Determination of unknown thermal coefficients of a semi-infinite material for the one-phase Lame-Clapeyron (Stefan) problem through the Solomon-Wilson-Alexiades' mushy zone model

Tarzia, Domingo A.

doi:10.1016/s0735-1933(87)81012-6

Cited by 7 publications

(18 citation statements)

References 4 publications

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“…One can observe that condition (13) of Theorem 1 is equivalent to D 1 (0) ̸ = 0, and since the functions in (22) are continuous in [0, T ] we obtain that D 1 (t) ̸ = 0 in an upper neighbourhood…”

Section: Remarksmentioning

confidence: 90%

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Multiple time-dependent coefficient identification thermal problems with a free boundary

Hussein

Lesnic

Ivanchov

et al. 2016

Applied Numerical Mathematics

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Multiple time-dependent coefficient identification thermal problems with an unknown free boundary are investigated. The difficulty in solving such inverse and ill-posed free boundary problems is amplified by the fact that several quantities of physical interest (conduction, convection/advection and reaction coefficients) have to be simultaneously identified. The additional measurements which render a unique solution are given by the heat moments of various orders together with a Stefan boundary condition on the unknown moving boundary. Existence and uniqueness theorems are provided. The nonlinear and ill-posed problems are numerically discretised using the finite-difference method and the resulting system of equations is solved numerically using the MATLAB toolbox routine lsqnonlin applied to minimizing the nonlinear Tikhonov regularization functional subject to simple physical bounds on the variables. Numerically obtained results from some typical test examples are presented and discussed in order to illustrate the efficiency of the computational methodology adopted.

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Section: Remarksmentioning

confidence: 90%

“…Many practical problems involve a free boundary and the Stefan problem is a typical example of a problem of this kind, [22,23]. Under suitable changes of variables, free boundary problems can be reduced to ICIP's in a fixed domain.…”

Section: Introductionmentioning

confidence: 99%

Multiple time-dependent coefficient identification thermal problems with a free boundary

Hussein

Lesnic

Ivanchov

et al. 2016

Applied Numerical Mathematics

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“…where the dimensionless parameter ξ (see (24)) is a solution to equation (E5). Then, we need to prove that the two restrictions given by (R12) are necessary and sufficient conditions for the existence of a positive solution to equation (E5) and for obtain that the coefficient ǫ given in (33) is a number between 0 and 1.…”

Section: Explicit Formulae For the Unknown Thermal Coefficientsmentioning

confidence: 99%

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Ceretani¹,

Tarzia²

2016

JPHMT

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The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the SolomonWilson-Alexiades model is considered. The material is assumed to be initially liquid at its melting temperature and it is considered that the solidification process begins due to a heat flux imposed at the fixed face. The associated free boundary value problem is overspecified with a convective boundary condition with the aim of the simultaneous determination of the temperature of the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. The another free boundary of the mushy zone, the bulk temperature and the heat flux and heat transfer coefficients at the fixed face are assumed to be known. According to the choice of the unknown thermal coefficients, fifteen phasechange problems arise. The study of all of them is presented and explicit formulae for * aceretani@austral.edu.ar † dtarzia@austral.edu.ar 1 the unknowns are given, beside necessary and sufficient conditions on data in order to obtain them. Formulae for the unknown thermal coefficients, with their corresponding restrictions on data, are summarized in a table.

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“…www.intechopen.com (Tarzia, 1987). The simultaneous determination of two unknown thermal coefficients for phase-change problems with temperature-dependent thermal conductivity of the type (54) was given in (Salva & Tarzia, 2010) with a sensitivity analysis.…”

Section: Determination Of Two Unknown Thermal Coefficients For the Onmentioning

confidence: 99%

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

Tarzia¹

2011

Advanced Topics in Mass Transfer

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Determination of unknown thermal coefficients of a semi-infinite material for the one-phase Lame-Clapeyron (Stefan) problem through the Solomon-Wilson-Alexiades' mushy zone model

Cited by 7 publications

References 4 publications

Multiple time-dependent coefficient identification thermal problems with a free boundary

Multiple time-dependent coefficient identification thermal problems with a free boundary

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

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

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