Showing papers on "Stefan number published in 2021"

Thermal Analysis of Solid/Liquid Phase Change in a Cavity with One Wall at Periodic Temperature

Abstract: In this study, heat transfer in a square cavity filled with a Phase Change Material (PCM) under a sinusoidal wall temperature during solidification and melting is analyzed. All surfaces of the cavity are insulated except one surface, which is under the sinusoidal temperature change. The governing equations and boundary conditions are made dimensionless to reduce the number of governing parameters into two as dimensionless frequency and Stefan number. The governing equations were solved numerically by using Finite Volume Method for a wide range of Stefan number (0.1 < Ste < 1.0) and dimensionless frequency (0.23 < ω* < 2.04). Based on the obtained results, a chart in terms of Stefan number and dimensionless frequency is obtained to divide the heat transfer process in the cavity into three regions as uncompleted, completed, and overheated phase-change processes. For the uncompleted process, some parts of the cavity are inactive, and no phase change occurs in those parts of the cavity during the melting and freezing process. For the overheated phase change, the temperature of the cavity highly increases (or decreases), causing the sensible heat storage to compete with latent thermal storage. In the completed process, almost all thermal storage is done by the utilization of latent heat. The suggested graph helps thermal designers to avoid wrong designs and predict the type of thermal storage (sensible or latent) in the cavity without doing any computations.

Evolution of solid–liquid interface in bottom heated cavity for low Prandtl number using lattice Boltzmann method

Abstract: The influence of natural convection cells on heat transfer and the evolution of melt interface is studied for low Prandtl number fluid (Pr = 0.025) in phase-change Rayleigh–Benard convection using the lattice Boltzmann method. The thermal lattice Boltzmann model is used to evaluate the effect of Rayleigh number (Ra = 6708, 11 708, and 21 708) and cavity aspect ratio (γ = 0.062 5, 0.125, 0.25, 0.5, and 1) on the onset of convection, number of convection cells, and Nusselt number in the classical Rayleigh–Benard convection. The modified equilibrium distribution function-based thermal lattice Boltzmann model is applied to evaluate the effect of Stefan number (Ste = 0.025, 0.05, and 0.1) in the phase change Rayleigh–Benard convection. Distinct flow configurations depend on the Rayleigh number, aspect ratio, and Stefan number. The number of convection cells follows an inverse relation with the aspect ratio. Nusselt number increases with decreasing cavity aspect ratio and increasing Rayleigh number in the classical Rayleigh–Benard convection. With the variation in the aspect ratio based on the melt layer height during melting of phase change material, the number of convection cells changes resulting in the change in the evolution of the melt interface and convective heat transfer. Melting in a cavity of aspect ratio less than 0.5, the evolution of melt interface remains symmetrical. For an aspect ratio greater than 0.5, the interface evolution becomes unsymmetrical depending on the transition to single convection cell-dominated heat transfer.

A Comparative Study on the Performance of Single and Multi-Layer Encapsulated Phase Change Material Packed-Bed Thermocline Tanks

Abstract: This paper presents a numerical study that aims at investigating the effects of different parameters on the dynamic performance of single and multi-layer encapsulated phase material (PCM) thermocline tanks. A transient, one-dimensional, two-phase, concentric-dispersion model is formulated to evaluate such performance. Encapsulated paraffin waxes having different melting-points are used as PCMs, with water as heat transfer fluid. Comprehensive comparisons between single-PCM and multiple-PCMs systems are numerically analyzed first. Second, the effects of the PCM volume fraction (VF) and the inverse Stefan number have been discussed. The results show that among the various cases the single-PCM70 system has the highest performance in terms of charging and discharging efficiency, followed by a multiple-PCMs system with average performance. Compared with the PCM40 case, the PCM70 case has a 29% increase in the output energy from the system. The VF of PCMs influences the system output, both in terms of energy storage and release, the heat storage period and the total energy stored increased by 4.5%, when the VF of the PCM70 increases from 33.33% to 50%, respectively. Furthermore, it increases the system’s overall efficiency and total utilization ratio by 13.7% and 25%, respectively, when compared to the arrangement in which the PCM40 occupies 50% of the total bed height. The effect of the inverse Stefan number has a significant impact on the system’s utilization ratio. Compared with all other 3-PCM systems, the scenario with the lowest inverse Stefan number in the middle PCM has the highest charging and discharging efficiencies of 83.9% and 80.8%, respectively. The findings may be beneficial for the design and optimization of packed-bed tanks.

