On the Analysis of Laminar Flow of Viscous Fluid through a Porous Channel with Suction/Injection at Slowly Expanding or Contracting Walls

[1] A. S. Berman, “Laminar flow in channels with porous walls,” Journal of Applied Physics, vol. 24, pp. 1232–1235, 1953.

[2] R. M. Terrill, “Laminar flow in a uniformly porous channel,” The Aeronautical Quarterly, vol. 15, pp. 299–310, 1964.

[3] R. M. Terrill, “Laminar flow in a uniformly porous channel with large injection,” Aeronaut. Q. 16, 323–332 (1965)

[4] E. C. Dauenhauer and J. Majdalani, “Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls,” Physics of Fluids, vol. 15, no. 6, pp. 1485–1495, 2003.

[5] J. Majdalani, “The oscillatory channel flow with arbitrary wall injection,” Zeitschrift fur Angewandte Mathematik und Physik, vol. 52, no. 1, pp. 33–61, 2001.

[6]  J. Majdalani and T.-S. Roh, “The oscillatory channel flow with large wall injection,” Proceedings of the Royal Society of London. Series A, vol. 456, no. 1999, pp. 1625–1657, 2000.

[7] J. Majdalani and W. K. van Moorhem, “Multiple-scales solution to the acoustic boundary layer insolid rocket motors,” Journal of Propulsion and Power, vol. 13, no. 2, pp. 186–193, 1997

[8] L. Oxarango, P. Schmitz, and M. Quintard, “Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems,” Chemical Engineering Science,vol.59,no.5, pp. 1039–1051, 2004.

[9] T. A. Jankowski and J. Majdalani, “Symmetric solutions for the oscillatory channel flow with arbitrary suction,” Journal of Sound and Vibration, vol. 294, no. 4, pp. 880–893, 2006.

[10] A. Jankowski and J. Majdalani, “Laminar flow in a porous channel with large wall suction and a weakly oscillatory pressure,” Physics of Fluids, vol. 14, no. 3, pp. 1101–1110, 2002.

[11] Zhou and J. Majdalani, “Improved mean-flow solution for slab rocket motors with regressing walls,” Journal of Propulsion and Power, vol. 18, no. 3, pp. 703–711, 2002.

[12] J. Majdalani and C. Zhou, “Moderate-to-large injection and suction driven channel flows with expanding or contracting walls,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 83, no. 3,pp. 181–196, 2003.

[13] W. A. Robinson, The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls, J. Eng. Math. 10, 23–40 (1976).

[14] M. B. Zaturska, P. G. Drazin, and W. H. H. Banks, “On the flow of a viscous fluid driven along a channel by suction at porous walls,” Fluid Dynamics Research, vol. 4, no. 3, pp. 151–178, 1988.

[15] . H. Si, L. C. Zheng, X. X. Zhang, Y. Chao: Existence of multiple solutions for the laminar flow in a porous channel with suction at both slowly expanding or contracting walls. Int. J. Miner. Metal. Mater. 11, 494-501 (2011)

[16] X. H. Si, L. C. Zheng, X. X. Zhang, M. Li, J. H. Yang, Y. Chao: Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall. Appl. Math. Comput. 218, 3515-3521 (2011)

[17] J. Majdalani, C. Zhou, and C. A. Dawson, “Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability,” Journal of Biomechanics, vol. 35, no. 10, pp. 1399–1403, 2002.

[18] S. Dinarvand, A. Doosthoseini, E. Doosthoseini, and M. M. Rashidi, “Comparison of HAM and HPM methods for Berman’s model of two-dimensional viscous flow in porous channel with wall suction or injection,” Advances in Theoretical and Applied Mechanics, vol. 1, no. 7, pp. 337–347, 2008

[19] J. Xu, Z. L. Lin, S. J. Liao, J. Z. Wu, J. Majdalani: Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Phys. Fluids 22, 053601 (2010).

[20] S. Dinarvand and M. M. Rashidi, “A reliable treatment of a homotopy analysis method for two dimensional viscous flow in a rectangular domain bounded by two moving porous walls,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1502–1512, 2010.

[21] M. G. Sobamowo. Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering 99(2016), 1316–1330.

[22] M. A. Noor, S. T. Mohyud-Din, A. Waheed. Variation of parameters method for solving fifth-order boundary value problems. Appl Math Inf Sci 2008;2:135–41

[23] S. T. Mohyud-Din, M. A. Noor, A. Waheed. Variation of parameter method for solving sixth-order boundary value problems. Commun Korean Math Soc 2009;24:605–15

[24] S. T. Mohyud-Din, N. A. Noor, A. Waheed A. Variation of parameter method for initial and boundary value problems. World Appl Sci J 2010;11:622–39

[25] S. T. Mohyud-Din, M. A. Noor, A, Waheed. Modified variation of parameters method for second-order integro-differential equations and coupled systems. World Appl Sci J 2009;6:1139–46

[26] J. Ramos. On the variational iteration method and other iterative techniques for nonlinear differential equations. Appl Math Comput 2008;199:39–69.

[27] N. Ahmed, S. U. Jan, U. Khan, S. T. Mohyub-Din. Heat transfer analysis of third-grade fluid flow between parallel plates: Analytical solutions. Int. J. Appl. Comput. Math, 2015