Showing papers on "Stefan number published in 2003"
TL;DR: In this paper, the authors present an original systematic experimental investigation of the transient transport phenomena occurring during the pile-up of molten, picoliter-size liquid metal droplets.
61 citations
TL;DR: In this paper, the problem of the inward solidification of a two-dimensional region of fluid is considered, and the resulting one-phase Stefan problem is reformulated using the Baiocchi transform and examined using matched asymptotic expansions under the assumption that the Stefan number is large.
Abstract: The problem of the inward solidification of a two-dimensional region of fluid is considered, it being assumed that the liquid is initially at its fusion temperature and that heat flows by conduction only. The resulting one-phase Stefan problem is reformulated using the Baiocchi transform and is examined using matched asymptotic expansions under the assumption that the Stefan number is large. Analysis on the first time-scale reveals that the liquid-solid free boundary becomes elliptic in shape at times just before complete freezing. However, as with the radially symmetric case considered previously, this analysis leads to an unphysical singularity in the final temperature distribution. A second time-scale therefore needs to be considered, and it is shown that the free boundary retains its shape until another non-uniformity is formed. Finally, a third (exponentially short) time-scale, which also describes the generic extinction behaviour for all Stefan numbers, is needed to resolve the non-uniformity. By matching between the last two time-scales we are able to determine a uniformly valid description of the temperature field and the location of the free boundary at times just before extinction. Recipes for computing the time it takes to completely freeze the body and the location at which the final freezing occurs are also derived.
27 citations
TL;DR: In this paper, the behavior of the one-phase Stefan problem with nonlinear kinetic undercooling is studied and a method similar to the Boltzmann-Matano method for determining nonlinear diffusivities is described.
Abstract: The behaviour of the one-phase Stefan problem with nonlinear kinetic undercooling is studied. This system is physically relevant in a number of contexts, in particular as the sharp-interface (fast-reaction) limit of a variety of reaction-diffusion systems. The similarities and differences with the linear kinetic condition (studied by Evans and King) are highlighted for both one- and two-dimensional problems. Asymptotic results (both in time and in the Stefan number) are obtained for the power-law form of the kinetic condition. Significantly, the one-dimensional growth behaviour of the moving boundary is seen to be relatively insensitive to the precise form of the nonlinear kinetic condition, and this in effect has hindered its experimental determination in applications such as silicon oxidation. By contrast, the two-dimensional development of the moving boundary around a mask edge depends strongly on the form of the kinetic condition and consequently a method, similar to the Boltzmann-Matano method for determining nonlinear diffusivities, is described to determine the kinetic undercooling relation from experiment
21 citations
TL;DR: In this article, the role of convection and inertia on close contact melting of a phase change material (PCM) resting on a sliding heated plate was examined. And it was shown that inertia has no effect on contact melting regardless of the magnitude of the melt layer Reynolds number.
15 citations
TL;DR: In this paper, a generalized model has been developed to approximate the rate of ice crystal growth in a laminar developing falling film, and the results of the numerical simulations were analyzed based on the combined effects of the Reynolds (flow rate) and Stefan numbers on the ice crystal concentrations and the associated heat transfer parameters.
12 citations
TL;DR: In this article, the linear stability theory is used to investigate analytically the Coriolis effect on convection in a rotating mushy layer for a new formulation of the Darcy equation.
Abstract: The Coriolis effect on a solidifying mushy layer is considered. A near-eutectic approximation and large far-field temperature is employed in the current study for large Stefan numbers. The linear stability theory is used to investigate analytically the Coriolis effect on convection in a rotating mushy layer for a new formulation of the Darcy equation. It was found that a large Stefan number scaling allows for the presence of both the stationary and oscillatory modes of convection. In contrast to the problem of a stationary mushy layer, rotating the mushy layer has a stabilising effect on convection. It was observed that increasing the Taylor number or the Stefan number encouraged the oscillatory mode of convection.
11 citations
TL;DR: In this paper, the authors considered convective melting of a spherical particle and provided an understanding of how both subcooling and convection of heat and mass affect the melting process.
6 citations
TL;DR: In this paper, the authors proposed that the one-dimensional rapid freezing in the splat is governed by nonequilibrium kinetics at the solidification front while the melting in the substrate is determined from the traditional phase change condition.
6 citations
TL;DR: In this paper, an integral model in non-dimensional form is developed for freezing and melting of the melt material onto the surface of the additive that resembles a plate, which provides the governing equations coupled and nonlinear and indicates the dependence of this phenomenon on independent parameters-preheat temperatures, Stefan number St, the Biot number B"i, the property ratio B, and the bath temperature @q"a.
6 citations
01 Jan 2003
TL;DR: In this paper, the effects of porosity, Stefan number, and subcooling on the surface temperature and solid-liquid interface were investigated for three-dimensional selective laser sintering (SLS) process.
Abstract: Melting of a subcooled powder bed with the finite thickness that contains a mixture of two metal powders with significantly different melting points is investigated analytically. Shrinkage induced by melting is taken into account in the physical model. The temperature distributions in the liquid and solid phases were obtained using an exact solution and an integral approximate solution, respectively. The effects of porosity, Stefan number, and subcooling on the surface temperature and solid-liquid interface are also investigated. The present work built solid foundation to investigate the complex three-dimensional selective laser sintering (SLS) process.Copyright © 2003 by ASME
4 citations
TL;DR: In this article, the steady state convection amplitude for solutal convection occurring during the solidification of a rotating mushy layer in a binary alloy system for a new Darcy equation formulation was investigated.
Abstract: We investigate the steady state convection amplitude for solutal convection occurring during the solidification of a rotating mushy layer in a binary alloy system for a new Darcy equation formulation. We adopt a large far field temperature and assume that the initial composition is very close to the eutectic composition. The linear stability analysis showed that rotation stabilised solutal convection. The results of the weak non-linear analysis of stationary convection indicates the presence of Hopf bifurcation, associated with the oscillatory mode, developing at Ta = 3.