Correlations for Melting Time and Melt Fraction for Bottom Charged Tube in Tube Phase Change Material Heat Exchanger

Multiple factors govern the Thermo-hydraulic behaviour of Latent heat storage devices. The correlation among these factors varies from case to case. In this work, a concentric tube in tube latent heat storage system is numerically modelled for the bottom charging case. Fixed grid enthalpy porosity approach is adopted to account for phase change. The numerical model’s independence is achieved by testing mesh size, time step, and maximum iterations per time step. The computational approach is validated against the experimental data. Non-dimensional parameters viz Rayleigh Number (3.04x105 to 65.75 x105), Stefan Number (0.2 to 1), Reynolds Number (600 to 3000), and L/D ratio (2 to 15) are varied in the respective ranges mentioned in parenthesis. Stefan number is found to have a major influence on the Melt Fraction and Melting time, compared to Rayleigh Number and Reynolds Number. Correlations are presented for quantifying the melt fraction and dimensionless melting time.

Heat capacity of dispersed rocks

Protection of automobile roads from negative cryogenic processes is a current issue to which significant attention is devoted in both scientific and engineering communities. In many cases important for practice, the the thermal factor determines the reliability and security of the use of the road in the cryolithic zone. The heat capacity of dispersed rocks is among the most important indicators of the physical properties determining the intensity of thermal processes in the road surfaces and road foundations. The precision of determination of the total heat capacity of the rocks in thawed and frozen state largely determines the precision of the forecast of the thermal regime of roads in the cryolithic zone. A complex assessment of the impact of ice content of the dispersed rocks on the value of total heat capacity was done. 2D and 3D charts which allow to assess the possible range of change in the heat capacity of the dispersed rocks in thawed and frozen state, in both a wide range and in the typical range of values, were produced. Among the main criteria determining the extent of the seasonal freezing and thawing of the soils of the active layer is the Stefan number, a dimensionless criterion. An overall assessment of the impact of ice content on the ground (rock) foundations of the roads and of the air temperature in the warm period of the year on the quantitative values of the Stefan number was done. Charts allowing to determine in both a wide and typical range the changes of values of the Stefan numbers, permitting to assess the possible range of changes of the Stefan number, were made. It was determined, in particular, that for the typical dispersed rocks of the road foundations in the cryolithic zone the range of change in the Stefan numbers is 2.1-6.5.

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

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 < < 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.

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

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.

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

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.

Analytical Modeling of Outward Solidification With Convective Boundary in Cylindrical Coordinates

Solidification consists of three stages at macroscale: subcooling, freezing and cooling. Classical two-phase Stefan problems describe freezing (or melting) phenomenon initially not at the fusion temperature. Since these problems only define subcooling and freezing stages, an extension to characterize the cooling stage is required to complete solidification. However, the moving boundary in solid-liquid interface is highly nonlinear, and thus exact solution is restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, like a small Stefan number. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder. By assuming a small Stefan number, three temporal regimes and four spatial layers are considered in the asymptotic analysis. The results are compared with numerical method. Further, effects of Biot numbers are also investigated regarding interface motion and temperature profile.

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

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), the modified HBIM and 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 generalised 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 minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem.

Melting process modeling of Carreau non-Newtonian phase- change material in dual porous vertical concentric cylinders

In this paper a numerical simulation of the melting process of Carreau non- Newtonian phase-change material (PCM) inside two porous vertical concentric cylinders included constant temperatures of the inner and outer walls, represented by Th and Tc respectively. Half of the void between the two pipes is filled with copper porous media and paraffin wax as a phase change material. The governing equations are converted into a dimentionless form and are solved using the finite element method. The enthalpy- porosity theory is applied to simulate the phase change of PCM while the porous media follow to the Darcy law. Outcomes are shown and compared in terms of the streamline, isotherm, melting fraction and mean Nusselt numbers. The solid- liquid interface location and the temperature distribution are predicted to describe the melting process. The effects of the Carreau index, porosity and non-dimensional parameters such as Stefan number, Darcy number and Rayleigh number are analyzed. Our results indicate a good agreement between this study and the previous investigations. The results show that an increase in Rayleigh number, Stefan number and Darcy number increases the melting volume fraction and reduces the melting time. Also, the time of melting non-Newtonian phase change material decreases when Carreau index and porosity decrease.