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Exact analytical solution of a nonlinear equation arising in heat transfer. (English) Zbl 1235.35273
Summary: This Letter shows that the nonlinear equation arising in heat transfer recently investigated in [D. D. Ganji, Phys. Lett., A 355, No. 4–5, 337–341 (2006; Zbl 1255.80026); S. Abbasbandy, ibid. 360, No. 1, 109–113 (2006; Zbl 1236.80010); H. Tari, D. D. Ganji and H. Babazadeh, ibid. 363, No. 3, 213–217 (2007; Zbl 1197.80059); M. S. H. Chowdhury and I. Hashim, ibid. 372, No. 8, 1240–1243 (2008; Zbl 1217.35089)] is exactly solvable, analyses the equation fully and, furthermore, gives analytic exact solution in implicit form for each value of parameters of equation.

MSC:
35Q79 PDEs in connection with classical thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
35G20 Nonlinear higher-order PDEs
33C05 Classical hypergeometric functions, \({}_2F_1\)
33B15 Gamma, beta and polygamma functions
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References:
[1] Chowdhury, M.S.H.; Hashim, I., Phys. lett. A, 372, 1240, (2008)
[2] Ganji, D.D., Phys. lett. A, 355, 337, (2006)
[3] Tari, Hafez; Ganji, D.D.; Babazadeh, H., Phys. lett. A, 363, 213, (2007)
[4] Abbasbandy, S., Phys. lett. A, 360, 109, (2006)
[5] Magyari, E., Chem. eng. J., 143, 167, (2008)
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