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Stefan number
About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.
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TL;DR: In this paper, an approximate enthalpy model is employed for the formulation of the energy equation to present the phase-change process of the nano-PCM emulsion, and the averaged heat transfer effectiveness of water-based nano-MCM flow is considerably increased with its nano-pcM particle fraction under decreasing S t e b f ∗.
3 citations
TL;DR: In this article, the problem of the steady squeezing of a viscous fluid between a hot wall and a surface of the phase-change material is studied theoretically, and the partial differential system consisting of the Navier-Stokes equation, the energy equation and the boundary conditions is found to be reduced to an ordinary differential system depending on only one coordinate in the direction normal to the surface of hot wall.
Abstract: The problem of the thermofluid mechanics of the steady squeezing of a viscous fluid between a hot wall and a surface of the phase-change material is studied theoretically. The partial differential system consisting of the Navier-Stokes equation, the energy equation and the boundary conditions is found to be reduced to an ordinary differential system depending on only one coordinate in the direction normal to the surface of the hot wall. This ordinary differential system is solved by using the approximate and numerical methods. The problem is governed by two nondimensional parameters, that is, the Stefan number and the Prandtl number. It is found that the surface of the phase-change material melted by a flat wall with a higher temperature than the melting temperature is always left flat. The relationship between the thickness of the liquid layer, the melting rate and the force acting on the interface is obtained, as well as the distributions of the velocity, the pressure and the temperature in the liquid layer. If the inertia term in the Navier-Stokes equation is disregarded, the ordinary differential system is solved analytically. Its solution is obtained in the closed form. It is found to be very useful in many practical cases.
3 citations
TL;DR: In this paper, the two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature, assuming that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant.
Abstract: The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.
3 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.
3 citations
TL;DR: In this paper, a near-eutectic approximation with large far field temperature is considered for the case of solidification of bottom cooled binary alloy, and the magnetohydrodynamic stationary and oscillatory convective stability in the mushy layer is investigated analytically using normal mode linear stability analysis.
3 citations