×

Approximate solution for the electrohydrodynamic flow in a circular cylindrical conduit. (English) Zbl 1286.76164

Summary: This paper considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The velocity field was solved using the new homotopy perturbation method (NHPM), considering the electrical field and strength of the nonlinearity. The approximate analytical procedure depends only on two components and polynomial initial condition. The analytical solution is obtained and the numerical results presented graphically. The effects of the Hartmann electric number \(\mathcal H a\) and the strength of nonlinearity \(\alpha\) are discussed and presented graphically. We also compare this method with numerical solution (N.S) and show that the present approach is less computational and is applicable for solving nonlinear boundary value problem (BVP).

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Mckee, R. Watson, J. A. Cuminato, J. Caldwell, and M. S. Chen, “Calculation of electrohydrodynamic flow in a circular cylindrical conduit,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 77, no. 6, pp. 457-465, 1997. · Zbl 0883.76093 · doi:10.1002/zamm.19970770612
[2] J. E. Paullet, “On the solutions of electrohydrodynamic flow in a circular cylindrical conduit,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 79, no. 5, pp. 357-360, 1999. · Zbl 0926.76136 · doi:10.1002/(SICI)1521-4001(199905)79:5<357::AID-ZAMM357>3.0.CO;2-B
[3] A. Mastroberardino, “Homotopy analysis method applied to electrohydrodynamic flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2730-2736, 2011. · Zbl 1221.76151 · doi:10.1016/j.cnsns.2010.10.004
[4] H. Aminikhah and M. Hemmatnezhad, “An efficient method for quadratic Riccati differential equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 4, pp. 835-839, 2010. · Zbl 1221.65193 · doi:10.1016/j.cnsns.2009.05.009
[5] N. A. Khan, A. Ara, and M. Jamil, “An approach for solving the Riccati equation with fractional orders,” Computers & Mathematics with Applications, vol. 61, pp. 2683-2689, 2011. · Zbl 1221.65205 · doi:10.1016/j.camwa.2011.03.017
[6] N. A. Khan, A. Ara, M. Jamil, and N.-U. Khan, “On efficient method for system of fractional differential equations,” Advances in Difference Equations, vol. 2011, Article ID 303472, 2011. · Zbl 1217.65134 · doi:10.1155/2011/303472
[7] J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257-262, 1999. · Zbl 0956.70017
[8] J. H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37-43, 2000. · Zbl 1068.74618 · doi:10.1016/S0020-7462(98)00085-7
[9] J. H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73-79, 2003. · Zbl 1030.34013 · doi:10.1016/S0096-3003(01)00312-5
[10] N. A. Khan, A. Ara, and A. Mahmood, “Approximate solution of time-fractional chemical engineering equations: a comparative study,” International Journal of Chemical Reactor Engineering, vol. 8, article A19, 2010.
[11] N. A. Khan, A. Ara, S. A. Ali, and M. Jamil, “Orthognal flow impinging on a wall with suction or blowing,” International Journal of Chemical Reactor Engineering, vol. 9, article A47, 2011.
[12] N. A. Khan, A. Ara, S. A. Ali, and A. Mahmood, “Analytical study of Navier-Stokes equation with fractional orders using He’s homotopy perturbation and variational iteration methods,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 9, pp. 1127-1134, 2009. · Zbl 06942487
[13] A. M. Wazwaz, “The modified decomposition method and Pade’ approximants for a boundary layer equation in unbounded domain,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 737-744, 2006. · Zbl 1096.65072 · doi:10.1016/j.amc.2005.09.102
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.