A finite element method is presented for the solution of a free boundary problem which arises during planar melting of a semi-infinite medium initially at a temperature which is slightly below the melting temperature of the solid. The surface temperature is assumed to vary with time. Two different situations are considered (I) when thermal diffusivity is independent of temperature and (II) when thermal diffusivity varies linearly with temperature. The differential equation governing the process is converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied, a linear differential equation can be represented by a set of linear algebraic equations and a nonlinear differential equation can be represented by a set of nonlinear algebraic equations. The solution of the problem is then found in terms of Chebyshev polynomial of second kind. The solution of this initial value problem is utilized iteratively in the interface heat flux equation to determine interface location as well as the temperature in two regions. The method appears to be accurate in cases for which closed form solutions are available, it agrees well with them. The effect of several parameters on the melting are analysed and discussed.
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ASME 2004 Heat Transfer/Fluids Engineering Summer Conference
July 11–15, 2004
Charlotte, North Carolina, USA
Conference Sponsors:
- Heat Transfer Division and Fluids Engineering Division
ISBN:
0-7918-4691-1
PROCEEDINGS PAPER
A Finite Element Method for the Solution of Free Boundary Problem Available to Purchase
K. N. Rai
Banaras Hindu University, Varanasi, U.P., India
D. C. Rai
Banaras Hindu University, Varanasi, U.P., India
Paper No:
HT-FED2004-56777, pp. 1237-1245; 9 pages
Published Online:
February 24, 2009
Citation
Rai, KN, & Rai, DC. "A Finite Element Method for the Solution of Free Boundary Problem." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 2, Parts A and B. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 1237-1245. ASME. https://doi.org/10.1115/HT-FED2004-56777
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