Heat Transfer by Natural Convection in a Square Enclosure Containing PCM Suspensions

Abstract: Research on using phase change material (PCM) suspension to improve the heat transfer and energy storage capabilities of thermal systems is booming; however, there are limited studies on the application of PCM suspension in transient natural convection. In this paper, the implicit finite difference method was used to numerically investigate the transient and steady-state natural convection heat transfer in a square enclosure containing a PCM suspension. The following parameters were included in the simulation: aspect ratio of the physical model = 1, ratio of the buoyancies caused by temperature and concentration gradients = 1, Raleigh number (RaT) = 103–105, Stefan number (Ste) = 0.005–0.1, subcooling factor (Sb) = 0–1.0, and initial mass fraction (or concentration) of PCM particles (ci) = 0–0.1. The results showed that the use of a PCM suspension can effectively enhance heat transfer by natural convection. For example, when RaT = 103, Ste = 0.01, ci = 0.1, and Sb = 1, the steady-state natural convection heat transfer rate inside the square enclosure can be improved by 70% compared with that of pure water. With increasing Sb, the Nusselt number can change nonlinearly, resulting in a local optimal value.

Latent Heat Phase Change Heat Transfer of a Nanoliquid with Nano–Encapsulated Phase Change Materials in a Wavy-Wall Enclosure with an Active Rotating Cylinder

Abstract: A Nano-Encapsulated Phase-Change Material (NEPCM) suspension is made of nanoparticles containing a Phase Change Material in their core and dispersed in a fluid. These particles can contribute to thermal energy storage and heat transfer by their latent heat of phase change as moving with the host fluid. Thus, such novel nanoliquids are promising for applications in waste heat recovery and thermal energy storage systems. In the present research, the mixed convection of NEPCM suspensions was addressed in a wavy wall cavity containing a rotating solid cylinder. As the nanoparticles move with the liquid, they undergo a phase change and transfer the latent heat. The phase change of nanoparticles was considered as temperature-dependent heat capacity. The governing equations of mass, momentum, and energy conservation were presented as partial differential equations. Then, the governing equations were converted to a non-dimensional form to generalize the solution, and solved by the finite element method. The influence of control parameters such as volume concentration of nanoparticles, fusion temperature of nanoparticles, Stefan number, wall undulations number, and as well as the cylinder size, angular rotation, and thermal conductivities was addressed on the heat transfer in the enclosure. The wall undulation number induces a remarkable change in the Nusselt number. There are optimum fusion temperatures for nanoparticles, which could maximize the heat transfer rate. The increase of the latent heat of nanoparticles (a decline of Stefan number) boosts the heat transfer advantage of employing the phase change particles.

Numerical investigation of the melting process in a half horizontal cylinder with radial fins

Abstract: In the present study, the melting phenomenon in a half horizontal cylinder cavity with rectangular heat sources is investigated using numerical lattice Boltzmann method. The cylinder is modeled two dimensionally and its boundaries are insulated. Also, the high temperature rectangular heat sources with constant area are located in radial position on cavity. The enthalpy-based lattice Boltzmann method is used for simulating the phase change problem in the cavity. Melting of lead with Stefan number of 0.86 and Prandtl number of 0.0236 is simulated in the cavity. The effects of pertinent parameters such as the aspect ratio of the fins 1, 2.5 ,5, 7.5 , the Rayleigh number 103,104,105 and the angular position of the heat sources 0,15,45 are studied on the melting phenomenon. The results show that increasing the aspect ratio of the fin with constant area reduces the melting time and increases the liquid fraction at the same time. Also higher value of the Rayleigh number improves the natural convection effect and raises the rate of melting. Finally, it is observed that the highest rate of melting is obtained when two fins are positioned at 45 degrees with aspect ratio of 7.5 at Rayleigh number of 105.

Natural convection heat transfer in PCM suspensions in a square enclosure with bottom heating and top cooling

Abstract: Research on the use of phase change material (PCM) suspensions to improve the natural convection efficiency of thermal systems is booming; however, there are few studies on the transient behavior of PCM suspensions. In this study, numerical simulations were used to investigate transient and steady-state natural convection in a square enclosure containing a PCM suspension. The implicit finite-difference method was adopted. The left and right walls of the enclosure were adiabatic sections, the bottom was an isothermal heating, and the top was an isothermal cooling. The following parameters were considered: PCM = n-octadecane (C18H38), enclosure aspect ratio = 1, buoyancy ratio for mass-to-heat transfer = 1, Rayleigh number ( R a T ) = 103–104, Stefan number (Ste) = 0.005–0.05, subcooling factor (Sb) = 0–10, and initial mass fraction ( c m , i ) = 0–20%. The results show that all the parameters ( R a T , Ste, Sb, and c m , i ) affect the flow pattern, and convection oscillations occur at Sb = 0.5–1. The heat transfer rate increases with R a T . Both c m , i and Sb affect the heat transfer rate but in a case-specific manner, and no well-defined correlations are observed.

Melting driven by rotating Rayleigh–Bénard convection

Abstract: We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order , convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry – periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary, thereby controlling its morphology characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.