kinetics of nucleation and dendrite growth. In the present paper strategies for including columnar and equiaxed solidification kinetics into a finite element model are reviewed. A detailed model for columnar solidification is then presented together with results obtained from calculations on an Al–5 wt-%Cu alloy and a multicomponent nickel based superalloy. It is shown that the inclusion of a dendrite tip undercooling is important, particularly in systems having a low Stefan number. Furthermore, the thermal histories in the superalloy can only be accurately calculated if an experimentally determined solid fraction versus temperat...

An experimental study of steam injection into a uniform water flow through porous media

Abstract: An experimental study of steam injection into a porous media was carried out in a 2-dimensional plane porous channel. The steam was injected into a uniform downward water flow in a vertically aligned porous channel. The steam-water interface was carefully observed to understand the underlying physics. Two steam injection rate bounds were found for a given water flow rate and water subcooling. The upper bound is the steam flow rate at which the steam zone grows without limit and the lower bound is the steam flow rate at which a steam zone is just initiated. The bounds were determined experimentally for a porous channel with different permeabilities and thermal conductivities. For large particle size, chaotic oscillation of steam water interface was observed. The oscillation is believed to enhance heat and momentum transfer mechanisms. The steam zone size and shape were measured to evaluate heat transfer characteristics. The average Nusselt number is presented in terms of steam and water Reynolds numbers and the Stefan number.

Freezing heat transfer in water-saturated porous media in a vertical rectangular vessel

Abstract: Numerical and experimental study is performed for the freezing of water-saturated porous media in a vertical rectangular vessel. The governing equations are solved by using a variable transformation and employing a finite difference scheme. The SOR method is utilized to solve numerically the equations. Different size and types of spherical beads are used as the porous media. The temperature of cold wall is kept at −10°C, while that of the hot wall is varied from 2°C to 22°C. Comparisons of the analytical results with the experimental ones are made. The effects of the Stefan number, the Darcy number, the modified Prandtl number and the ratio of the temperature of cold wall to the temperature of hot wall are discussed for freezing of the water-saturated porous media.

Solutions of some axisymmetric low stefan number melting problems by an improved finite differences method

Abstract: The use of explicit finite difference schemes for low Stefan number problems with moving interface was largely abandoned because they require small time intervals (large CPU time) to obtain accurate non‐oscillatory solutions. This paper uses these type of schemes for better estimations of the dynamics of the solid—liquid interface. The scheme in which time and radial intervals are constant, uses a local, continuous, time‐dependent radial coordinate to define the instantaneous location of the interface. Taylor series expansions which result in a polynomial fit are used for forward and backward interpolation of temperatures of nodal points in the vicinity of the interface. A distinction is made between the left and right position of the interface relative to the closest nodal point. The algorithm handles accurately and effectively the non‐linearities near the interface thus producing accurate stable solutions with relatively low CPU time. The scheme which obviously may be applied to large Stefan number problems, is also suitable for time dependent boundary conditions as well as temperature dependent physical properties. The results obtained by the scheme were in excellent agreement with ones derived from an approximate analytical solution which is applicable in the low Stefan number range.