An analytical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Olguín, Mariela C.; Salvadori, Viviana Olga; Mascheroni, Rodolfo Horacio; Tarzia, Domingo A.

doi:10.1016/j.ijheatmasstransfer.2008.01.031

Cited by 13 publications

(18 citation statements)

References 15 publications

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“…This last assertion can be easily proved taking into account that M.0/ < K and using that M.T/ is continuous (this continuity can be obtained using the results of the Appendix, keeping in mind that u 1 …”

Section: Proofmentioning

confidence: 93%

“…In fact, condition (9) is a generalization condition of the one given in [1] because in the physical case we have…”

Section: Introductionmentioning

confidence: 99%

“…The rate and extent of these transfers is determined by different factors [1]. For the description of the freezing process, the material can be divided into three zones: unfrozen, frozen and dehydrated.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper the temperatures are measured in Kelvin. To calculate the evolution of temperature and water content in time, in [1] the following nonstandard, coupled twophase free boundary problem is taken into account: Find the temperatures T d D T d .x, t/ (of the dehydrated region) and T f D T f .x, t/ (of the frozen region), the vapour concentration C v D C v .x, t/ (of the dehydrated region), the two free boundaries x D s d .t/ (sublimation front) and x D s f .t/ (frozen front), and the temperature T 0 D T 0 .t/ at x D s d .t/, which satisfy the following differential equations and conditions:…”

Section: Introductionmentioning

confidence: 99%

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Existence and uniqueness of a classical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Gianni

Tarzia

2011

Math. Meth. Appl. Sci.

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A recent model for the coupled problem of heat and mass transfer during the solidification of high-water content materials like soils, foods, tissues and phase-change materials was developed. This model takes into account the role played by material properties and process variables on the advance of freezing and sublimation fronts, temperature and water vapour profiles and weight loss. The goal of this paper is to determine the existence of a unique local classical solution for the corresponding two-phase coupled free boundary problem in an adequate functional space. Copyright (c) 2011 John Wiley & Sons, Ltd

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Section: Proofmentioning

confidence: 93%

“…In fact, condition (9) is a generalization condition of the one given in [1] because in the physical case we have…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence and uniqueness of a classical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Gianni

Tarzia

2011

Math. Meth. Appl. Sci.

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“…Typical examples include freezing of soil and solidification of phase change materials. It is known that the solidification process involves complex heat and mass transfer and hence is difficult to solve [8][9][10][11][12][13] . With the advance of computer technology, numerical solution is possible but is still very expensive.…”

mentioning

confidence: 99%

Asymptotic solution for coupled heat and mass transfer during the solidification of high water content materials

et al. 2010

Trans. Tianjin Univ.

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Abstract：This paper focuses on obtaining an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials. It is found that a complicated function involved in governing equations can be approached by Taylor polynomials unlimitedly, which leads to the simplification of governing equations. The unknown functions involved in governing equations can then be approximated by Chebyshev polynomials. The coefficients of Chebyshev polynomials are determined and an asymptotic solution is obtained. With the asymptotic solution, the dehydration and freezing fronts of materials are evaluated easily, and are consistent with numerical results obtained by using an explicit finite difference method.The solidification of high water content materials is an important phenomenon in both engineering and daily life [1][2][3][4][5][6][7] . Typical examples include freezing of soil and solidification of phase change materials. It is known that the solidification process involves complex heat and mass transfer and hence is difficult to solve [8][9][10][11][12][13] . With the advance of computer technology, numerical solution is possible but is still very expensive. Therefore, it is ideal to find analytical solutions. The authors of Ref. [13] tried to find such a solution, but they only presented numerical results by using an explicit finite difference method instead. In this paper, we focus on finding an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials.

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Numerical and experimental study on the heat and mass transfer of porous plate water sublimator with constant heat flux boundary condition

Wang

Zhong

et al. 2014

Applied Thermal Engineering

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An analytical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Cited by 13 publications

References 15 publications

Existence and uniqueness of a classical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Existence and uniqueness of a classical solution for the coupled heat and mass transfer during the freezing of high-water content materials

Asymptotic solution for coupled heat and mass transfer during the solidification of high water content materials

Numerical and experimental study on the heat and mass transfer of porous plate water sublimator with constant heat flux boundary condition

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