Analysis of Multidimensional Conduction Phase Change Via the Enthalpy Model

1975 ◽  
Vol 97 (3) ◽  
pp. 333-340 ◽  
Author(s):  
N. Shamsundar ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Mathematical Representation ◽  
Interface Position ◽  
Transfer Rates ◽  
Fully Implicit ◽  
Implicit Finite Difference Scheme ◽  
Wide Range ◽  
Solid Liquid Interface ◽  
Solid Liquid

The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

scholarly journals Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hamid El Qarnia ◽  
Fayssal El Adnani ◽  
El Khadir Lakhal
Keyword(s):  
Analytical Solution ◽  
Phase Change ◽  
Phase Change Material ◽  
Liquid Interface ◽  
Solid Shell ◽  
Interface Position ◽  
Temperature Distributions ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Change Material

This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number,ε. This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed.

Analytical Solution on the Relation of Technique Parameters for Continuous Casting with Heated Mould

2011 ◽  
Vol 337 ◽  
pp. 225-231
Author(s):  
Feng Ni ◽  
Shi Zhong Wei ◽  
Rui Long
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Continuous Casting ◽  
Casting Speed ◽  
Specific Conductance ◽  
Liquid Interface ◽  
Mould Temperature ◽  
Interface Position ◽  
Solid Liquid Interface ◽  
Solid Liquid

The technique of continuous casting with heated mould is a kind of near-net-shape processing technology, which combines unidirectional solidification with continuous casting and has been used widely for new material development and processing. A steady-state heat-transfer model was suggested for pure metal case. Some of modeling parameters, such as equivalent specific conductance and equivalent heat-transfer coefficient, etc, had been defined. The analytic solution of temperature profile along the axis of casting rod was obtained for solid-liquid interface to be as origin of position coordinate, by which the relations had been solved among mould temperature, casting speed, solid-liquid interface position, equivalent specific conductance between mould and metal, equivalent heat-transfer coefficient of cooling of cast rod, temperature gradient and cooling rate of melt in front of solid-liquid interface. As an example, the coordinate relations of solid-liquid interface position, mould temperature and casting speed were calculated and compared with experimental results in the case of pure copper. The calculation results conformed very well to the experimental ones. And it was indicated that the cooling rate of melt in front of solid-liquid interface had a nonlinear relation with casting speed during steady continuous casting process.

Phase Change Heat Transfer During Melting and Resolidification of Melt Around Cylindrical Heat Source(s)/Sink(s)

1989 ◽  
Vol 111 (1) ◽  
pp. 43-49 ◽  
Author(s):  
K. Sasaguchi ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Phase Change Material ◽  
Liquid Interface ◽  
Cylinder Surface ◽  
Storage Unit ◽  
Energy Storage Unit ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Change Material

Melting and resolidification of a phase change material around two cylindrical heat exchangers spaced vertically have been investigated experimentally. Experiments have been performed to examine the effects of the cylinder surface temperatures on heat transfer during the melting and freezing cycle. The processes have been clarified on the basis of observations of timewise variations in the solid/liquid interface and of temperature distribution measurements in the phase change material. The results show that the solid/liquid interface contour during the melting and resolidification of the liquid from the upper cylinder is greatly affected by the surface temperature of the lower cylinder. The results show that multiple liquid regions may develop in the phase change material around the embedded heat sources/sinks, and the temperature swings and melting and freezing periods need to be selected properly in order to effectively utilize the phase change material in a latent heat energy storage unit.

Phase Change Heat Transfer Enhancement Using Copper Porous Foam

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Ali Siahpush ◽  
James O’Brien ◽  
John Crepeau
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Phase Change ◽  
Effective Thermal Conductivity ◽  
Storage System ◽  
Vertical Cylinder ◽  
Energy Storage System ◽  
Scaling Analysis ◽  
Interface Position ◽  
Solid Liquid

A detailed experimental and analytical study has been performed to evaluate how copper porous foam (CPF) enhances the heat transfer performance in a cylindrical solid/liquid phase change thermal energy storage system. The CPF used in this study had a 95% porosity and the phase change material (PCM) was 99% pure eicosane. The PCM and CPF were contained in a vertical cylinder where the temperature at its radial boundary was held constant, allowing both inward freezing and melting of the PCM. Detailed quantitative time-dependent volumetric temperature distributions and melt/freeze front motion and shape data were obtained. As the material changed phase, a thermal resistance layer built up, resulting in a reduced heat transfer rate between the surface of the container and the phase change front. In the freezing analysis, we analytically determined the effective thermal conductivity of the combined PCM/CPF system and the results compared well to the experimental values. The CPF increased the effective thermal conductivity from 0.423W∕mKto3.06W∕mK. For the melting studies, we employed a heat transfer scaling analysis to model the system and develop heat transfer correlations. The scaling analysis predictions closely matched the experimental data of the solid/liquid interface position and Nusselt number.

Heat Transfer During Melting From an Isothermal Vertical Wall

1984 ◽  
Vol 106 (1) ◽  
pp. 12-19 ◽  
Author(s):  
C.-J. Ho ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Vertical Wall ◽  
Local Heat ◽  
Source Surface ◽  
Interface Motion ◽  
Numerical Predictions ◽  
Buoyancy Driven Convection ◽  
Solid Liquid Interface ◽  
Solid Liquid

This paper reports basic heat transfer data during melting of n-octadecane from an isothermal vertical wall of a rectangular cavity. The shadowgraph technique was used to measure local heat transfr coefficents at the heat source surface and the solid-liquid interface motion during phase change was recorded photographically. Experimental results clearly showed that, except in the very early stages of melting, the rates of melting and of heat transfer were greatly affected by the buoyancy-driven convection in the liquid. Initial subcooling of the solid substanially impeded the phase change process. A numerical simulation of the corresponding two-dimensional melting in the presence of natural convection was performed, and the numerical predictions are compared with experimental data.

Molecular Dynamics Simulation of Heat Transfer and Phase Change During Laser Material Interaction

2001 ◽  
Vol 124 (2) ◽  
pp. 265-274 ◽  
Author(s):  
Xinwei Wang ◽  
Xianfan Xu
Keyword(s):  
Heat Transfer ◽  
Molecular Dynamics ◽  
Phase Change ◽  
Pulsed Laser ◽  
Liquid Structure ◽  
Dynamics Simulation ◽  
Dynamics Simulations ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Material Interaction

In this work, heat transfer and phase change of an argon crystal irradiated by a picosecond pulsed laser are investigated using molecular dynamics simulations. The result reveals no clear interface when phase change occurs, but a transition region where the crystal structure and the liquid structure co-exist. Superheating is observed during the melting and vaporizing processes. The solid-liquid interface is found to move with a velocity of hundreds of meters per second, and the vapor is ejected from the surface with a vapor front velocity of hundreds of meters per second.

scholarly journals Numerical Phase-Field Model Validation for Dissolution of Minerals

2021 ◽  
Vol 11 (6) ◽  
pp. 2464
Author(s):  
Sha Yang ◽  
Neven Ukrainczyk ◽  
Antonio Caggiano ◽  
Eddie Koenders
Keyword(s):  
Phase Field ◽  
Liquid Interface ◽  
Mineral Dissolution ◽  
Experimental Results ◽  
Wide Range ◽  
Congruent Dissolution ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Dissolution Of Minerals ◽  
Meso Scale

Modelling of a mineral dissolution front propagation is of interest in a wide range of scientific and engineering fields. The dissolution of minerals often involves complex physico-chemical processes at the solid–liquid interface (at nano-scale), which at the micro-to-meso-scale can be simplified to the problem of continuously moving boundaries. In this work, we studied the diffusion-controlled congruent dissolution of minerals from a meso-scale phase transition perspective. The dynamic evolution of the solid–liquid interface, during the dissolution process, is numerically simulated by employing the Finite Element Method (FEM) and using the phase–field (PF) approach, the latter implemented in the open-source Multiphysics Object Oriented Simulation Environment (MOOSE). The parameterization of the PF numerical approach is discussed in detail and validated against the experimental results for a congruent dissolution case of NaCl (taken from literature) as well as on analytical models for simple geometries. In addition, the effect of the shape of a dissolving mineral particle was analysed, thus demonstrating that the PF approach is suitable for simulating the mesoscopic morphological evolution of arbitrary geometries. Finally, the comparison of the PF method with experimental results demonstrated the importance of the dissolution rate mechanisms, which can be controlled by the interface reaction rate or by the diffusive transport mechanism.

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