Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia, Domingo A.

doi:10.5772/14537

Cited by 9 publications

(3 citation statements)

References 109 publications

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“…Compendia of exact solutions for further Stefan problems can be found in Lunardini, 23 Crank, 27 Carslaw and Jaeger 30 and Tarzia. 31 Modern solutions on problems with (very) specific conditions can be found, among others, in Cherniha and Kovalenko, 32 Voller, 33 Ramos, 34 Voller, Swenson, 35 Gottlieb, 36 Kumar and Singh 37 and Salva. 38 Carslaw and Jaeger.…”

Section: State Of the Art In Transient Phase-change Problems In Cylin...mentioning

confidence: 99%

An adjusted analytical solution for thermal design in artificial ground freezing

Calderón

Palacio

García

et al. 2023

International Journal of Rock Mechanics and Mining Sciences

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Section: State Of the Art In Transient Phase-change Problems In Cylin...mentioning

confidence: 99%

An adjusted analytical solution for thermal design in artificial ground freezing

Calderón

Palacio

García

et al. 2023

International Journal of Rock Mechanics and Mining Sciences

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“…The goal of this paper is to find the necessary and/or sufficient conditions for data (initial and boundary conditions, and thermal coefficients of the binary alloy) in order to obtain an instantaneous phase‐change process with the corresponding explicit solution of the similarity type. A review of explicit solution for Stefan‐like problems is [28].…”

Section: Introductionmentioning

confidence: 99%

Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

Lucas

Cirelli

Tarzia

2023

Math Methods in App Sciences

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Similarity solutions for the two‐phase Rubinstein binary‐alloy solidification problem in a semi‐infinite material are developed. These new explicit solutions are obtained by considering two cases: A heat flux or a convective boundary conditions at the fixed face, and the necessary and sufficient conditions on data are also given in order to have an instantaneous solidification process. We also show that all solutions for the binary‐alloy solidification problem are equivalent under some restrictions for data. Moreover, this implies that the coefficient that characterizes the solidification front for the Rubinstein solution must verify an inequality as a function of all thermal and boundary conditions.

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“…The solution to (1.1)-(1.5) is given as a function of the solution of (1.7) through the similarity variable x/(2 √ α 0 t), see [5,6,12]. More explanations are given in [1,9,14].…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of the p-generalized modified error function

Bollati,

Semitiel,

Natale

et al. 2020

ejde

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In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x=0. We prove existence and uniqueness of a non-negative \(C^{\infty}\) solution by using a fixed point argument. We show that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p=1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/35/abstr.html

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Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Cited by 9 publications

References 109 publications

An adjusted analytical solution for thermal design in artificial ground freezing

An adjusted analytical solution for thermal design in artificial ground freezing

Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

Existence and uniqueness of the p-generalized modified error function

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