Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls. (English) Zbl 1270.76081
Summary: In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method is employed to obtain the expressions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 76M55 | Dimensional analysis and similarity applied to problems in fluid mechanics |
Keywords:
homotopy analysis method; expanding or contracting wall; asymmetric laminar flow; porous channel; expansion ratioReferences:
| [1] | Berman, A.S.: Laminar flow in channels with porous walls. Journal of Applied Physics 24, 1232–1235 (1953) · Zbl 0050.41101 · doi:10.1063/1.1721476 |
| [2] | Terrill, R.M., Thomas, P.W.: Laminar flow in a uniformly porous pipe. Applied Science Research 21, 37–67 (1969) · Zbl 0179.56904 · doi:10.1007/BF00411596 |
| [3] | Terrill, R.M.: On some exponentially small terms arising in flow through a porous pipe. The Quarterly Journal of Mechanics and Applied Mathematics 26, 347–354 (1973) · Zbl 0276.76048 · doi:10.1093/qjmam/26.3.347 |
| [4] | Terrill, R.M.: Laminar flow in a uniformly porous channel. Article title. The Aeronautical Quarterly 15, 299–310 (1964) |
| [5] | Robinson, W.A.: The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls. Journal of Engineering Mathematics 10, 23–40 (1976) · Zbl 0325.76035 · doi:10.1007/BF01535424 |
| [6] | Lu, C.: On the asymptotic behavior of laminar flow through a porous pipe. In: Proceeding of the First World Congress of Nonlinear Analysis, Tampa, Florida, 201–209 (1996) · Zbl 0846.34021 |
| [7] | Terrill, R.M., Shrestha, G.M.: Laminar flow through parallel and uniformly porous walls of different permeability. ZAMP 16, 470–482 (1965) · Zbl 0151.41204 · doi:10.1007/BF01593923 |
| [8] | Chang, H.N., Ha, J.S., Park, J.K., et al.: Velocity field of pulsatile flow in a porous tube. Journal of Biomechanics 22, 1257–1262 (1989) · doi:10.1016/0021-9290(89)90228-5 |
| [9] | Uchida, S, Aoki, H.: Unsteady flows in a semi-infinite contract ing or expanding pipe. Journal of FluidMechanics 82, 371–387 (1977) · Zbl 0367.76100 · doi:10.1017/S0022112077000718 |
| [10] | Ohki, M.: Unsteady flows in a porous, elastic, circular tube-1 the wall contracting or expanding in an axial direction. Bulletin of the JSME 23, 679–686 (1980) · doi:10.1299/jsme1958.23.679 |
| [11] | Goto, M., Uchida, S.: Unsteady flows in a semi-infinite expanding pipe with injection through wall. Japan Society for Aeronautical and Space Science 33, 14–27 (1990) |
| [12] | Bujurke, N.M., Pai, N.P, Jayaraman, G.: Computer extended series solution for unsteady flow in a contracting or expanding pipe. IMA Journal of Applied Mathematics 60, 151–165 (1998) · Zbl 0920.76065 · doi:10.1093/imamat/60.2.151 |
| [13] | Ma, Y., van Moorhem, W.K., Shorthill, R.W.: Experimental investigation of velocity coupling in combustion instability. Journal of Propulsion and Power 7, 692–699 (1991) · doi:10.2514/3.23381 |
| [14] | Ma, Y., van Moorhem, W.K., Shorthill. R.W.: Innovative method of investigating the role of turbulence in the velocity coupling phenomenon. ASME Journal of Vibration and Acoustics 112, 550–555 (1990) · doi:10.1115/1.2930141 |
| [15] | Barron, J., Majdalani, J., van Moorhem, W.K.: A novel investigation of the oscillatory field over a transpiring surface. Journal of Sound and Vibration 235, 281–297 (2000) · doi:10.1006/jsvi.2000.2920 |
