Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lamé-Clapeyron-Stefan Problem

Domingo Alberto Tarzia

doi:10.4236/am.2015.613191

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Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lamé-Clapeyron-Stefan Problem

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DOI: 10.4236/am.2015.613191 2,979 Downloads 3,349 Views Citations

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Domingo Alberto Tarzia

Affiliation(s)

CONICET and Department of Mathematics, FCE, Universidad Austral, Rosario, Argentina.

ABSTRACT

We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lamé-Clapeyron-Stefan problem with an over-specified boundary condition on the fixed face

. The partial differential equation and one of the conditions on the free boundary include a time Caputo’s fractional derivative of order

. Moreover, we obtain the necessary and sufficient conditions on data in order to have a unique solution by using recent results obtained for the fractional diffusion equation exploiting the properties of the Wright and Mainardi functions, given in: 1) Roscani-Santillan Marcus, Fract. Calc. Appl. Anal., 16 (2013), 802 - 815; 2) Roscani-Tarzia, Adv. Math. Sci. Appl., 24 (2014), 237 - 249 and 3) Voller, Int. J. Heat Mass Transfer, 74 (2014), 269 - 277. This work generalizes the method developed for the determination of unknown thermal coefficients for the classical Lamé-Clapeyron-Stefan problem given in Tarzia, Adv. Appl. Math., 3 (1982), 74 - 82, which is recovered by taking the limit when the order

KEYWORDS

Free Boundary Problems, Fractional Diffusion, Lamé-Clapeyron-Stefan Problem, Unknown Thermal Coefficients, Explicit Solution, Over-Specified Boundary Condition

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Tarzia, D. (2015) Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lamé-Clapeyron-Stefan Problem. Applied Mathematics, 6, 2182-2191. doi: 10.4236/am.2015.613191.

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