The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

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Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

A review of experimental/computational studies to enhance the thermal conductivity of phase change materials (PCM) that were conducted over many decades is presented. Thermal management of electronics for aeronautics and space exploration appears to be the original intended application, with later extension to storage of thermal energy for solar thermal applications. The present review will focus on studies that concern with positioning of fixed, stationary high conductivity inserts/structures. Copper, aluminum, nickel, stainless steel and carbon fiber in various forms (fins, honeycomb, wool, brush, etc.) were generally utilized as the materials of the thermal conductivity promoters. The reviewed research studies covered a variety of PCM, operating conditions, heat exchange and thermal energy storage arrangements. The energy storage vessels included isolated thermal storage units (rectangular boxes, cylindrical and annular tubes and spheres) and containers that transferred heat to a moving fluid medium passing through it. A few studies have focused on the marked role of flow regimes that are formed due to the presence of thermally unstable fluid layers that in turn give rise to greater convective mixing and thus expedited melting of PCM. In general, it can be stated that due to utilization of fixed high conductivity inserts/structures, the conducting pathways linking the hot and cold ends must be minimized.

Thermal conductivity enhancement of phase change materials for thermal energy storage: A review ☆

A new approach to the modelling of grain structure formation in solidification processes is proposed. Based upon a two-dimensional cellular automata technique, the model includes the mechanisms of heterogeneous nucleation and of grain growth. Nucleation occurring at the mould wall as well as in the liquid metal are treated by using two distributions of nucleation sites. The location and the crystallographic orientation of the grains are chosen randomly among a large number of cells and a certain number of orientation classes, respectively. The growth kinetics of the dendrite tip and the preferential 〈100〉 growth directions of cubic metals are taken into account. The model is then applied to small specimens of uniform temperature. The columnar-to-equiaxed transition, the selection and extension of columnar grains which occur in the columnar zone and the impingement of equiaxed grains are clearly shown by this technique. The calculated effect of the alloy concentration and cooling rate upon the resultant microstructure agree with experimental observations.

Probabilistic modelling of microstructure formation in solidification processes

Nanoparticle-enhanced phase change materials (nepcm) with great potential for improved thermal energy storage

Energy storage components improve the energy efficiency of systems by reducing the mismatch between supply and demand. For this purpose, phase-change materials are particularly attractive since they provide a high-energy storage density at a constant temperature which corresponds to the phase transition temperature of the material. Nevertheless, the incorporation of phase-change materials (PCMs) in a particular application calls for an analysis that will enable the researcher to optimize performances of systems. Due to the non-linear nature of the problem, numerical analysis is generally required to obtain appropriate solutions for the thermal behavior of systems. Therefore, a large amount of research has been carried out on PCMs behavior predictions. The review will present models based on the first law and on the second law of thermodynamics. It shows selected results for several configurations, from numerous authors so as to enable one to start his/her research with an exhaustive overview of the subject. This overview stresses the need to match experimental investigations with recent numerical analyses since in recent years, models mostly rely on other models in their validation stages.

A review on phase-change materials: Mathematical modeling and simulations

The melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change. The major advantage of this technique is that it allows a fixed-grid solution of the coupled momentum and energy equations to be undertaken without resorting to variable transformations. In this work, a two-dimensional dynamic model is used and the influence of laminar natural-convection flow on the melting process is considered. Excellent agreement exists between the numerical predictions and experimental results available in the literature. The enthalpy-porosity approach has been found to converge rapidly, and is capable of producing accurate results for both the position and morphology of the melt front at different times with relatively modest computational requirements. These results may be taken to be a sound validation of this technique for modeling isothermal phase changes in metallurgical systems.

A. D. Brent

Papers

Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal

The modelling of heat, mass and solute transport in solidification systems

Modelling the mushy region in a binary alloy

Enthalpy-porosity technique for modeling convection-diffusion phase change