Mathematical Modeling of Melting and Freezing Processes

Alexiades, Vasilios; Solomon, Allen M.

doi:10.1201/9780203749449

Cited by 147 publications

(255 citation statements)

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“…The location of interface of solid and liquid in Region 2, that is in direction Y, Y (t) is defined following the Megerlin method 13 as below.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…[1][2][3] The analytical solution for the onedimensional (1D) MBP termed as Stefan's problem. 11,12 Analytical solutions of 1D MBP for different boundary conditions were reported by Alexiades and Solomon 13 and Ozisik. 12 These include the perturbation method, the Megerlin method, the quasi-stationary approximation, Kantorovich method, and the heat balance integral method (HBIM).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

et al. 2019

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Summary Here, a simplified analytical model has been proposed to predict solid fraction, solid–liquid interface, solidification time, and temperature distribution during solidification of phase change material (PCM) in a two‐dimensional latent heat thermal energy storage system (LHTES) with horizontal internal plate fins. Host of boundary conditions such as imposed constant heat flux, end‐wall temperature, and convective air environment on the vertical walls are considered for the analysis. Heat balance integral method was used to obtain the solution. Present model yields closed‐form solution for temperature variation and solid fraction as a function of various modeling parameters. Also, solidification time of PCM, which is useful in optimum design of PCM‐based thermal energy storages, has been evaluated during the analysis. The solidification time was found to be reduced by 93% by reducing the aspect ratio from 8 to 0.125 for constant heat flux boundary condition. While, for constant wall temperature boundary condition, the solidification time reduces by 99% by changing the aspect ratio from 5 to 0.05. In case of convective air boundary surrounding, the solidification time is found to reduce by 88% by reducing the aspect ratio from 8 to 0.125. Based on the analytical solution, correlations have been proposed to predict solidification time in terms of aspect ratio and end‐wall boundary condition.

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“…The location of interface of solid and liquid in Region 2, that is in direction Y, Y (t) is defined following the Megerlin method 13 as below.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Many heat diffusion processes that involve phase change are the so-called Stefan problems. [1][2][3][4][5][6][7][8][9][10] These are characterized by the presence of an unknown moving surface that separates both phases.…”

Section: Introductionmentioning

confidence: 99%

“…However, two types of density change are relevant in phase-change processes. 1 One is due to the dependence of density on temperature arising in heat transfer process and the other is due to the difference between the solid and liquid densities at the melting temperature. According to the bibliography, there are also several papers [11][12][13][14] that analyze free boundary problems including a density change and the induced motion caused by the phase transition.…”

Section: Introductionmentioning

confidence: 99%

“…From now on, we assume that 1 ≠ 2 ; for most materials, they differ by up to 10% and in extreme cases by up to 30%. 1 In previous studies, 15,16 an explicit solution of similarity type for the temperature of both phases and the solid-liquid interface was obtained. The explicit solution to the particular case 1 = 2 was given in Zubair and Chaudhry.…”

Section: Introductionmentioning

confidence: 99%

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On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

Briozzo

Natale

2020

Math Methods in App Sciences

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We consider a two‐phase Stefan problem for a semi‐infinite body x>0, with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type hfalse/t, h>0 whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient h→+∞. Moreover, we analyze the dependence of the free boundary respecting to the jump density.

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A Mathematical Model of Melt Lake Development on an Ice Shelf

Buzzard

Feltham

Flocco

2018

J Adv Model Earth Syst

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The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. Melt lakes have been implicated in ice shelf collapse; Antarctica's Larsen B Ice Shelf was observed to have a large amount of surface melt lakes present preceding its collapse in 2002. Such collapse can affect ocean circulation and temperature, cause habitat loss and contribute to sea level rise through the acceleration of tributary glaciers. We present a mathematical model of a surface melt lake on an idealized ice shelf. The model incorporates a calculation of the ice shelf surface energy balance, heat transfer through the firn, the production and percolation of meltwater into the firn, the formation of ice lenses, and the development and refreezing of surface melt lakes. The model is applied to the Larsen C Ice Shelf, where melt lakes have been observed. This region has warmed several times the global average over the last century and the Larsen C firn layer could become saturated with meltwater by the end of the century. When forced with weather station data, our model produces surface melting, meltwater accumulation, and melt lake development consistent with observations. We examine the sensitivity of lake formation to uncertain parameters and provide evidence of the importance of processes such as lateral meltwater transport. We conclude that melt lakes impact surface melt and firn density and warrant inclusion in dynamic‐thermodynamic models of ice shelf evolution within climate models, of which our model could form the basis for the thermodynamic component.

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Mathematical Modeling of Melting and Freezing Processes

Cited by 147 publications

References 0 publications

Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

A Mathematical Model of Melt Lake Development on an Ice Shelf

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