Conducting dusty fluid flow through a constriction in a porous medium
-
2016-02-10 https://doi.org/10.14419/ijamr.v5i1.5581 -
Bessel function, Dusty fluid, Naviers Strokes equations, Porous media. -
Abstract
The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.
-
References
[1] P. G. Saffman, On the stability of laminar flow of a dusty gas, Journal of Fluid Mechanics, 13 (1962), 120-128.
[2] D. H. Michael and D. A. Miller, Plane parallel flow of a dusty gas, Mathematika, 13 (1966), 97-109.
[3] Brent E. Sleep, Modelling transient organic vapor transport in porous media with the dusty gas model, Advances in Water Resources, 22, 3, (1998), 247-256.
[4] P. Mitra and P. Bhattacharyya, Unsteady hydromagnetic laminar flow of a conducting dusty fluid between two parallel plates started impulsively from rest, Acta Mechanica, 39 (1981), 171-182.
[5] K. R. Madhura and M. S. Uma, Flow of An Unsteady Conducting Dusty Fluid Through A Channel of Triangular Cross-section, International Journal of Pure and Applied Mathematical Sciences, 6 (2013), 273-298.
[6] A. J. Chamka, Unsteady flow of an electrically conducting dusty gas in a channel due to an oscillating pressure gradient, Applied Mathematical Modelling, 21 (1997), 287-292.
[7] A. J. Chamka, The Stokes Problem for a Dusty Fluid in the Presence of Magnetic Field, Heat Generation and Wall Suction Effects, International Journal of Numerical Methods for Heat and Fluid Flow, 10 (2000), 116-133.
[8] Lokenath Debnath and A. K. Ghosh, On unsteady hydromagnetic flows of a dusty Fluid between Two Oscillating Plates, Journal of Appllied Scientific Research, 45 (1988), 353-365.
[9] Nicholas Mutua, Ishmail Musyoka, Mathew Kinyanjui and Jackson Kioko, Magnetohydrodynamic Free Convention Flow of a Heat Generating Fluid past a Semi-Infinite Vertical Porous Plate with Variable Suction, International Journal of Applied Mathematical Research, 2 (2013), 345-351.
[10] C. S. Bagewadi and B. J. Gireesha, A study of two dimensional unsteady dusty fluid flow under varying pressure gradient, Tensor, N.S., 64 (2003), 232-240.
[11] K. R. Madhura, B. J. Gireesha and C. S. Bagewadi, Exact solutions of unsteady dusty fluid flow through porous media in an open rectangular channel, Advances in Theoretical and Applied Mechanics, 2 (2009),1-7.
[12] D. F. Young, Effect of a time-dependent stenosis on flow through a tube, Journal of Engineering and Industrial ransactions, 90 (1968),248-254.
[13] B. E. Morgan, and D. F. Young, An integral method for the analysis of flow in arterial stenosis. Bulletin of Mathematical Biology, 36 (1974), 39-53.
[14] R. N. Pralhad and D. H. Schultz, Two-layered poiseuille flow model for blood flow through arteries of small diameter and arterioles, Biorehology, 25, 5, (1988), 715-726.
[15] R. N. Pralhad and D.H. Schultz, Modeling of arterial stenosis and its applications to blood diseases, Mathematical Biosciences, 190 (2004), 203-220.
[16] R. Ponalagusamy, Blood flow through an artery with mild stenosis: A two layered model, different shapes of stenosis and slip velocity at the wall, Journal of Applied Sciences, 7 (2007), 1071-1077.
[17] P. Chaturani and P. N. Kaloni, Two-layered poiseuille flow model for blood flow through arteries of small diameter and arterioles, Biorehology, 13 (1976), 243-250.
[18] P. Chaturani and V. S. Upadhya, A two-layered model for blood flow through small diameter tubes, Biorehology, 16 (1979), 109-118.[19] J. C. Mishra and S. Chakravarty, Flow in arteries in the presence of stenosis, Journal of Biomechanics, 19 (1986), 907-918.
[20] J. C. Mishra and B. K. Kar, Momentum integral method for studying flow characterstics of blood through a stenosed vessel, Biorheology, 26 (1989), 23-35.
[21] A. D. Patel, I. A. Salehbhai, J. Banerjee, V. K. Katiyar, A. K. Shukla, An analytical soluiton of fluid flow through narrowing systems, Italian Journal of Pure and Applied Mathematics, 29 (2012), 63-70.
[22] M. S. Uma, K. R.Madhura, Analytical solutions for a dusty fluid flow through a narrowing channel in a porous medium, Advances and Applications in Fluid Mechanics, 16 (2014), 2017-2021.
-
Downloads
-
How to Cite
K R, M., & M S, U. (2016). Conducting dusty fluid flow through a constriction in a porous medium. International Journal of Applied Mathematical Research, 5(1), 29-38. https://doi.org/10.14419/ijamr.v5i1.5581Received date: 2015-11-26
Accepted date: 2016-01-28
Published date: 2016-02-10