| [16] | Majdalani, J., Zhou, C., Dawson, C.A.: Two-dimensional viscous flows between slowly expanding or contracting walls with weak permeability. Journal of Biomechanics 35, 1399–1403 (2002) · doi:10.1016/S0021-9290(02)00186-0 |
| [17] | Majdalani, J., Zhou, C.: Moderate-to-large injection and suction driven channel flows with expanding and contracting walls. ZAMM. Zeitschrift fur Angewandte Mathematik und Mechanik 83, 181–196 (2003) · Zbl 1116.76348 · doi:10.1002/zamm.200310018 |
| [18] | Dauenhauer, C.E., Majdalani, J.: Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Physics of Fluids 15, 1485–1495 (2003) · Zbl 1186.76126 · doi:10.1063/1.1567719 |
| [19] | Asghar, S., Mushtaq, M., Hayat, T.: Flow in a slowly deforming channel with weak permeability: an analytical approach. Nonlinear Analysis: Real World Applications 11, 555–561 (2010) · Zbl 1287.76053 · doi:10.1016/j.nonrwa.2009.01.049 |
| [20] | Si, X.H., Zheng L.C., Zhang X.X., et al.: Asymptotic solution for unsteady flow in expanding or contracting channel with large suction Reynolds number. Journal of University of Science and Technology Beijing 31 1463–1466 (2009) (in Chinese) |
| [21] | Villarroel, F., Lanham, C.E., Bischoff, K.B., et al.: Gas transfer to blood flowing in semipermeable tubes under steady and pulsatile flow cinditions. CEP Symp. Ser 67, 94–104 (1971) |
| [22] | Wang, C.Y.: Pulsatile flow in a porous channel. Transactions of the ASME, Journal of Applied Mechanics 38, 553–555 (1971) · doi:10.1115/1.3408822 |
| [23] | Bhatnager, R.K.: Fluctuating flow of a viscoelastic fluid in a porous channel. Transactions of the ASME, Journal of Applied Mechanics 46, 21–25 (1979) · Zbl 0404.76004 · doi:10.1115/1.3424507 |
| [24] | Muhammad Ashraf, Anwar Kamal, M., Syed, K.S.: Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel. Computers & Fluids 38, 1895–1902 (2009) · Zbl 1242.76009 · doi:10.1016/j.compfluid.2009.04.009 |
| [25] | Liao, S.J.: Beyond Perturbation: Introduction to Homotopy Analysis Method. Boca. Raton: Chapman Hall/CRC Press (2003) |
| [26] | Liao, S.J: On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation 147, 499–513 (2004) · Zbl 1086.35005 · doi:10.1016/S0096-3003(02)00790-7 |
| [27] | Hayat, T., Khan, M.: Homotopy solution for a generalized second grade fluid past a porous plate. Nonlinear Dynamics 42, 395–405 (2005) · Zbl 1094.76005 · doi:10.1007/s11071-005-7346-z |
| [28] | Hayat, T., Khan, M., Asghar, S.: Magnetohydrodynamic flow of an oldroyd 6-constant fluid. Applied Mathematics and Computation 155, 417–225 (2004) · Zbl 1126.76388 · doi:10.1016/S0096-3003(03)00787-2 |
| [29] | Hayat, T., Khan, M., Asghar, S., et al.: Transient flows of a second grade fluid. International Journal of Nonlinear Mechanics 39, 1621–1633 (2004) · Zbl 1348.76017 · doi:10.1016/j.ijnonlinmec.2002.12.001 |
| [30] | Abbas, Z., Sajid, M., Hayat, T.: MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theoretical and Computational Fluid Dynamics 20, 229–238 (2006) · Zbl 1109.76065 · doi:10.1007/s00162-006-0025-y |
| [31] | Sajid, M., Hayat, T., Asghar, S.: On the analytic solution of the steady flow of a fourth grade fluid. Physics Letters A 355, 18–26 (2006) · doi:10.1016/j.physleta.2006.01.092 |
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