INV SUPERIOR JUBILADO
TARZIA domingo alberto
artículos
Título:
Exact solution for a Stefan problem with convective boundary condition and density jump
Autor/es:
D.A. TARZIA
Revista:
Proceedings on Applied Mathematics and Mechanics
Editorial:
Wiley Interscience
Referencias:
Lugar: New York; Año: 2007 vol. 7 p. 1040307 - 1040308
ISSN:
1617-7061
Resumen:
We consider the solidification of a semi-infinite material which is initially at its liquid phase at a uniform temperature $T_{i}$. Suddenly at time $t>0$ the fixed face $x=0$ is submitted to a convective cooling condition with a time-dependent heat transfer coefficient of the type $ Hleft( t ight) =ht^{-1/2}$ $left( h>0 ight)$ The bulk temperature of the liquid at a large distance from the solid-liquid interface is $T_{infty }$, a constant temperature such that $T_{infty }<T_{f}<T_{i}$ where $T_{f}$ is the freezing temperature. We also consider the density jump between the two phases. We obtain that the corresponding phase-change (solidification) process has an explicit solution of a similarity type for the temperature of both phases and the solid-liquid interface, if and only if the coefficient $h$ is large enough, that is $h>h_{0}= rac{k_{l}}{sqrt{pi alpha _{l}}} rac{T_{i}-T_{f}}{T_{i}-T_{infty }}$ where $k_{l}$ and $alpha _{l}$ are the conductivity and diffusion coefficients of the initial liquid phase. Moreover, when $hleq h_{0}$ we only have a heat conduction problem for the initial liquid phase and the corresponding change of phase does not occur. We do the mathematical analysis of a problem which was presented in S.M. Zubair - M.A. Chaudhry, W"{a}rme-und-Stoff"{u}bertragung, 30 (1994), 77-81 and we generalized the results obtained in D.A. Tarzia, MAT-Serie A, 8 (2004), 21-27 when the density jump between the two phases was neglected.