Stefan number

About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.

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.

Thermal characteristics in latent heat energy storage system using paraffin wax

Abstract: An energy storage system has been designed to study the heat transfer characteristics of paraffin wax during melting and solidification processes in a vertical annulus energy storage system. In the experimental study, three important issues are focussed. The first one is temperature distribution in the phase change material (PCM) during the phase change processes. The second one is the thermal characteristics of the paraffin wax, which includes total melting and total solidification times, the nature of heat transfer phenomena in melted and solidified PCM and the effect of Reynolds number as inlet heat transfer fluid (HTF) conditions on the heat transfer parameters. The final one is to calculate heat transfer coefficient and effectiveness during solidification process. The experimental results proved that the PCM melts and solidifies congruently, and the melting front moved from top to the bottom of the PCM container whereas the solidification front moved from bottom to the top along the axial distances in the PCM. Experiment has been performed for different water flow rates at constant inlet temperature of heat transfer fluid for recovery and use of heat. Heat transfer characteristics are studied and the dimensionless phase transition time is related to Stefan number by a simple correlation.

Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat

Abstract: The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), a modified heat balance integral method, the refined integral method (RIM) . Taking advantage of the exact analytical solutions we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalized Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimizing the least-squares error, obtaining also approximate solutions for the classical Stefan problem.

Modeling of Freezing Phenomena Induced by Chemical Reactions

Abstract: Spatial variations in the concentration of a reactive solute in solution are often encountered in a catalyst particle, and this leads to variation in the freezing point of the solution. Depending on the operating temperature, this can result in freezing of the solvent oil a portion of catalyst, rendering that part of the active area ineffective Freezing call occur by formation of a sharp front or it mush that separates the solid and fluid phases. In this paper, we model the extent of reduction in the active area due to freezing. Assuming that the freezing point decreases linearly with solute concentration, conditions for freezing to occur have been derived. At steady state, the ineffective fraction of catalyst pellet is found to be the same irrespective of the mode of freezing. Progress of freezing is determined by both the heat of reaction and the latent heat of fusion Unlike in freezing of alloys where the latter plays a dominant role, the exothermicity of the reaction has a significant effect on freezing in the presence of chemical reactions. A dimensionless group analogous to the Stefan number could be defined to capture the combined effect of both of these.