zbMATH — the first resource for mathematics

The effect of transpiration on self-similar boundary layer flow over moving surfaces. (English) Zbl 1213.76064
Summary: The simultaneous effects of normal transpiration through and tangential movement of a semi-infinite plate on self-similar boundary layer flow beneath a uniform free stream is considered. The flow is therefore governed by a plate velocity parameter \(\lambda \) and a transpiration parameter \(\mu \) and the computed wall shear stress parameter is \(f''(0)\). Dual solutions are found for each value of \(\mu \) in \(\lambda -f''(0)\) parameter space. It is shown that the range of known dual solutions for zero transpiration increases with suction and decreases with blowing. A stability analysis for this self-similar flow reveals that, for each value of \(\mu \), lower solution branches are unstable while upper solution branches are stable.

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
Full Text: DOI
[1] Klemp, J.B.; Acrivos, A.A., A method for integrating the boundary-layer equations through a region of reverse flow, J. fluid mech., 53, 177-199, (1972) · Zbl 0242.76019
[2] Klemp, J.B.; Acrivos, A.A., A moving-wall boundary layer with reverse flow, J. fluid mech., 76, 363-381, (1976) · Zbl 0344.76026
[3] Hussaini, M.Y.; Lakin, W.D.; Nachman, N., On similarity solutions of a boundary layer problem with an upstream moving wall, SIAM J. appl. math., 47, 699-709, (1987) · Zbl 0634.76034
[4] Riley, N.; Weidman, P.D., Multiple solutions of the falkner – skan equation for flow past a stretching boundary, SIAM J. appl. math., 49, 1350-1358, (1989) · Zbl 0682.76026
[5] Cheng, P., Combined free and forced convection flow about inclined surfaces in porous media, Int. J. heat mass transfer, 20, 807-814, (1977) · Zbl 0387.76076
[6] Merkin, J.H., Mixed convection boundary layer flow on a vertical surface in a saturated porous medium, J. engng. math., 14, 301-313, (1980) · Zbl 0433.76078
[7] Merkin, J.H., On dual solutions occurring in mixed convection in a porous medium, J. engng. math., 20, 171-179, (1985) · Zbl 0597.76081
[8] Panton, R.L., Incompressible flow, (1996), Wiley New York
[9] Rosenhead, L., Laminar boundary layers, (1963), Clarendon Press Oxford · Zbl 0115.20705
[10] Abramowitz, M.; Stegun, I., Handbook of mathematical functions, (1972), U.S. Government Printing Office Washington
[11] A A. Griffith and F.W. Meredith, Royal Aircraft Establishment Report No. E 3501, 1936.
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.