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Moghimi, S. M.; Domairry, G.; Soleimani, Soheil; Ghasemi, E.; Bararnia, H.

Application of homotopy analysis method to solve MHD Jeffery-Hamel flows in non-parallel walls. (English) Zbl 1316.76078

Adv. Eng. Softw. 42, No. 3, 108-113 (2011).
Summary: The MHD Jeffery-Hamel flows in non-parallel walls are investigated analytically for strongly nonlinear ordinary differential equations using homotopy analysis method (HAM). Results for velocity profiles in divergent and convergent channels are presented for various values of Hartmann and Reynolds numbers. The convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. Comparison between HAM and numerical solutions showed excellent agreement.

Cited in 13 Documents

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics

Keywords:

MHD Jeffery-Hamel flows; HAM; nonlinear ordinary differential equations; numerical solutions; non-parallel walls

Software:

Ode15s
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\textit{S. M. Moghimi} et al., Adv. Eng. Softw. 42, No. 3, 108--113 (2011; Zbl 1316.76078)
Full Text: DOI

References:

[1] Jeffery, G. B.: The two-dimensional steady motion of a viscous fluid, Phil mag 6, 455-465 (1915) · JFM 45.1088.01
[2] Hamel, G.: Spiralförmige bewgungen zäher flüssigkeiten, Jahresber deutsch math-verein 25, 34-60 (1916) · JFM 46.1255.01
[3] Rosenhead, L.: The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc R soc A 175, 436-467 (1940) · Zbl 0025.37501
[4] Batchelor K. An introduction to fluid dynamics. Cambridge University Press; 1967. · Zbl 0152.44402
[5] SadriRM. Channel entrance flow. Ph.D. thesis, Department of Mechanical Engineering, The University of Western Ontario; 1997.
[6] Sobey, I. J.; Drazin, P. G.: Bifurcations of two-dimensional channel flows, J fluid mech 171, 263-287 (1986) · Zbl 0609.76050
[7] Hamadiche, M.; Scott, J.; Jeandel, D.: Temporal stability of Jeffery – Hamel flow, J fluid mech 268, 71-88 (1994) · Zbl 0809.76039
[8] Fraenkel, L. E.: Laminar flow in symmetrical channels with slightly curved walls. I: on the Jeffery – Hamel solutions for flow between plane walls, Proc R soc lond A 267, 119-138 (1962) · Zbl 0104.42403
[9] Makinde, O. D.; Mhone, P. Y.: Hermite-Padé approximation approach to MHD Jeffery – Hamel flows, Appl math comput 181, 966-972 (2006) · Zbl 1102.76049
[10] Schlichting, H.: Boundary-layer theory, (2000) · Zbl 0940.76003
[11] Rathy, R. K.: An introduction to fluid dynamics, (1976)
[12] Mcalpine, A.; Drazin, P. G.: On the spatio-temporal development of small perturbations of Jeffery – Hamel flows, Fluid dyn res 22, 123-138 (1998) · Zbl 1051.76554
[13] Goldstein S, editor. Modem developments in fluid dynamics, vol. 1, Oxford; 1938.
[14] Axford, W. I.: The magnetohydrodynamic Jeffrey – Hamel problem for a weakly conducting fluid, J mechanics appl math 14, No. 3, 335-351 (1961) · Zbl 0106.40801
[15] Liao, S. J.: An explicit, totally analytic approximate solution for Blasius viscous flow problems, J non-linear mech 34, 759-778 (1999) · Zbl 1342.74180
[16] Liao, S. J.: A uniformly valid analytic solution of two-dimensional viscous flow over a semiinfinite flat plate, J fluid mech 385, 101-128 (1999) · Zbl 0931.76017
[17] Bararnia, H.; Ghotbi, Abdoul R.; Domairry, G.: On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium, Commun nonlinear sci numer simul 14, 2689-2701 (2009) · Zbl 1221.76138
[18] Abdoul, R. Ghotbi; Bararnia, H.; Domairry, G.; Barari, A.: Investigation of a powerful analytical method into natural convection boundary layer flow, Commun nonlinear sci numer simulat 14, 2222-2228 (2009) · Zbl 1221.76145
[19] Bararnia, H.; Ghasemi, E.; Domairry, G.; Soleimani, S.: Behavior of micropolar flow due to linear stretching of porous sheet with injection and suction, Adv eng software 41, 893-897 (2010) · Zbl 1346.76192
[20] Shampine, L. F.; Corless, R. M.: Initial value problems for odes in problem solving environments, J comput appl math 125, No. 1 – 2, 31-40 (2000) · Zbl 0971.65062
[21] Fehlberg E. Low-order classical Runge – Kutta formulas with stepsize control, NASA TR R-315; 1982.
[22] Schlichting, H.: Boundary-layer theory, (2000) · Zbl 0940.76003
[23] Liao, S. J.: Beyond perturbation: introduction to homotopy analysis method, (2003)
[24] Liao, S. J.: On the homotopy analysis method for nonlinear problems, Appl math comput 47, 499-513 (2004) · Zbl 1086.35005
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.