EXPLICIT SOLUTION FOR THE ONE-PHASE STEFAN PROBLEM WITH LATENT HEAT DEPENDING ON THE POSITION AND A CONVECTIVE BOUNDARY CONDITION AT THE FIXED FACE

JULIETA BOLLATI; DOMINGO TARZIA

Title	EXPLICIT SOLUTION FOR THE ONE-PHASE STEFAN PROBLEM WITH LATENT HEAT DEPENDING ON THE POSITION AND A CONVECTIVE BOUNDARY CONDITION AT THE FIXED FACE
Publication Type	Journal Article
Year of Publication	2018
Authors	BOLLATI, JULIETA, TARZIA, DOMINGO
Volume	22
Issue	2
Start Page	309
Pagination	24
Date Published	2018
ISSN	1083-2564
AMS	35C05, 35R35, 80A22
Abstract	An explicit solution of a similarity type is obtained for a onephase Stefan problem in a semi-infinite material using Kummer functions. It is considered a phase-change problem with a latent heat defined as a power function of the position with a non-negative real exponent and a convective boundary condition at the fixed face ${ \ x=0 }$. Existence and uniqueness of the solution is proved. Relationship between this problem and the problems with temperature and flux boundary condition is also analysed. Furthermore it is studied the limit behaviour of the solution when the coefficient which characterizes the heat transfer at the fixed boundary tends to infinity. Computing this limit allows to demonstrate that the problem proposed in this paper with a convective boundary condition generalizes the problem with Dirichlet boundary condition. Numerical computation of the solution is done over certain examples, with a view to comparing this results with those obtained by general algorithms that solve Stefan problems.
URL	https://acadsol.eu/en/articles/22/2/10.pdf
DOI	10.12732/caa.v22i2.10
Refereed Designation	Refereed
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