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The purpose of this study is to analyze heat transfer for solid–liquid phase change in two inclined cavities assisted with open cell and closed cell porous structures for enhancement of heat transfer and compare them.

The heat transfer analysis is done numerically. The set of conservation equations for mass, momentum and energy for phase change material (PCM) and conduction heat transfer equation for metal frame are solved. Furthermore, temperature and solid–liquid fraction distributions for a cavity filled only with PCM are also obtained for comparison. The porosity is 0.9 for both porous structures. Rayleigh number and inclination angle change from 1 to 10⁸, and from −90° to 90°, respectively.

The present study reveals that the use of closed cell structures not only can make phase change faster than open cell structure (except for Ra = 10⁸ and = 90°) but also provide more stable process. The use of a closed cell porous structure in a cavity with PCM can reduce melting period up to 55% more than a cavity with an open cell porous structure. The rate of this additional enhancement depends on Rayleigh number and inclination angle.

To the best of the authors’ knowledge, this is the first time that the comparison between closed cell and open cell porous structures for heat transfer enhancement in a solid/liquid phase change process is reported. Authors believe that the present study will lead more attentions on the use of closed cell porous structures.

This paper aims to investigate laminar boundary layer flow and heat transfer from a warm laminar Casson liquid to a melting sheet moving parallel to a melting stream. The governing equations, i.e. continuity, momentum and heat transfer, are coupled non-linear partial differential equations. These equations are reduced to non-linear ordinary differential equations by means of similarity transformations, converted into first-order differential equations, and are solved numerically using the Runge–Kutta–Felhberg method with an efficient shooting technique. The velocity and temperature profiles are plotted for various values of the governing parameters, such as the moving parameter, Prandlt number, melting parameter and Casson parameter. It is found that the problem admits multiple solutions. The results of this study are validated by comparing them with the earlier published studies’ results. Thus, a good agreement is obtained.

This study carries out numerical solution of melting heat transfer analysis.

The findings of this study show the analysis of flow and melting heat transfer characteristics.

In this study, analysis of dual solution is carried out.

In this paper, the melting heat transfer analysis on Blasius flow of a Casson fluid is taken into consideration. To the best of the author’s knowledge, no investigations have been reported on this topic.

This paper aims to investigate melting heat transfer of a non-Newtonian phase change material (PCM) in a cylindrical enclosure-space between two tubes using a deformed mesh method.

Metal foam porous layers support the inner and outer walls of the enclosure. The porous layers and clear space of the enclosure are filled with PCM. The natural convection effects during the phase change are taken into account, and the governing equations for the molten region and solid region of the enclosure are introduced. The governing equations are transformed into non-dimensional form and then solved using finite element method. The results are compared with the literary works and found in good agreement. The non-Newtonian effects on the phase change heat transfer and melting front are studied.

The results show that the increase of non-Newtonian effects (the decrease of the power-law index) enhances the heat melting process in the cavity at the moderate times of phase change heat transfer. The temperature gradients in porous metal foam over the hot wall are small, and hence, the porous layer notably increases the melting rate. When the melting front reaches the cold porous layer, strong non-linear behaviors of the melting front can be observed.

The phase change heat transfer of non-Newtonian fluid in a cylindrical enclosure partially filled with metal foams is addressed for the first time.

The purpose of this study is to examine the melting heat transfer of magnetohydrodynamics Casson nanofluid flow with viscous dissipation, radiation, and complete slip effects on a porous stretching sheet. Since, the study of melting heat transfer has mesmerized the attention of scientists and engineers in the sense of its enormous uses in industrial processes, solidification, casting, and technology.

Bejan number and entropy are analyzed. Exploration of irreversibility is modeled using the thermodynamics second law. There is a discussion on thermophoresis and Brownian diffusion along with first-order chemical reactions. Adequate transformations are introduced to convert the controlling partial differential equations to ordinary differential equations. The three-phase Lobatto solvers (bvp5c) are used to obtain numerical solutions of the transmitted equations.

