## THERMAL SCIENCE

International Scientific Journal

### INFLUENCE OF MIXED CONVECTION ON BLOOD FLOW OF JEFFREY FLUID THROUGH A TAPERED STENOSED ARTERY

**ABSTRACT**

Effect of heat and mass transfer on the blood flow through a tapered artery with stenosis is examined assuming blood as Jeffrey fluid. The governing equations have been modelled in cylindrical coordinates. Series solutions are constructed for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Attention has been mainly focused to the analysis of embedded parameters in converging, diverging and non-tapered situations.

**KEYWORDS**

PAPER SUBMITTED: 2011-11-22

PAPER REVISED: 2011-12-01

PAPER ACCEPTED: 2011-12-11

**THERMAL SCIENCE** YEAR

**2013**, VOLUME

**17**, ISSUE

**2**, PAGES [533 - 546]

- Massoudi, M. and Phuoc, T. X. Pulsatile flow of blood using a modified second-grade fluid model, Comput , Math with Appl, 2008, vol.56, pp.199-211.
- Humphrey, J.D. and Delange, S.L. An Introduction to Biomechanics, Springer Science + Business Media, Inc., New York, 2004.
- Eringen, A.C., Continuum theory of dense rigid suspension, Rheol. Acta. 1991, vol.30, pp. 23-32.
- Thurston, G.B. , Viscoelasticity of human blood, Biophys. J, 1972, vol.12, pp.1205-1217.
- Chien, S. , King, R.G. , Skalak, R. , Usami S. and Copley, A.L. Viscoelastic properties of human blood and red cell suspension, Biorheology, 1975, vol.12, pp. 341-346.
- Jones, R.T., Blood flow, Ann. Rev. Fluid Mech, 1969,vol.1, pp.223-244.
- Siddiqui, S.U. , Verma, N.K. , Mishra, S. and Gupta, R.S. , Mathematical modelling of pulsatile flow of Casson's fluid in arterial stenosis, Appl. Math. Comput, 2009, vol. 210, pp.1-10.
- Mekheimer Kh. S. and El Kot, M. A. , The micropolar fluid model for blood flow through a tapered artery with a stenosis, Acta Mech Sin, 2008, vol.24, pp.637-644.
- Mandal, P. K. , An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, Int. J. of Non-linear . Mech, 2005, vol.40, pp.151-164.
- Varshney, G., Katiyar V.K. and Kumar, S. , Effect of magnetic field on the blood flow in artery having multiple stenosis: a numerical study, Int. J. Eng. Sci. and Tech, 2010, vol.2, pp. 67-82.
- Nadeem S. and Akbar, N. S., Hayat , T. and Hendi, Awatif A , Power law fluid model for blood flow through a tapered artery with a stenosis, Appl. Math. Comput, 2011, vol.217, pp. 7108-7116.
- Nadeem S. and Akbar, N. S., Jeffrey fluid model for blood flow through a tapered artery with a stenosis, J. Mech. Medicine and Biology, 2011, vol.11, pp. 529-545.
- Mustafa, N. , Mandal, P.K. , Abdullah, I., Amin, N.S. and Hayat, T., Numerical Simulation of generalized Newtonian blood flow past a couple of irregular arterial stenosis, Numer.Meth.Partial Diff. Eqs. 2011, Vol.27, pp.960-981.
- Abdullah, I. , Amin, N. S. and Hayat, T., Magnetohydrodynamic effects on blood flow through an irregular stenosis, Int.J.Number.Method Fluids DOI : 10.1002 / fld.2436.
- Khanafer, K. , Bull, J. L. , Pop , I. and Berguer, R. , Influence of pulsatile blood flow and heating scheme on the temperature distribution during hyperthermia treatment, Int.J. Heat and Mass Transfer, 2007, vol. 50, pp.4883-4890.
- Valencia, A. and Villanueva, M., Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction, Int. Comm. Heat Mass Transfer, 2006, vol.33, pp. 966-975.
- Back, L. H. , Crawford, D. W. and Barndt, R. , Flow field and mass transport analysis in arteries with longitudinal ridges, J Appl Physiol, 1976, vol.41 , pp.910-919.
- Ma, P. , Li , X. and Ku, D.N. Heat and mass transfer in a separated flow region for high Prandtl and Schmidt numbers under pulsatile conditions. Int J Heat Mass Transfer, 1994, vol.37, pp.2723-2736.
- Akbar, N. S. and Nadeem, S. , Simulation of heat and chemical reactions on Reiner Rivlin fluid model for blood flow through a tapered artery with a stenosis, Heat Mass transfer, 2010, vol.46, pp.531-539.
- Nadeem, S. , Akbar, N. S. , Influence of heat and chemical reactions on Walter's B fluid model for blood flow through a tapered artery, Taiwan Institute of Chemical Engineers, 2011, vol.42, pp. 67-75.
- He, J.H. Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons & Fractals . 2005, vol.26, pp.695-700.
- Ellahi, R. Steady and unsteady flow for newtonian and non-Newtonian fluids: Basics, concepts and methods", Publisher, VDM Germany (2009).
- Khan,Y., Wo. Qingbiao., Faraz, N and Yildrim., A, . The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet, , Comput. & Math. with Appl. 2011, vol.61, pp.3391-3399.
- Yildrim., A, . New Equations for Kinetic Analysis of Non-isothermal Thermogravimetry, Asian. J. of Chem., 2008, vol.20, pp. 2057-2063.
- Shan, P., Bohn, D., Ren, J., Surken, N. Parameter Survey of Thermally Highly Loaded, Porous and Cooled Multi-Layer Systems for Turbine Blades, J. of Therm. Sci., 2007, Vol.12. pp. 181-185.
- Kato, H., Taniguchi, H. , Matsuda, K., Funazaki, K. , Kato, D., and Pallot, G. Experimental and Numerical Investigation on Compressor Cascade Flows with Tip Clearance at a Low Reynolds Number Condition. J. of Therm. Sci., 2011, Vol.20. pp. 481-485.