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An advanced heat transfer model for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs has been developed. The thin film evaporation and condensation models have been incorporated with the model to predict the behavior of vapor plugs and liquid slugs in the PHP. The results show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat. Higher surface tension results in a slight increase in the total heat transfer. The diameter, heating wall temperature, and charging ratio have significant effects on the performance of the PHP. Total heat transfer significantly decreased with a decrease in the heating wall temperature. Increasing the diameter of the tube resulted in higher total heat transfer. The results also showed that the PHP could not operate for higher charge ratios.

To study the effects of velocity correction schemes for a temperature transforming model (TTM) for convection controlled solid‐liquid phase‐change problem.

The effects of three different solid velocity correction schemes, the ramped switch‐off method (RSOM), the ramped source term method (RSTM) and the variable viscosity method (VVM), on a TTM for numerical simulation of convection controlled solid‐liquid phase‐change problems are investigated in this paper. The comparison is accomplished by analyzing numerical simulation and experimental results of a convection/diffusion phase‐change problem in a rectangular cavity. Model consistency of the discretized TTM is also examined in this paper. The simulation results using RSOM, RSTM and VVM in TTM are compared with experimental results.

In order to efficiently use the discretized TTM model and obtain convergent and reasonable results, a grid size must be chosen with a suitable time step (which should not be too small). Applications of RSOM and RSTM‐TTM yield identical results which are more accurate than VVM.

This paper provides generalized guidelines about the solid velocity correction scheme and criteria for selection of time step/grid size for the convection controlled phase change problem.

To demonstrate, through numerical models, that it is possible to simulated low‐gravity phase change (melting), of an electrically conducting material (gallium), in terrestrial conditions via the application of electromagnetic fields.

A complete three‐dimensional mathematical formulation governing a phase change process in the presence of an electromagnetic field has been developed. In addition a comprehensive parametric study has been completed to study the various effects of gravity, Stefan number, Hartmann number and electromagnetic pressure number upon the phase change process.

The results show that the application of an electromagnetic filed can be used to simulate key melting characteristics found for actual low‐gravity. However, the resulting three‐dimensional flow field in the melted region differs from actual low‐gravity. The application of an electromagnetic field creates a flow phenomenon not found in actual low‐gravity or previously seen in two‐dimensional problems.

Future work may include the use of oscillating electromagnetic fields to enhance convection in energy storage systems in a low‐gravity environment.

The ability to suppress unwanted convective flows in a phase change process without the high magnetic fields necessary in magnetic field only suppression systems.

This work fills a void in the literature related to conducting fluids and the effects of magnetic and electromagnetic fields.

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

The purpose of this paper is to solve solidification of liquid copper saturated in porous structure fabricated by sintered steel particles using a temperature‐transforming model (TTM).

The convection in the liquid region is modeled using Navier‐Stokes equation with Darcy's term and Forchheimer's extension. The effect of natural convection is considered using the Boussinesq approximation. For the solid region, the velocity is set to zero by the Ramped Switch‐Off Method (RSOM). The model was validated by comparing the results with existing experimental and numerical results with gallium as phase change material and packed glass beads as porous structure. Solidification of liquid copper saturated in sintered copper particles is then simulated and the effects of various parameters on solidification process were studied.

The results indicate that the stronger convection effects are shown for the cases with high Raleigh number or high Darcy's number. However, when either Raleigh number or Darcy's number is reduced to below a certain order of magnitude, the solidification becomes conduction‐controlled.

This work is the first application of the TTM to solve solidification in porous media, which can find its application in post‐processing of laser sintered parts.

The purpose of this paper is to present a numerical investigation on pulsating heat pipe (PHP) to study the slug velocities as a function of various parameters.

The governing equation of PHP is solved using explicit embedded Runge‐Kutta method, the Dormand–Prince pair in conjunction with MATLAB with the nomenclature 45 for the determination of displacement and the velocity of the slug.

The results show that lower fill ratio, higher diameter, higher operating temperature and higher temperature difference between evaporator and condenser for a given working fluid results in higher slug velocities, indicating higher momentum transfer and hence better heat transport.

Under steady state conditions, the design of a PHP is facilitated through the introduction of non‐dimensional numbers.

The displacement and slug velocities for additional working fluids, namely ethanol and methanol, are determined for the first time. The behaviour of non‐dimensional numbers, i.e. Poiseuille number, capillary number and Eckert number in a PHP as a function of various parameters have been studied for the first time.

The purpose of this paper is to describe two‐ and three‐dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm.

A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic‐based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs.

For the first time, a stable fully explicit algorithm has been applied to detailed multi‐dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature.

For the first time, thanks to a stabilization analysis conducted, the AC‐CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid‐electrode interface.

Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform temperature or heat flux, assuming that the rest of the cavity is completely adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity.

The problem is written with non-homogeneous boundary conditions. Momentum and energy equations are numerically solved in space by a spectral collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the resolution in time.

The results clearly show the evolution of multicellular regime during the process of fusion and the kinetics of phase change depends on the boundary condition imposed on the bottom cell wall. Thus the charge and discharge processes in energy storage cells can be controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal convective heat and mass transfer are highlighted during the transient regime. This model is particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in the process of storage/release energy.

The time-dependent physical properties that induce non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in the present model. The present model is actually extended to these coupled situations. This problem requires smoother geometries. One can try to palliate this disadvantage by constructing smoother approximations of non-smooth geometries. The augmentation of polynomials developments orders increases strongly the computing time. When the external heat flux or temperature imposed at the PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to assume the algorithms convergence.

Among the areas where this work can be used, are: buildings where the PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical, to minimize temperature variations of food, drug or sensitive materials; and the textile industry, PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM intervene to regulate heat transfer between the body and the outside.

The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions.