The Stefan problem with variable thermophysical properties and phase change temperature

Myers, T.G.; Hennessy, Matthew G.; Calvo-Schwarzwälder, Marc

doi:10.1016/j.ijheatmasstransfer.2019.118975

Cited by 23 publications

(7 citation statements)

References 55 publications

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“…The cooling process of water droplets has been studied by different authors over the years [35][36][37][38][39][40][41]. In the present work, a basic heat balance model is used to obtain the rate at which the temperature of a droplet varies over time, assuming that the particle integrates a thermodynamic system in which heat transfer takes place from the droplet to the surrounding environment and vice versa.…”

Section: Cooling Processmentioning

confidence: 99%

Description of a Eulerian–Lagrangian Approach for the Modeling of Cooling Water Droplets

et al. 2021

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The present paper describes a tool developed in-house for the modeling of free-falling water droplet cooling processes. A two-way coupling model is employed to account for the interactions between the droplets and the carrier fluid, following a Eulerian–Lagrangian approach. In addition, a stochastic separated flow technique is employed, involving random sampling of the fluctuating fluid velocity. In physical modeling, two empirical correlations are considered for determining the heat and mass transfer coefficients, with the possibility of accounting for vibrations. The numerical results indicate the preponderance of the interactions between droplet and carrier fluid at various humidity ratios.

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Section: Cooling Processmentioning

confidence: 99%

Description of a Eulerian–Lagrangian Approach for the Modeling of Cooling Water Droplets

et al. 2021

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“…The unsteady behavior of a PCM melting in a cylindrical shell and tube LHTES system with moving interface boundary conditions and constant inner tube temperature is captured through an analytical approach. The melting of PCM is assumed to be dominated by conduction heat transfer and the effect of gravity and the viscous effect is considered negligible 28,29 . However, this assumption can be supported by the fact that if the tube wall is stagnantly hot and transferring heat to PCM at a constant temperature, heat flow is primarily governed by thermal conduction 30 .…”

Section: Analytical Modelmentioning

confidence: 99%

“…The melting of PCM is assumed to be dominated by conduction heat transfer and the effect of gravity and the viscous effect is considered negligible. 28,29 However, this assumption can be supported by the fact that if the tube wall is stagnantly hot and transferring heat to PCM at a constant temperature, heat flow is primarily governed by thermal conduction. 30 Furthermore, when a small amount of PCM is charged inside a closed container, conduction is the dominating mode of heat transfer.…”

Section: Analytical Modelmentioning

confidence: 99%

A novel analytical approach to study the charging characteristics of a shell and tube thermal energy storage system

2021

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This study presents a novel analytical solution of the phase change problem in a shell and tube arrangement of latent heat thermal energy storage (LHTES) system. The transient melting behavior of phase change material (PCM) is captured using time‐dependent boundary conditions and moving interface energy equation. An approximate mathematical model is developed with the help of dimensionless number (η), exponential integral function, Lambert W function, and Swamee and Oijha approximation. The proposed analytical solution is used for investigating the thermal performance of low, medium, and high melting temperature PCM for building, solar absorption cooling, and concentrated solar power (CSP) applications, respectively. The results obtained from the analytical approach are compared with a numerical model based on the enthalpy method. It is found that the root mean square difference between the average PCM temperature obtained from analytical solution and detailed numerical analysis is 3.3°C, 1.2°C, and 0.1°C for the low, medium, and high‐temperature systems, respectively. The temporal variation of melt front position and the effect of inner tube temperature are further investigated using the analytical solution. The mathematical model could be proposed as an effective tool for the assessment of shell and tube LHTES systems.

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“…where ∆H f is the latent heat of solidification. The term ∝ (ds/dt) 2 in ( 7) is the kinetic energy contribution at the interface due to the bulk liquid motion [1,13,33]. The system is closed with the initial conditions…”

Section: Continuum Solidification Modelmentioning

confidence: 99%

Non-equilibrium molecular dynamics and continuum modelling of transient freezing of atomistic solids

Font,

Micou,

Bresme

2020

Preprint

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In this work we investigate the transient solidification of a Lennard-Jones liquid using nonequilibrium molecular dynamics simulations and continuum heat transfer theory. The simulations are performed in slab-shaped boxes, where a cold thermostat placed at the centre of the box drives the solidification of the liquid. Two well-defined solid fronts propagate outwards from the centre towards the ends of the box until solidification is completed. A continuum phase change model that accounts for the difference between the solid and the liquid densities is formulated to describe the evolution of the temperature and the position of the solidification front. Simulation results for a small and a large nanoscale system, of sizes 30.27 nm and 60.54 nm, are compared with the predictions of the theoretical model. Following a transient period of ∼20-40 ps and a displacement of the solidification front of 1-2.5 nm we find that the simulations and the continuum theory show good agreement. We use this fact to combine the simulation and theoretical approaches to design a simple procedure to calculate the latent heat of the material. We also perform simulations of the homogeneous freezing process, i.e. in the absence of a temperature gradient and at constant temperature, by quenching the liquid at supercooled temperatures. We demonstrate that the solidification rate of homogenous freezing is much faster than the one obtained under a thermal gradient for systems of the same size subject to the same thermostat temperature. Our study and conclusions should be of general interest to a wide range of atomistic solids.

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The Stefan problem with variable thermophysical properties and phase change temperature

Cited by 23 publications

References 55 publications

Description of a Eulerian–Lagrangian Approach for the Modeling of Cooling Water Droplets

Description of a Eulerian–Lagrangian Approach for the Modeling of Cooling Water Droplets

A novel analytical approach to study the charging characteristics of a shell and tube thermal energy storage system

Non-equilibrium molecular dynamics and continuum modelling of transient freezing of atomistic solids

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