The effects of various factors on temperature, velocity, concentration, Bejan number and entropy rate are shown graphically. The velocity field is enhanced by increasing the melting heat parameter, and it declines for growing magnetic parameters. Temperature is decreased for increasing parametric values of melting heat, porous and Casson parameters. A 7% decrease in the Sherwood distribution is seen when we increase the Brownian motion parameter from 0.1 to 0.2. Similarly, an 11% decrement is found in the Nusselt distribution for increasing the Brinkman number from 0.5 to 1.

Entropy and Bejan number experience dual tendencies whenever the melting heat parameter increases. Nusselt number and skin friction experience the opposite behavior for the increasing values of melting parameter. Sherwood number decreases for the increasing values of melting parameter. The velocity profile is directly related to the melting parameter and inversely related to porous and magnetic parameters. Thermophoresis and Brinkman parameters boost the temperature profile and it is controlled by melting and porous parameters. Some notable fields where the present study is used inevitably are silicon wafering, geothermal energy recovery and semiconductor manufacturing.

Phase change energy storage is an important solution for overcoming human energy crisis. This study aims to present an evaluation for the thermal performances of a phase change material (PCM) and a PCM–metal foam composite. Effects of pore size, pore density, thermal conductivity of solid structure and mushy region on the thermal storage process are examined.

In this paper, temperature, flow field and solid–liquid interface of a PCM with or without porous media were theoretically assessed. The influences of basic parameters on the melting process were analyzed. A PCM thermal storage device with a metal foam composite is designed and a thermodynamic analysis for it is conducted. The optimal PCM temperature and the optimal HTF temperature in the metal foam-enhanced thermal storage device are derived.

The results show that the solid–liquid interface of pure PCM is a line area and that of the mixture PCM is a mushy area. The natural convection in the melting liquid is intensive for a PCM without porous medium. The porous medium weakens the natural convection and makes the temperature field, flow field and solid–liquid interface distribution more homogeneous. The metal foam can greatly improve the heat storage rate of a PCM.

Thermal storage rate of a PCM is compared with that of a PCM–metal foam composite. A thermal analysis is performed on the multi-layered parallel-plate thermal storage device with a PCM embedded in a highly conductive porous medium, and an optimal melting temperature is obtained with the exergy optimization. The heat transfer enhancement with metal foams proved to be necessary for the thermal storage application.

The purpose of this paper is to study thermal performance of metal foam/phase change materials composite under the influence of the enclosure aspect ratios (ratio of enclosure height: length). In this study, a compound metal foam/phase change material (PCM), which has been proved to be one of the most promising approaches for thermal conductivity promotion on PCMs, was used.

The PCM is considered initially at its melting temperature. The enclosure for all the cases has a constant volume with various aspect ratios. The left side of the enclosure is suddenly exposed to a thermal source having a constant heat flux, while the other three surfaces are kept thermally insulated. A two-dimensional numerical model considering the non-equilibrium thermal factor, non-Darcy effect and local natural convection was proposed. The coupling between velocity and pressure is solved using the SIMPLEC, and the Rhie and Chow interpolation is used to avoid the checker-board solutions for the pressure.

The effects of foam porosity and aspect ratio of the enclosure on the PCM’s melting time were investigated. The results indicated that enclosure aspect ratio plays a fundamental role in phase change of copper foam/PCM composites. For higher porosities, enclosures with bigger aspect ratios proved to led to optimal melting time. Besides, the best enclosure aspect ratio and foam porosity for a fixed-volume enclosure to have the shortest melting time are 2.1 and 91.66 per cent, respectively. However, for a specific amount of PCM inside a variable volume enclosure, the optimal melting time was for foam with ε = 95 per cent. The achieved results prove the great importance of selection of aspect ratio to benefit both conduction and convection heat transfer simultaneously.

The area of energy storage systems is original.

