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A note on a symmetry analysis and exact solutions of a nonlinear fin equation. (English) Zbl 1143.35311

Summary: A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A. Z. Sahin [Appl. Math. Lett. 19, No. 4, 378–384 (2006; Zbl 1114.80003)]. Here, we consider a further group theoretic analysis that leads to an alternative set of exact solutions or reduced equations with an emphasis on travelling wave solutions, steady state type solutions and solutions not appearing elsewhere.

MSC:

35C05 Solutions to PDEs in closed form
35A30 Geometric theory, characteristics, transformations in context of PDEs
35K55 Nonlinear parabolic equations
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds

Citations:

Zbl 1114.80003
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References:

[1] Kern, Q. D.; Kraus, D. A., Extended Surface Heat Transfer (1972), McGraw-Hill: McGraw-Hill New York
[2] Hung, H. M.; Appl, F. C., Heat transfer of thin fins with temperature dependent thermal properties and internal heat generation, J. Heat Transfer Trans. ASME, 89, 155-161 (1967)
[3] Razelos, P.; Imre, K., The optimum dimension of circular fins with variable thermal parameters, J. Heat Transfer Trans. ASME, 102, 420-425 (1980)
[4] Jany, P.; Bejan, A., Ernst Schmidt’s approach to fin optimization: an extension to fins with variable conductivity and the design of ducts for fluid flow, Int. J. Heat Mass Transfer, 31, 8, 1635-1644 (1988)
[5] Razelos, P., A critical review of extended surface heat transfer, Heat Transfer Eng., 24, 6, 11-28 (2003)
[6] Aziz, S. M.; Enamul Hug, S. M., Perturbation solution for convecting fin with variable thermal conductivity, J. Heat Transfer Trans. ASME, 97, 300-301 (1975)
[7] Krane, R. J., Discussion on a previously published paper by A. Aziz and S.M. Euq, J. Heat Transfer Trans. ASME, 98, 685-686 (1976)
[8] Muzzio, Approximate solution for convective fins with variable thermal conductivity, J. Heat Transfer Trans. ASME, 98, 680-682 (1976)
[9] Chiu, C.-H.; Chen, C.-K., A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, Int. J. Heat Mass Transfer, 45, 2067-2075 (2002) · Zbl 1011.80011
[10] Adomian, G., A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 2, 501-544 (1988) · Zbl 0671.34053
[11] M. Pakdemirli, A.Z. Sahin, Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press); M. Pakdemirli, A.Z. Sahin, Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press) · Zbl 1114.80003
[12] Bluman, G.; Kumei, S., Symmetries and Differential Equations (1989), Springer-Verlag: Springer-Verlag New York · Zbl 0698.35001
[13] Olver, P., Applications of Lie Groups to Differential Equations (1986), Springer-Verlag: Springer-Verlag New York
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