Showing papers on "Stefan number published in 1996"

A new oscillatory instability in a mushy layer during the solidification of binary alloys

Abstract: We consider the solidification of a binary alloy in a mushy layer and analyse the linear stability of a quiescent state with specific interest in identifying an oscillatory convective instability. We employ a near-eutectic approximation and consider the limit of large far-field temperature. These asymptotic limits allow us to examine the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of uniform permeability. We consider also the limit of large Stefan number, which incorporates a key balance necessary for the existence of the oscillatory instability. The model we consider here contains no double-diffusive effects and no region in which a statically stable density gradient exists. The mechanism underlying the oscillatory instability we discover is instead associated with a complex interaction between heat transfer, convection and solidification.

Solidification of pressure-driven flow in a finite rigid channel with application to volcanic eruptions

Abstract: Competition between conductive cooling and advective heating occurs whenever hot fluid invades a cold environment. Here the solidification of hot viscous flow driven by a fixed pressure drop through an initially planar or cylindrical channel embedded in a cold rigid solid is analysed. At early times, or far from the channel entrance, the flow starts to solidify and block the channel, thus reducing the flow rate. Close to the channel entrance, and at later times, the supply of new hot fluid starts to melt back the initial chill. Eventually, either solidification or meltback becomes dominant throughout the channel, and flow either ceases or continues until the source is exhausted. The evolution of the dimensionless system, which is characterized by the initial Peclet number Pe, the Stefan number S and the dimensionless solidification temperature Θ, is calculated numerically and by a variety of asymptotic schemes. The results show the importance of variations along the channel and caution against models based on a single 'representative' width. The critical Peclet number Pe c , which marks the boundary between eventual solidification and eventual meltback, is determined for a wide range of parameters and found to be much larger for cylindrical channels than for planar channels, owing to the slower rate of decay of the heat flux into the solid in a cylindrical geometry. For a planar channel Pe c , is given by the simple algebraic result Pe c ∼ 0.46[θ 2 /(1-Θ)(S + 2/π)] 3 when (1 - Θ) -1 >> S >> 1, but in general it requires numerical solution. Similar analyses, in which there is a spatially varying and time-dependent interaction between the rates of solidification and flow, have a range of applications to geological and industrial processes.

Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer

Abstract: The present paper presents a numerical analysis concerning thermal protection characteristics of a vertical rectangular composite cell filled with a solid-liquid phase change material (PCM) and air layer. Inside the composite cell the PCM layer is separated from air layer by a solid partition of negligible thickness. The buoyancy-induced flows developed in both the air-filled layer and the molten PCM zone inside the PCM layer were modeled as two-dimensional laminar Newtonian fluid flow adhering to the Boussinesq approximation. Meanwhile, two-dimensional conduction heat transfer was accounted for the unmelted solid PCM region. Delineation is made via a parametric simulation of the effects of the pertinent parameters:Ste (Stefan number),Sc (subcooling factor),Ra (Rayleigh number), aspect ratio of composite cell,A, and relative thickness ratioA p /A a , on the transient thermal protection performance of the composite cell. Results demonstrate that by means of the latent-heat absorption inside the PCM layer, heat penetration across the composite cell can be greatly retarded over an effective duration until a critical instant until the melting front of PCM reaches the partition wall. Such an effective thermal protection duration is found to be a strong function ofRa, Ste, A p /A a , andA. In addition, the results of the transient heat transfer rate penetrating through the composite cell are examined as a function of the pertinent parameters of the problem.

A theory of shallow smoulder waves

Abstract: A smoulder wave travelling through a porous solid slab is analysed as a small Stefan number free-boundary problem, assuming that the wave depth is small compared to its length. It is shown that the wave aspect ratio AR (= length/depth) depends on two parameters : the Peclet number ρUH/ρD, where ρ is the air density, U is the wave speed, H is the wavelength, and D is the diffusion coefficient of oxygen ; and the stoichiometric volume ratio of solid to air, which is small on account of the large solid/air density ratio. Assuming Peclet numbers near 1, it is shown that when free-stream convection is modest the aspect ratio is large. When convection is large, however, no general statement is possible, although shallow waves can occur for realistic parameter values. Wave shapes are calculated, as are the oxygen and temperature fields. For large convection velocities the results are in qualitative agreement with recent numerical simulations, and with experimental observations.

Effects of rotation on ice formation

Abstract: The objective of this paper is to investigate the role of rotation in controlling ice crystals and enhancing heat transfer during freezing. Experimental techniques were used to determine the effects of rotation on the growth rate of the ice crystals. Each experimental run was characterized by four governing parameters: the initial temperature of the liquid water, the rotation speed, the temperature of the freezing bath, and the freezing period. The results are expressed in four dimensionless groups: the Froude number, the solid-phase Stefan number, the liquid-phase Stefan number, and the Fourier number. The research provides fundamental information about the role of rotation in controlling ice crystal growth and enhancing heat transfer during freezing.

Experimental study of natural convection in the melting of PCM in horizontal cylindrical annuli

Abstract: Heat transfer characteristics, including the convective flow driven by melting of subcooled phase change material (PCM) in the horizontal annulus gap, were experimentally studied The inner cylinder was heated with a constant surface heat flux and the outer cylinder had a constant temperature. The history of the temperature field was measured with an infrared scanning system. It is shown in this paper that contribution of natural convection in the melt region becomes significant as the Stefan number increases. In recent years numerous experimental and numerical studies or analytical solutions, have been performed to explain the prinCipal mechanism of energy transfer occurring during the melting or solidification. In many of these practical cases natural convection effects, in the melted region, dominate over diffusion. Also an experimental and numerical investigation has been conducted at the Institute of Heat Engineering to study the characteristics of natural convection for the melting of n-octadecan inside a horizontal annulus gap [1-4]. Understanding and predicting the melt behavior of phase change material (PCM) is of special importance in designing cost-effective heat receivers of latent thermal energy storage (L TES). The temperature field and the solid-liquid interface boundary can be conventionally studied with the help of thermocouples. Another technique used in measurements of such kind is the application of thermochromic liquid crystals (TLC) suspended as small tracer particles. The Particle Image Thermometry (Pin is based on temperature-dependent reflectivity of TLC at visible light wavelengths [5]. Another sensor to study the solid-liquid interface is optical fiber [6]. This paper reports experimental results on the melting in a horizontal annulus gap using infrared (IR) thermography. This method has several advantages over measurements performed with usage of thermocouples, especially in experiments on natural convective melting/solidification heat transfer. Some advantages of IR thermography are: it is a non-intrusive measurement of temperature in the whole test cell (not only in the chosen points), it leads to simultaneous measurements of temperature and progress of the liquid-solid interface, it avoids disturbance of the heat flow caused by the presence of the numerous thermocouples.

Contact melting process on an arbitrary shape wall coated by porous layer

Abstract: This paper presents a theoretical study of direct contact melting process in a capsule with an arbitrary two-dimensional heating wall One of the important applications of this system is that of thermal energy storage systems Latent heat energy is used in this system effectively The phase change material (PCM) is stored in a small capsule The heating wall shape of the capsule in this system is not simple Sometimes it is complicated In recent research, this process was only solved for several limited simple wall shapes Governing equations were solved using approximated methods or numerical methods In this paper, the authors analytically solve governing equations systems with heat convection terms It is shown that the governing equations systems can be transformed into ordinary differential equations systems by a similarity transformation It is also shown that there exists an exact solution that is obtained without using any approximate method This solution is valid for the whole range of Stefan number