The Effect of Slip Velocity on Unsteady Peristalsis MHD Blood Flow through a Constricted Artery Experiencing Body Acceleration
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Department of Mathematics, M.D. University, Rohtak-, 124001, Haryana, India
A.I.J.H.M. College, Rohtak -, 124001, Haryana, India
Online publication date: 2019-08-09
Publication date: 2019-09-01
International Journal of Applied Mechanics and Engineering 2019;24(3):645-659
In this analysis, we present a theoretical study to examine the combined effect of both slip velocity and periodic body acceleration on an unsteady generalized non-Newtonian blood flow through a stenosed artery with permeable wall. A constant transverse magnetic field is applied on the peristaltic flow of blood, treating it as an elastico-viscous, electrically conducting and incompressible fluid. Appropriate transformation methods are adopted to solve the unsteady non-Newtonian axially symmetric momentum equation in the cylindrical polar coordinate system with suitably prescribed conditions. To validate the applicability of the proposed analysis, analytical expressions for the axial velocity, fluid acceleration, wall shear stress and volumetric flow rate are computed and for having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted with varying values of flow variables, to analyse the influence of the axial velocity, wall shear stress and volumetric flow rate of streaming blood.
Beaver G.S. and Joseph D.D. (1967): Boundary conditions at a naturally permeable wall. – J. Fluid Mech., vol.30, pp.197-207.
Oka S. and Murata T. (1970): A theoretical study of flow of blood in a capillary with permeable wall. – Jpn. J. Appl. Sci., vol.9, pp.345-352.
Saffman P.D. (1971): On the boundary conditions at the surface of a porous medium. – Stud. Appl. Math., vol.50, pp.93-101.
Popel A.S., Regirer S.A. and Usick P.I. (1974): A continuum model of blood flow. – Biorheology, vol.11, pp.427-437.
Yuan S.W. (1976): Foundation of Fluid Mechanics. – New Delhi: Prentice Hall of India Pvt. Ltd..
McDonald D.A. (1979): On steady blood flow through modelled vascular stenosis. – J. Biomech., vol.12, pp.13-20.
Shukla J.B., Parihar R.S. and Rao B.R.P. (1980): Effect of stenosis on non-Newtonian flow of blood in an artery. – Bull. Math. Bio., vol.42, pp.283-294.
Sinha P. and Singh C. (1984): Effects of couple stresses on the blood flow through an artery with mild stenosis. – Biorheology, vol.21, pp.303-315.
Fung Y.C. (1984): Biodynamics - Circulation. – New York: Springer Verlag.
Srivastava L.M. (1985): Flow of couple stress fluid through stenotic blood vessels. – J. Biomech., vol.1, pp.479-485.
Lee T.S. (1990): Numerical studies of fluid flow through tubes with double constrictions. – J. Numer. Methods Fluids, vol.11, pp.1113-1126.
Fung Y.C. (1990): Biodynamics Motion, Flow, Stress and Growth. – New York: Springer Verlag.
Mazumdar J.N. (1992): Biofluid Mechanics. – Singapore: World Scientific.
Misra J.C., Patra M.K. and Misra S.C. (1993): A non-Newtonian model for blood flow through arteries under stenotic conditions. – J. Biomech., vol.26, pp.1129-1141.
Haldar K. and Ghosh S.N. (1994): Effect of a magnetic field on blood flow through an indented tube in the presence of erythrocytes. – Indian J. Pure Appl. Math., vol.25, pp.345-352.
Murata T. (1998): Theoretical analysis of flow properties of aggregating red cell suspensions in narrow horizontal tubes. – Clini. Hemorh., vol.14, pp.519-530.
Chakravarty S. and Mandal P.K. (2001): Two-dimentional blood flow through tapered arteries under stenotic conditions. – Int. J. Non-Linear Mech., vol.36, pp.731-741.
Srivastava V.P. (2003): Flow of a couple stress fluid representing blood through stenotic vessels with a peripheral layer. – Indian J. Pure Appl. Math., vol.34, pp.1727-1740.
Pralhad R.N. and Schultz D.H. (2004): Modelling of arterial stenosis and its applications to blood diseases. – J. Math. Biosci., vol.190, pp.203-220.
Rathod V.P. and Tanveer S. (2009): Pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field. – Bull. Malaysian Math. Sci. Soc., vol.32, pp.245-259.
Varshney G., Katiyar V.K. and Kumar S. (2010): Effect of magnetic field on the blood flow in artery having multiple stenosis. – A numerical Study; Int. J. Eng. Sci. and Technol., vol.2, pp.67-82.
Shit G.C. and Roy M. (2012): Hydro-magnetic pulsatory flow of blood in a constricted porous channel. – A Theoretical Study; Proc. World Congr. Eng., vol.1, pp.83-88.
Rathee R. and Singh J. (2013): Analysis of two- layered model of blood flow through composite stenosed artery in porous medium under the effect of magnetic field. – J. Rajasthan Academy Phys. Sci., vol.12, pp.259-276.
Eldesoky I.M.I. (2014): Unsteady MHD pulsatile blood flow through porous medium in stenotic channel with slip at permeable walls subjected to time dependent velocity (injection/suction). – Walailak J. Sci. Tech., vol.11, No.11, pp.901-922.
Siddiqui S.U., Shah S.R. and Geeta (2014): Effect of body acceleration and slip velocity on the pulsatile flow of casson fluid through stenosed artery. – Adv. Appl. Sci. Res., vol.5, No.3, pp.213-225.
Gaur M. and Gupta M.K. (2015): Unsteady slip flow of blood through constricted artery. – Adv. Appl. Sci. Res., vol.6, pp.49-58.
Elangovan K. and Selvaraj K. (2016): Study of multiple stenosed artery with periodic body acceleration in presence of magnetic field. – Int. J. Sci. Res. Manag., vol.4, No.06, pp.4214-4226.
Malek A. and Horque A. (2017): Hematocrit level on blood flow through a stenosed artery with permeable wall. – Int. J. Appl. Appl. Math., vol.12, No.1, pp.291-304.
Sankad G.C. and Nagathan P.S. (2017): Transport of MHD couple stress fluid through peristalsis in a porous medium under the influence of heat transfer and slip effects. – Int. J. of Appl. Mech. Engg., vol.22, No.2, pp.403-414.
Tripathi B. and Sharma B.K. (2018): Effect of variable viscosity on MHD inclined arterial blood flow with chemical reaction. – Int. J. of Appl. Mech. Engg., vol.23, No.3, pp.767-785.
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