Showing papers on "Stefan number published in 2008"

Classical two-phase Stefan problem for spheres

Abstract: The classical Stefan problem for freezing (or melting) a sphere is usually treated by assuming that the sphere is initially at the fusion temperature, so that heat flows in one phase only. Even in this idealized case there is no (known) exact solution, and the only way to obtain meaningful results is through numerical or approximate means. In this study, the full two-phase problem is considered, and in particular, attention is given to the large Stefan number limit. By applying the method of matched asymptotic expansions, the temperature in both the phases is shown to depend algebraically on the inverse Stefan number on the first time scale, but at later times the two phases essentially decouple, with the inner core contributing only exponentially small terms to the location of the solid–melt interface. This analysis is complemented by applying a small-time perturbation scheme and by presenting numerical results calculated using an enthalpy method. The limits of zero Stefan number and slow diffusion in the inner core are also noted.

A model for flash weakening by asperity melting during high-speed earthquake slip

Abstract: [1] Recent results from laboratory experiments on a broad range of mineral systems exhibit dramatic drops in the effective friction coefficient μ once the slip rate exceeds a critical level Vw, which is typically O(01) m/s This “flash weakening” has been attributed to the effects of localized heating at highly stressed microscopic asperities We extend previous phenomenological treatments to assess whether melting at asperity contacts can explain the observed changes in strength Using physical parameters obtained from the literature on the phase behavior and mechanical properties of quartz, albite, dolomite, gabbro, Westerly granite, and serpentinite, the predictions of our simplified model are in reasonable agreement with available experimental data We derive approximate analytical expressions that suggest that strength changes are insensitive to the melt viscosity under conditions that likely include those during earthquake slip along major fault systems Instead, the primary controls on μ are the ratio of slip rate V to Vw and the Stefan number S, which is defined as the ratio of the latent heat of fusion to the sensible heat required to raise the temperature from ambient levels The phase behavior during the short lifetimes and at the high confining pressures of asperity contacts is a significant source of uncertainty in the parameter choices, as are the presence and availability of water Nevertheless, our results are encouraging for further efforts to incorporate the microphysics of fault zone processes into earthquake simulations

Unified Formulation for Contact Melting Inside Symmetric Enclosure

Abstract: The contact melting progress of phase-change material inside the symmetric enclosure with a continuous boundary is generally studied, and a unified treatment for the heat transfer is proposed. The mathematical expressions of the dimensionless film thickness, melting rate, dimensionless time to complete melting, and Nusselt number for the contact melting processes are derived generally, which can be used for the analysis of the contact melting inside different geometric enclosures. By applying the expressions to the analysis of contact melting inside the cylindrical and elliptical tubes, as well as the spherical capsule, the concrete methods and steps are given. It is found that some major results in the published literature are easily deduced and unified in this paper.

Mathematical modelling of nanoparticle melting or freezing

Abstract: This thesis presents a mathematical modelling in nanotechnology. Many experiments and molecular dynamics simulations demonstrate that the melting point of nanoparticles shows a size-dependent characteristic in the nanoscale. Based on the assumption that the material is a pure one, the melting process of spherical and cylindrical particles, especially nanoparticles, is treated as a Stefan moving boundary problem. Analytical or semi-analytical approaches, such as small-time perturbation expansions with front-fixing techniques, large Stefan number limit, integral iterative scheme, and numerical methods, such as enthalpy scheme and front-fixing method, are applied to the oneand or twophase Stefan problem in spherical and cylindrical domains by taking into account the effect of the interfacial or surface tension. The results from these methods are compared and show excellent agreement to some extent. This thesis may provide a possibility of explaining some interesting phenomena occurring in the physical experiments, i.e. superheating and “abrupt melting”, or work as a guide for the potential applications of nanoparticles, for example, drug delivery, nanoimprinting and targeted ablation of tumor cells In Chapter 1, a simply survey of the research background is given. Chapter 2 studies the full classical two-phase Stefan problems without surface or interfacial tension. By using the approach from large Stefan number limit and small-time perturbation methods, longand short-time solutions are obtained, and the results from these methods are compared with the numerical enthalpy scheme. The limits of zero Stefan-number and slow diffusion in the inner core are also noted. Chapter 3 presents the melting of a spherical or cylindrical nanoparticle by including the effects of surface tension through the Gibbs-Thomson condition. A single-phase melting limit is derived from the general two-phase formulation, and the resulting equations are studied analytically in the limit of small time and large Stefan number. Further analytical approximations for the temperature distribution and the position of the solid-melt interface are found by applying an integral formulation together with an iterative scheme. All these analytical results are compared with numerical solutions obtained using a numerical front-fixing method, and they are shown to provide good approximations in various regimes. In Chapters 4 and 5, the methods used in above sections are extended to the melting problem for spherical and cylindrical

Growth characteristics of ice layer in pipe when low temperature surface water freezing at laminar condition

Abstract: In order to develop the environmental friendly renewable energy sources, such as surface water, and give a solution to the conventional surface water source heat pump system on its economic and the technical difficulties in the cold region, this paper brings forward a new heat pump system with latent heat collection in which the heat collection device is a key equipment. So the freezing characteristics need to be grasped in the tube of the device. The problem of inner-water freezing in laminar flow at the constant wall temperature was analyzed based on approximate methods, and the freezing characteristics of the growth of ice layer in different parameters were simulated. The results show that the sensible heat is neglectable at small Stefan number, and the quasi-steady state method can be used in the proximate analysis of freezing, and it is controlled by the surface heat convection parameter between the water and the ice layer. Effects of a certain parameter on the ice growth are not obvious in the initial period, while increase gradually. The approximate results is important for the design of the device, and this technology can be applied in the urban sewage source heat pump system of insufficient sewage flux.

Simulation of a single melting solid particle rising in a fluid

Abstract: This work is intended to predict the behavior of a single melting particle rising in a fluid. A twophase numerical simulation approach based on the 1-Fluid method is adopted. The present approach considers the solid particle as a rigid body immersed in a Newtonian liquid. The incompressibility constraint is enforced locally in the solid and liquid. Preliminary simulations are carried out in two dimensions. Numerical validations have been carried out by comparison with the DNS results of Gan et al. (2003a). Numerical simulations of melting particles are presented for various values of Grashof (Gr) and Reynolds numbers. Results of the present model show good agreement with literature data at short times. Results for longer times exhibit significant deviations due to discretization in space. However, the qualitative behavior is very similar. The impact of heat transfer on particle motion is investigated for a cylindrical body moving in a warmer fluid characterized by a lower density than the particle. The dynamic and thermal features of the flow are shown to be largely dependent on the value of Stefan number (Ste). The present method is shown to have a very good potential in simulating complex flows of melting particles with low computational cost.

Temperature Range and Conjugate Effects in Microencapsulated Phase-Change Suspensions

Abstract: The melting process of some phase-change materials does not occur at a single temperature, but rather occurs over a temperature range. The effect of a phase-change temperature range for microencapsulated phase-change-material slurry was investigated numerically for a hydrodynamically fully developed laminar flow in a circular tube with a constant wall heat flux. The wall temperature and exit radial temperature were investigated for several phase-change temperature ranges, including a single phase-change temperature. The dominant dimensionless parameters: Stefan number, melt temperature range, and subcooling were varied and results presented. For code verification, results were compared with previous experimental and numerical data using eicosane as the phase-change material. Using heat flow measurements over the melt region from current literature, a curve fit for eicosane was made and used in the numerical model. The numerical results compared well with existing experimental and numerical findings and showed the phase-change region was the cause of temperature discrepancies cited in previous numerical work.