Effect of Variable Viscosity on MHD Inclined Arterial Blood Flow with Chemical Reaction
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Department of Mathematics, BITS Pilani (Pilani Campus), Pilani, Rajasthan-, 333031, India
Online publication date: 2018-08-20
Publication date: 2018-08-01
International Journal of Applied Mechanics and Engineering 2018;23(3):767-785
In this paper, we present the mathematical study of heat and mass transfer effects on an arterial blood flow under the influence of an applied magnetic field with chemical reaction. A case of mild stenosis is considered in a non-tapered artery which is inclined at an angle γ from the axis. The variable viscosity of the blood is considered varying with the hematocrit ratio. Governing non-linear differential equations have been solved by using an analytical scheme, homotopy perturbation method to obtain the solution for the velocity, temperature and concentration profiles of the blood flow. For having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted for wall shear stress, velocity, temperature and concentration profiles with varying values of the applied magnetic field, chemical reaction parameter and porosity parameter. The results show that in an inclined artery, the magnitude of the wall shear stress at stenosis throat increases as values of the applied magnetic field increase while it reduces as the values of both the chemical reaction and porosity parameters increase. Contour plots have been plotted to show the variations of the velocity profile of blood flow as the values of the height of the stenosis as well as the influence of the applied magnetic field increase.
Ellahi R., Rahman S.U. and Nadeem S. (2014): Blood flow of Jeffrey fluid in a catherized tapered artery with the suspension of nanoparticles. – Physics Letters A, vol.378, No.40, pp.2973-2980.
Rabby M.G., Razzak A. and Molla M.M. (2013): Pulsatile non-Newtonian blood flow through a model of arterial stenosis. – Procedia Engineering, vol.56, No.5, pp.225-231.
Srivastava V.P. and Saxena M. (1997): Suspension model for blood flow through stenotic arteries with a cell-free plasma layer. – Mathematical Biosciences, vol.139, No.2, pp.79-102.
Falk E., Prediman K.S. and Fuster V. (1995): Coronary plaque disruption. – Circulation, vol.92, No.3, pp.657-671.
Fung Y.C. (2013): Biomechanics: mechanical properties of living tissues. – Springer Science and Business Media.
Ellahi R., Rahman S.U., Gulzar M.M., Nadeem S. and Vafai K. (2014): A mathematical study of non-Newtonian micropolar fluid in arterial blood flow through composite stenosis. – Applied Mathematics and Information Sciences, vol.8, No.4, pp.1567-1573.
Pralhad R.N. and Schultz D.H. (2004). Modeling of arterial stenosis and its applications to blood diseases. – Mathematical Biosciences, vol.190, No.2, pp.203-220.
Baldwin A.L. and Wilson L.M. (1994): Stationary red blood cells induce a negative charge on mucosal capillary endothelium. – American Journal of Physiology-Gastrointestinal and Liver Physiology, vol.266, No.4, pp.G685-G694.
Haik Y., Pai V. and Chen C.J. (1999): Development of magnetic device for cell separation. – Journal of Magnetism and Magnetic Materials, vol.194, No.1, pp.254-261.
Tzirtzilakis E.E. (2005): A mathematical model for blood flow in magnetic field. – Physics of Fluids (1994- present), vol.17, No.7, 077103-077118.
Srivastava N. (2014): Analysis of flow characteristics of the blood flowing through an inclined tapered porous artery with mild stenosis under the influence of an inclined magnetic field. – Journal of Biophysics, 2014:9 pages.
Akbarzadeh P. (2015): Pulsatile magneto-hydrodynamic blood flows through porous blood vessels using a third grade non-Newtonian fluids model. – Computer Methods and Programs in Biomedicine, vol.126, pp.3-19.
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 Journal of Science and Technology, vol.11, No.11, pp.901-922.
Khaled A.R.A. and Vafai K. (2003): The role of porous media in modeling flow and heat transfer in biological tissues. – International Journal of Heat and Mass Transfer, vol.46, No.26, pp.4989-5003.
Shit G.C. and Majee S. (2015): Pulsatile flow of blood and heat transfer with variable viscosity under magnetic and vibration environment. – Journal of Magnetism and Magnetic Materials, No.388, pp.106-115.
Layek G.C., Mukhopadhyay S. and Gorla R.S.R. (2009): Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction. – International Journal of Engineering Science, vol.47, No.5, pp.649-659.
Sinha A. and Misra J.C. (2014): MHD flow of blood through a dually stenosed artery: Effects of viscosity variation, variable hematocrit and velocity-slip. – The Canadian Journal of Chemical Engineering, vol.92, No.1, pp.23-31.
