×

zbMATH — the first resource for mathematics

Group classification of fin equation with variable thermal properties. (English) Zbl 1211.35141
Summary: A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Lie Group theory is applied to the equation. Group classification with respect to the thermal conductivity and heat transfer coefficient is performed. Results are summarized in a table for convenience. Some similarity transformations are used to convert the partial differential equation into an ordinary differential equation.

MSC:
35K55 Nonlinear parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
PDF BibTeX Cite
Full Text: DOI
References:
[1] Aziz, A.; Na, T.Y., International journal of heat and mass transfer, 24, 1397-1404, (1981) · Zbl 0458.76076
[2] Bluman, G.W.; Kumei, S., Symmetries and differential equations, (1989), Springer-Verlag New York · Zbl 0718.35003
[3] Ibragimov, N.H., ()
[4] Stephani, H., Differential equations: their solutions using symmetries, (1989), Cambridge University Press Cambridge
[5] Edelen, D.G.B., Applied exterior calculus, (1985), Wiley New York · Zbl 0386.73002
[6] ┼×uhubi, E.S., International journal of engineering science, 29, 133, (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.