Explicit solution for freezing of humid porous half-space with a heat flux condition

Marcus, Eduardo A. Santillan; Tarzia, Domingo A.

doi:10.1016/s0020-7225(00)00009-4

Cited by 15 publications

(12 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(58), we know that if we replace q c in the solution of Eqs. (10) and (11) with J s using the form of Eq. (59), then all the equations of this Stefan problem can be satisfied, and the corresponding solution can be obtained readily…”

Section: Similar Stefan Problem Under Constant Surface Seepage Velocitymentioning

confidence: 99%

“…The physical background of the Stefan problem lies in many aspects, such as the solidification of the alloy melt [6], the melting and ablation during the laser heating process [7,8], the shore-line movement problem [9,10], the freeze and thaw of humid porous media [11,12], the hydration process of the soybean [13,14], and the flow in porous media [15,16]. In most situations, the Stefan problem can only be solved numerically; however, finding analytical solutions for the problem has always been of great interest to the researchers.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Zhou

Shi

2017

Acta Mech. Sin.

View full text Add to dashboard Cite

One-dimensional non-Darcy flow in a semiinfinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.

show abstract

Section: Similar Stefan Problem Under Constant Surface Seepage Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Zhou

Shi

2017

Acta Mech. Sin.

View full text Add to dashboard Cite

show abstract

“…The system has been studied both by analytical procedures [3,5], and with numerical methods [2,3,6]. The process with only-sublimation of the already-frozen system has been extensively studied for freeze-drying of food and pharmaceutical materials [7,8].…”

Section: Introductionmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

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

show abstract

“…Mathematical formulation of the heat and mass transfer in capillary porous bodies has been established by Luikov [13], [14], [15], [16], [17]. Other problems in this direction are [3], [6], [7], [9], [20], [22]. #532/01.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for drying with coupled phase-change in a porous medium with a heat flux condition on the surface

Marcus¹,

Tarzia²

2003

Comput. Appl. Math.

View full text Add to dashboard Cite

show abstract

Explicit solution for freezing of humid porous half-space with a heat flux condition

Cited by 15 publications

References 8 publications

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

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

Exact solutions for drying with coupled phase-change in a porous medium with a heat flux condition on the surface

Contact Info

Product

Resources

About