Numerical solution of steady viscous flow of a micropolar fluid driven by injection between two porous disks. (English) Zbl 1099.76065
Summary: Steady laminar incompressible two-dimensional flow of a micropolar fluid between two porous coaxial disks is considered. To describe the working fluid, we use the micropolar model given by A. C. Eringen [J. Math. Mech. 16, 118ff (1966)]. The governing equations of motion are reduced to a set of nonlinear coupled ordinary differential equations using Berman similarity transformation. The SOR iterative method is used to solve the differential equations numerically. For higher-order accuracy, the results obtained are further refined and enhanced by Richardson extrapolation method. The results on micropolar fluids are compared on different grid sizes.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 76A05 | Non-Newtonian fluids |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
References:
| [1] | Berman, A. S., Laminar flow in channels with porous walls, J. Appl. Phys., 24, 1232-1235 (1953) · Zbl 0050.41101 |
| [2] | Cox, S. M., Analysis of steady flow in a channel with one porous wall, or with accelerating walls, SIAM. J. Appl. Math., 51, 2, 429-438 (1991) · Zbl 0726.76035 |
| [3] | Brady, J. F., Flow development in a porous channel and tube, Phys. Fluids, 27, 1061-1067 (1984) |
| [4] | Shrestha, G. M.; Terrill, R. M., Laminar flow with large injection through parallel and uniformly porous walls of different permeability, Quart. J. Mech. Appl. Math., 21, 4, 413-432 (1968) · Zbl 0187.50903 |
| [5] | 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 |
| [6] | Terrill, R. M., Laminar flow in a uniformly porous channel with large injection, Aeronaut. Quart., 15, 299-310 (1965) |
| [7] | Robinson, W. A., 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) · Zbl 0325.76035 |
| [8] | Elcrt, A. R., On the radial flow of a viscous fluid between porous disks, Arch. Rat. Mech. Anal., 61, 91-96 (1976) · Zbl 0347.76022 |
| [9] | Rasmussen, H., Steady viscous flow between two porous disks, Z. Angew. Math. Phys., 21, 187 (1970) |
| [10] | Eringen, A. C., Theory of micropolar fluids, J. Math. Mech., 16, 118 (1966) · Zbl 0145.21302 |
| [11] | Guram, G. S.; Anwar, M., Micropolar flow due to a rotating disc with suction and injection, ZAMM, 61, 589-605 (1981) · Zbl 0481.76009 |
| [12] | Kelson, N. A.; Desseaux, A.; Farrell, T. W., Micropolar flow in a porous channel with high mass transfer, ANZIAM J., 44, E, C479-C495 (2003) · Zbl 1123.76362 |
| [13] | Anwar Kamal, M.; Hussain, S., Steady flow of a micropolar fluid in a channel/tube with an accelerating surface velocity, J. Nat. Sci. Math., 34, 1, 23-40 (1994), PK ISSN 0022-2941 · Zbl 0865.76003 |
| [14] | Anwar Kamal, M.; Hussain, S., Stretching a surface in a rotating micropolar fluid, Int. J. Sci. Technol., 30-36 (1994), (Spring Hall) |
| [15] | Gerald, C. F., Applied Numerical Analysis (1974), Addison-Wesley Publishing Company: Addison-Wesley Publishing Company Reading, Massachusetts · Zbl 0197.42901 |
| [16] | Milne, W. E., Numerical Solutions of Different Equations (1953), John Willey & Sons, Inc.: John Willey & Sons, Inc. New York · Zbl 0050.12202 |
| [17] | Hildebrand, F. B., Introduction to Numerical Analysis (1978), Tata McGraw Hill Publishing Company, Ltd. · Zbl 0070.12401 |
| [18] | Syed, K. S.; Tupholme, G. E.; Wood, A. S., Iterative solution of fluid flow in finned tubes, (Taylor, C.; Cross, J. T., Proceedings of the 10th International Conference on Numerical Methods in Laminar and Turbulent Flow (1997), Pineridge Press: Pineridge Press Swansea, UK), 429-440 |
| [19] | Deuflhard, P., Order and step-size control in extrapolation methods, Numer. Math., 41, 399-422 (1983) · Zbl 0543.65049 |
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