Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates. (English) Zbl 1152.80327

Siddiqui, A. M.; Zeb, A.; Ghori, Q. K.; Benharbit, A. M.

Chaos Solitons Fractals 36, No. 1, 182-192 (2008).

Summary: The present paper studies the heat transfer flow of a third grade fluid between two heated parallel plates for the constant viscosity model. Three flow problems, namely plane Couette flow, plane Poiseuille flow and plane Couette-Poiseuille flow have been considered. In each case the non-linear momentum equation and the energy equation have been solved using the homotopy perturbation method. Explicit analytical expressions for the velocity field and the temperature distribution have been derived.

MSC:

80M25	Other numerical methods (thermodynamics) (MSC2010)
35Q35	PDEs in connection with fluid mechanics

References:

[1]	Abbasbandi, S., Application of he’s homotopy perturbation method for Laplace transform, Chaos, solitons & fractals, 30, 5, 1206-1212, (2006) · Zbl 1142.65417
[2]	He, J.H., An approximation solution technique depending upon an artificial parameter, Commun nonlinear sci numer simulat, 3, 2, 92, (1998)
[3]	He, J.H., Homotopy perturbation techniques comput. methods, Appl mech engrg, 178, 257, (1999)
[4]	He, J.H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int J nonlinear mech, 35, 1, 527, (2000)
[5]	He, J.H., Homotopy perturbation method a new nonlinear analytical technique, Appl math comput, 135, 73, (2000)
[6]	He, J.H., Asymptotology by homotopy perturbation method, Appl math comput, 15, 3, 591, (2004) · Zbl 1061.65040
[7]	He, J.H., Comparison of homotopy perturbation and homotopy analysis method, Appl math comput, 156, 527, (2004) · Zbl 1062.65074
[8]	He, J.H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl math comput, 151, 1, 287, (2004) · Zbl 1039.65052
[9]	He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos, solitons & fractals, 26, 3, (2005)
[10]	He, J.H., Homotopy perturbation method for bifurcation of nonlinear problems, Int J nonlinear sci numer simulat, 6, 2, 207, (2005) · Zbl 1401.65085
[11]	He, J.H., Homotopy perturbation method for solving boundary value problems, Phys lett A, 350, 1-2, 87-88, (2006) · Zbl 1195.65207
[12]	He, J.H., Some asymptotic methods for strongly nonlinear equations, Int J mod phys, 20, 10, 1141-1199, (2006) · Zbl 1102.34039
[13]	He, J.H., Newton-like method for solving algebraic equations, Commun nonlinear sci numer simulat, 3, 2, 106, (1998) · Zbl 0918.65034
[14]	Massoudi, M.; Christie, I., Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe, Int J nonlinear mech, 30, 5, 687-699, (1995) · Zbl 0865.76005
[15]	Siddiqui, A.M.; Ahmed, M.; Ghori, Q.K., Couette and Poiseuille flows for non-Newtonian fluids, Int J nonlinear sci numer simulat, 7, 1, 15, (2006) · Zbl 1401.76018
[16]	Siddiqui AM, Ahmed M, Ghori QK. Thin film flow of non-Newtonian fluids on a moving belt. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2006.01.101. · Zbl 1129.76009
[17]	Siddiqui, A.M.; Mahmood, R.; Ghori, Q.K., Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phy lett A, 352, 404-410, (2006) · Zbl 1187.76622
[18]	Siddiqui, A.M.; Mahmood, R.; Ghori, Q.K., Thin film flow of a third grade fluid on a moving belt by he’s homotopy perturbation method, Int J nonlinear sci numer simulat, 7, 1, 7, (2006) · Zbl 1187.76622
[19]	Siddiqui AM, Mahmood R, Ghori QK. Thin film flow of a third grade fluid on an inclined plane. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2006.05.026.
[20]	Tsai CY, Novack M, Roffle G. Rheological and heat transfer characteristics of flowing coal-water mixtures. Final report, DOE/MC/23255-2763, 1988.