×

zbMATH — the first resource for mathematics

On accelerated flows of an Oldroyd-B fluid in a porous medium. (English) Zbl 1154.76317
Summary: In this work, the problems dealing with unsteady unidirectional flows of an Oldroyd-B fluid in a porous medium are investigated. By using modified Darcy’s law of an Oldroyd-B fluid, the equations governing the flow are modelled. Employing Fourier sine transform, the analytic solutions of the modelled equations are developed for the following two problems: (i) constant accelerated flow, (ii) variable accelerated flow. Explicit expressions for the velocity field and adequate tangential stress are obtained in each case. The solutions for Newtonian, second grade and Maxwell fluids in a porous medium appear as the limiting cases of the present analysis.

MSC:
76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Asghar, S.; Parveen, S.; Hanif, S.; Siddique, A.M.; Hayat, T., Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid, Int. J. eng. sci., 41, 609-619, (2003) · Zbl 1211.76138
[2] Baris, S., Steady flows of an Oldroyd 4-constant fluid in a corner region formed by two planes, Turk J. engin. environ. sci., 25, 587-594, (2001)
[3] Baris, S., Injection of a non-Newtonian fluid through one side of a long vertical channel, Acta mech., 151, 163-170, (2001) · Zbl 0992.76011
[4] Baris, S.; Dokuz, M.S., Three dimensional stagnation point flow of a second grade fluid towards a moving plate, Int. eng. sci., 44, 49-58, (2006)
[5] Fetecau, C.; Fetecau, C., Decay of potential vortex in an Oldroyd-B fluid, Int. J. eng. sci., 43, 340-351, (2005) · Zbl 1211.76008
[6] Fetecau, C.; Fetecau, C., Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section, Int. J. non-linear mech., 40, 1214-1219, (2005) · Zbl 1287.76045
[7] Fetecau, C.; Fetecau, C., On some axial Couette flows of non-Newtonian fluids, Z. angew. math. phys., 56, 1098-1106, (2005) · Zbl 1096.76003
[8] Fetecau, C.; Fetecau, C., Starting solutions for some unsteady unidirectional flows of a second grade fluid, Int. J. eng. sci., 43, 781-789, (2005) · Zbl 1211.76032
[9] C. Fetecau, S.C. Prasad, K.R. Rajagopal, A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid, Appl. Math. Model. 31 (2007) 647-654. · Zbl 1287.76047
[10] Hayat, T.; Kara, A.H., Couette flow of a third grade fluid with variable magnetic field, Math. comput. modell., 43, 132-137, (2006) · Zbl 1105.76007
[11] T. Hayat, S.B. Khan, M. Khan, The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium, Non-Linear Dyn. 47 (2007) 353-362. · Zbl 1180.76071
[12] Liao, S., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J. fluid mech., 488, 189-212, (2003) · Zbl 1063.76671
[13] Tan, W.C.; Masuoka, T., Stokes first problem for a second grade fluid in a porous half space with heated boundary, Int. J. non-linear mech., 40, 515-522, (2005) · Zbl 1349.76830
[14] Tan, W.C.; Masuoka, T., Stokes first problem for an Oldroyd-B fluid in a porous half space, Phys. fluid, 17, 023101-023107, (2005) · Zbl 1187.76517
[15] Vafai, K.; Tien, C.L., Boundary and inertia effects on flow and heat transfer in porous media, Int. J. heat mass transfer, 24, 195-203, (1981) · Zbl 0464.76073
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.