Approximation approach to multiple singularities of flow through a porous pipe with decelerating wall
DOI:
https://doi.org/10.3329/jname.v9i1.9283Keywords:
Multiple singularities, porous pipe, decelerating wall, bifurcation, approximation methodsAbstract
The multiple singularity behaviour of flow through a porous pipe with decelerating wall is numerically studied in the present paper. The behaviour of the Riccati equation is introduced as a model problem. Then the steady axisymmetric flow of a viscous incompressible fluid driven along a pipe by the combined effect of the wall deceleration and suction is investigated. Our approach uses the power series in order to observe the instability of the problems. The series is then summed by using various generalizations of the Pade´-Hermite approximants. Analysis based on approximate method suggests that the convergence of the series of stream-function, skin friction and centerline axial velocity in powers of Reynolds number is limited by a number of singularities. The location and nature of the singularities in the real plane are presented. The bifurcations of skin friction and centerline axial velocity are also depicted graphically.
DOI: http://dx.doi.org/10.3329/jname.v9i1.9283
Journal of Naval Architecture and Marine Engineering 9(2012) 35-42
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Alam, M. S. and Khan, M. A. H., (2010): Critical behaviour of the MHD flow in convergent-divergent channels, Journal of Naval Architecture and Marine Engineering, Vol. 7, No. 2, pp. 83-93.
Banks, W. H. H., Drazin, P. G., and Zaturska, M. B. (1988): On perturbation of Jeffery-Hamel flow, Journal of Fluid Mechanics, Vol. 186, pp.559-581.
Bender, C. and Orszag, S.A.(1978): Advanced Mathematical Methods for Scientists
and Engineers, McGraw-Hill, New York.
Berman, A. S.(1953):Laminar flow in channels with porous walls, Journal of Applied
Physics, Vol. 24, pp.1232-1235.
Brady, J. F. and Acrivos, J. (1981): Steady flow in a channel or tube with an
accelerating surface velocity. An exact solution to the Navier-Stokes equations with
reverse flow, Journal of Fluid Mechanics, Vol. 112, pp. 127-150.
Brady, J. F. (1984): Flow development in a porous channel and tube. Phys. Fluids
Vol.27, pp. 1061-1067.
Domb, C. and Sykes, M. F. (1957): On the susceptibility of a ferromagnetic above the curie point, Proceedings of the Royal Society of London, Ser A Vol. 240, pp. 214-228.
Fraenkel, L. E. (1962): Laminar flow in symmetrical channels with slightly curved walls. I: On the Jeffery-Hamel solutions for flow between plane walls, Proceedings of the Royal Society of London, Vol. 267, pp. 119-138.
Hamel, G., (1916): Spiralförmige Bewgungen Zäher Flüssigkeiten, Jahresbericht der Deutschen Math. Vereinigung, Vol. 25, pp. 34-60.
Jeffery, G. B., (1915): The two-dimensional steady motion of a viscous fluid, Philosophical Magazine, Vol. 6, pp. 455-465.
Khan, M.A.H., (2002): High-Order Differential Approximants, Journal of Computational and Applied Mathematics , Vol. 149, pp. 457-468.
Khan, M.A.H., Drazin, P. G., and Tourigny, Y., (2003): The summation of series in several variable and its applications in fluid dynamics, Fluid Dynamics Research, Vol. 33, pp. 191-205.
Kayvan, S., Navid K., and Seyed-Mohammad, T.(2007): Magnetohydrodynamic (MHD) flows of viscoelastic fluids in converging/diverging channels, International Journal of Engineering Science, Vol.45, No.11, pp. 923-938.
Makinde, O. D., (1997): Steady flow in a linearly diverging asymmetrical channel, Computer Assisted Mechanics and Engineering Sciences, Vol. 4, pp. 157-165.
Makinde, O. D., (1999): Extending the Utility of Perturbation Series in Problems of
Laminar Flow in a Porous Pipe and a Diverging Channel, Journal of Australian
Mathematical Society, Ser. B, Vol. 41, pp. 118-128.
Makinde, O. D., (2006): Hermite-Pade' Approximation approach to Hydromagnetic flows in convergent-divergent channels, Applied Mathematics and Computation, Vol. 181, No. 2, pp. 966-972.
Sobey, I. J., and Drazin, P. G., (1986): Bifurcations of two-dimensional channel flows, Journal of Fluid Mechanics, Vol. 171, pp. 263-287.
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