This study aims to evaluate the melting process of the phase-change RT-35 material in a shell and tube heat exchanger saturated with a porous medium. Titanium porous media with isotropic and inhomogeneous structures are studied. The considered tubes in the shell and tube exchanger are made of copper with specific thicknesses. The phase-change material has a non-Newtonian behavior and follows the endorsed Carreau–Yasuda Model.

The enthalpy–porosity method is used for modeling of the melting process. The governing equations were transferred to their dimensionless forms. Finally, the equations are solved by applying the Galerkin finite element method.

The findings for different values of the relative permeability (K*) and permeability deviation angle (λ) are represented in the forms of charts, streamlines and constant temperature contours. The considerable effects of the relative permeability (K*) and deviation angle (λ) on the flow line patterns of the melting phase-change material are some of the significant achievements of this works.

This study was conducted using data from relevant research articles provided by reputable academic sources. The data included in this manuscript have not been published previously and are not under consideration by any other journal.

The purpose of this paper is to study the impact of Joule heating on boundary layer flow and melting heat transfer of Prandtl fluid over a stretching sheet in the presence of fluid particles suspension. The transformed boundary layer equations are solved numerically by RKF-45 method. The influence of the non-dimensional parameters on velocity and temperature growths in the boundary layer region is analyzed in detail and the results are shown graphically. The results indicate that the larger estimation of α and β reduces for both velocity and temperature profile. Further, the rate of heat transfer decreases by increasing melting parameter.

The converted set of boundary layer equations is solved numerically by RKF-45 method. Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters. Furthermore, the skin friction coefficient and Nusselt number are also presented.

It is found that the heat transfer rates are advanced in the occurrence of non-linear radiation camper to linear radiation. Also, it is noticed that velocity profile increases by increasing Prandtl parameter but establishes opposite results for temperature profile.

The authors intend to analyze the boundary layer flow and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particles suspension. The governing systems of partial differential equations have been transformed to a set of coupled ordinary differential equations by applying appropriate similarity transformations. The reduced equations are solved numerically. The pertinent parameters are discussed through graphs and plotted graphs. The present results are compared with the existing limiting solutions, showing good agreement with each other.

The purpose of this paper is to conduct a numerical study to analyze the melting process along a vertical wavy surface with uniform surface temperature.

The cavity horizontal walls are insulated while the left hot wavy wall and the right cold wall are maintained at temperatures, TH=38.3°C and TC=28.3°C, respectively. The enclosure was filled by solid Gallium initially at temperature TC. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid-liquid phase change. The validity of the numerical code used is ascertained by comparing the results with previously published results.

The effect of number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics is investigated in detail. The numerical results show that the enhanced total heat transfer rate seems to depend on the amplitude of the wavy surface.

Flow and heat transfer from irregular surfaces are often encountered in many engineering applications to enhance heat transfer such as micro-electronic devices, flat plate solar collectors and flat-plate condensers in refrigerators, etc. Roughened surfaces could be used in latent storage systems where the wall heat flux is known. One of the reasons why a roughened surface is more efficient in heat transfer is its capability to promote fluid motion near the surface; in this way a complex wavy surface is expected to promote a larger heat transfer rate than a flat plate. This complex geometry will promote a correspondingly complicated motion in the fluid near the surface; this motion is described by the nonlinear boundary-layer equations.

A numerical study is reported of natural convection melting of ice within a vertical cylinder. A stream function‐vorticity‐temperature formulation is employed in conjunction with body‐fitted coordinates for tracking the irregular shape of the timewise varying solid‐liquid interface. A parabolic density profile versus temperature is assumed for water. Numerical experiments are carried out for a temperature of the cylinder wall ranging from 4°C to 10°C. Results show that natural convection heat transfer involving density anomaly leads to complex flow patterns and strongly affects the time evolution of the phase front. The maximum Nusselt number at the heated cylinder wall is obtained for Tw = 4°C while the minimum is observed for Tw = 8°C.