×

Micropolar flow past a porous stretching sheet. (English) Zbl 0589.76017

Summary: The flow of an incompressible, constant density micropolar fluid past a porous stretching sheet is investigated. The governing boundary layer equations are transformed into a numerically equivalent system of nonlinear ordinary differential equations. The resulting equations are solved numerically using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newtonian algorithm. The flow pattern depends on three nondimensional parameters and a suction (or injection) parameter A. A comparison between the \(A=0\) flow behavior representing an impermeable sheet and fluid flow behavior for the porous sheet (A\(\neq 0)\) is presented with the numerical results illustrated graphically.

MSC:

76A05 Non-Newtonian fluids
76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics

Software:

minpack
Full Text: DOI

References:

[1] Eringen, A. C., Simple microfluids, Int. J. Engng Sci., 2, 205-217 (1964) · Zbl 0136.45003
[2] Eringen, A. C., Theory of micropolar fluids, J. Math. Mech., 16, 1-18 (1966) · Zbl 0145.21302
[3] Peddieson, J. R.J.; McNitt, R. P., Boundary-layer theory for a micropolar fluid, Recent Advances in Engineering Science, Vol. 5, 405-426 (1970)
[4] Willson, A. J., Boundary layers in micropolar fluids, (Proc. Camb. Phil. Soc., 67 (1970)), 469-476 · Zbl 0198.29802
[5] Ahmadi, G., Self-similar solution of incompressible micropolar bondary layer flow over a semi-infinite plate, Int. J. Engng Sci., 14, 639-646 (1976) · Zbl 0329.76041
[6] Kummerer, H., Similar laminar boundary layers in incompressible micropolar fluids, Rheol. Acta, 16, 261-265 (1977) · Zbl 0357.76032
[7] Guram, G. S.; Smith, A. C., Stagnation flow of micropolar fluids with strong and weak interactions, Comput. Math. Appl., 6, 213-233 (1980) · Zbl 0434.76013
[8] Gorla, R. S.R., Micropolar boundary layer flow at a stagnation on a moving wall, Int. J. Engng Sci., 21, 25-33 (1983) · Zbl 0511.76015
[9] Singh, G.; Smith, A. C., Flows of micropolar fluids with suction and injection, Tensor N. S., 27, 131-134 (1973)
[10] Guram, G. S.; Smith, A. C., Micropolar flows with variable injection along a moving rigid wall, Tensor N. S., 29, 259-263 (1975) · Zbl 0295.76004
[11] Guram, G. S.; Anwar, M., Micropolar flow due to a rotating disc with suction and injection, ZAMM, 61, 589-595 (1981) · Zbl 0481.76009
[12] Jena, S. K.; Mathur, M. N., Similarity solutions for laminar free convection flow of a thermomicropolarfluid past a non-isothermal vertical flat plate, Int. J. Engng Sci., 19, 1431-1439 (1981) · Zbl 0476.76084
[13] K. K. Sankara and L. T. Watson, Micropolar flow past a stretching sheet. ZAMP; K. K. Sankara and L. T. Watson, Micropolar flow past a stretching sheet. ZAMP · Zbl 0585.76006
[14] Watson, L. T., Engineering applications of the Chow-Yorke algorithm, Appl. Math. Comput., 9, 111-133 (1981) · Zbl 0481.65029
[15] Watson, L. T.; Li, T. Y.; Wang, C. Y., Fluid dynamics of the elliptic porous slider, J. Appl. Mech., 45, 435-436 (1978)
[16] Wang, C. Y.; Watson, L. T., Squeezing of a viscous fluid between elliptic plates, Appl. Sci. Res., 35, 195-207 (1979) · Zbl 0414.76025
[17] Wang, C. Y.; Watson, L. T., Viscous flow between rotating discs with injection on the porous disc, ZAMP, 30, 773-787 (1979) · Zbl 0426.76032
[18] Watson, L. T., Numerical study of porous channel flow in a rotating system by a homotopy method, J. Comput. Appl. Math., 7, 21-26 (1981) · Zbl 0452.76025
[19] Watson, L. T., A globally convergent algorithm for computing fixed points of
((C^2\) maps, Appl. Math. Comput., 5, 297-311 (1979) · Zbl 0445.65032
[20] Watson, L. T.; Fenner, D., Chow-Yorke algorithm for fixed points or zeros of
((C^2\) maps, ACM Trans. Math. Software, 6, 252-259 (1980) · Zbl 0445.65033
[21] More, J. J.; Garbow, B. S.; Hillstrom, K. E., User guide for MINPACK-1, ANL-80-74 (1980), Argonne National Laboratory
[22] Dennis, J. E.; Schnabel, R., Numerical Methods for Unconstraited Optimization and Nonlinear Equations (1983), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0579.65058
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.