Makinde O.D. and Onyejekwe O.O. (2011): A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity. – Journal of Magnetism and Magnetic Materials, vol.323, No.22, pp.2757-2763.
Mekheimer K.S., Haroun M.H. and El Kot M.A. (2012): Influence of heat and chemical reactions on blood flow through an anisotropically tapered elastic arteries with overlapping stenosis. – Appl. Math, vol.6, No.2, pp.281-292.
El-Sayed M., Akbar A.N.S. and Nadeem S. (2012): Influence of heat and chemical reactions on hyperbolic tangent fluid model for blood flow through a tapered artery with a stenosis. – Heat and Mass Transfer, vol.43, No.1, pp.69-94.
Misra J.C. and Adhikary S.D. (2016): MHD oscillatory channel flow, heat and mass transfer in a physiological fluid in presence of chemical reaction. – Alexandria Engineering Journal, vol.55, No.1, pp.287-297.
Mohyud-Din S.T. and Noor M.A. (2009): Homotopy perturbation method for solving partial differential equations. – Zeitschrift für Naturforschung A, vol.64, No.(3-4), pp.157-170.
Mekheimer K.S. and El Kot M.A. (2008): The micropolar fluid model for blood flow through a tapered artery with a stenosis. – Acta Mechanica Sinica, vol.24, No.6, pp.637-644.
Shukla J.B., Parihar R.S. and Rao B.R.P. (1980): Effects of stenosis on non-newtonian flow of the blood in an artery. – Bulletin of Mathematical Biology, vol.42, No.3, pp.283-294.
Sanyal D.C., Das K. and Debnath S. (2007): Effect of magnetic field on pulsatile blood flow through an inclined circular tube with periodic body acceleration. – Vol.11, pp.43-56.
Ramesh K. (2016): Influence of heat and mass transfer on peristaltic flow of a couple stress fluid through porous medium in the presence of inclined magnetic field in an inclined asymmetric channel. Journal of Molecular Liquids, vol.219, pp.256-271.
Bhatti M.M. and Abbas M.A. (2016): Simultaneous effects of slip and MHD on peristaltic blood flow of Jeffrey fluid model through a porous medium. – Alexandria Engineering Journal, vol.55, No.2, pp.1017-1023.
Nadeem S., Akbar N.S., Hayat T. and Hendi A.A. (2011): Influence of heat and mass transfer on Newtonian biomagnetic fluid of blood flow through tapered porous arteries with a stenosis. – Transport in Porous Media, vol.91, No.1, pp.81-100.
Rao A., Sivaiah S. and Raju R.S. (2012): Chemical reaction effects on an unsteady MHD free convection fluid flow past a semi-infinite vertical plate embedded in a porous medium with heat absorption. – Journal of Applied Fluid Mechanics, vol.5, No.3, pp.63-70.
Zaman A., Ali N., Bég O.A. and Sajid M. (2016): Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery. – International Journal of Heat and Mass Transfer, vol.95, pp.1084-1095.
Thompson B.L., Gilbert R.J., Mejia M., Shukla N., Haverstick D.M., Garner G.T. and Landers J.P. (2016): Hematocrit analysis through the use of an inexpensive centrifugal polyester-toner device with finger-to-chip blood loading capability. – Analytica Chimica Acta, vol.924, pp.1-8.
Sharma S., Singh U. and Katiyar V.K. (2015): Magnetic field effect on flow parameters of blood along with magnetic particles in a cylindrical tube. – Journal of Magnetism and Magnetic Materials, vol.377, pp.395-401.
Swartz R.H., Bhuta S.S., Farb R.I., Agid R., Willinsky R.A., Butany J., Wasserman B.A., Johnstone D.M., Silver F.L. and Mikulis D.J. (2009): Intracranial arterial wall imaging using high-resolution 3-tesla contrast-enhanced MRI. – Neurology, vol.72, No.7, pp.627-634.
Misra J.C. and Shit G.C. (1988): Role of slip velocity in blood flow through stenosed arteries: a non-Newtonian model. – Journal of Mechanics in Medicine and Biology, vol.7, No.03, pp.337-353.
Misra J.C. and Kar B.K. (1988): Momentum integral method for studying flow characteristics of blood through a stenosed vessel. – Biorheology, vol.26, No.1, pp.23-35.
Kandasamy R., Periasamy K. and Prabhu K.K.S. (2005): Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection. International Journal of – Heat and Mass Transfer, vol.48, No.7, pp.1388-1394.
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