Pulsatile Flow of Blood with Volume Fraction of Micro-organisms in the Presence of Transverse Magnetic Field through Stenosed Tube

Dr.Srinivas K , Dr.V.P.Rathod. "Pulsatile Flow of Blood with Volume Fraction of Micro-organisms in the Presence of Transverse Magnetic Field through Stenosed Tube", *International Journal of Mathematical Trends and Technology (IJMTT). *V7:1-11 March 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

**Abstract**

This paper presents an analytical study of pulsatile flow of blood with micro-organisms through stenosed tubes in presence of transverse magnetic field.The effect of externally applied magnetic field on velocity, flow rate is studied.The analytical solutions for the velocity, volumetric flow rate are obtained using finite Hankel and Laplace transforms,and their natures are shown graphically for different values of involved parameters. **References**

[1] Bali, R. and Awasthi, U. Effect of magnetic field on the resistance to blood flow through stenotic artery. Applied Mathematics and Computation, Vol. 188, pp. 1635-1641,2007.

[2] Chakravarty, S. Effects of stenosis on the flow behaviour of blood in an artery.International Journal of Engineering Science, Vol. 25, No. 8, pp. 1003-1016,1987.

[3] Buchanan Jr., J. R., Kleinstreuer, C. and Corner J. K. Rheological effects on pulsatile hemodynamics in a stenosed tube. Computers & Fluids, Vol. 29, pp. 695-724, 2000.

[4] Deplano, V. and Siouffi, M. Experimental and Numerical study of pulsatile flowthrough a tapered artery with stenosis. Journal of Biomechanics, Vol. 32, pp. 1081-1090, 1999.

[5] Haldar, K. Effects of the shape of stenosis on the resistance to blood flow through an artery. Bulletin of Mathematical Biology, Vol. 47, No.4, pp. 545-550, 1985.

[6] Mandal, P. K. An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis. International Journal of Non-Linear Mechanics, Vol. 40, pp.151-164, 2005.

[7] Chakravarty, S. and Mandal, P. K. Mathematical modeling of blood flow through an overlapping arterial stenosis. Mathl. Comput. Modelling, Vol. 19, No. 1, pp. 59-70, 1994.

[8] Ismail, Z., Abdullah, I., Mustapha, N. and Amin, N. A power-law model of blood flow through a tapered overlapping stenosed artery.Applied Mathematics and Computation, Vol. 195, No. 2, pp. 669-680, 2007.

[9] Hernan, A. and Gonzalez, R. Numerical implementation of viscoelastic blood flow in a simplified arterial geometry. Medical Engineering and Physics, Vol. 29, pp. 491-496,2007.

[10] Katiyar, V. K. and Basavarajappa, K.S. Blood flow in the cardiovsular system in the presence of magnetic field. International Journal of Applied Science and Computations, Vol. 9, No. 3, pp. 118-127, 2002.

[11] Liepsch, D. An introduction to biofluid mechanics – basic models and applications. Journal of Biomechanics, Vol. 35, pp. 415-435, 2002.

[12] Liu, G. T., Wang, X. J., Ai, B. Q. and Liu, L. G. Numerical study of pulsatile flow through a tapered artery with stenosis. Chinese Journal of Physics, Vol. 42, No. 4-I, pp. 401-409, 2004.

[13] Prakash, J., Makinde, O. D. and Ogulu, A. Magnetic effect on oscillary blood flow in a constricted tube. Botswana Journal of Technology April , pp. 45-50,2004.

[14] Tashtoush, B. and Magableh, A. Magnetic field effect on heat transfer and fluid flow charecteristics of blood flow in multi-stenotic arteries.Heat and Mass Transfer, Vol. 44, No. 3, pp. 297-304, 2008.

[15] Tzirtzilakis, E. E. A mathematical model for blood flow in magnetic field.Physics of Fluids, Vol. 17:077103, pp. 1-15, 2005.

[16] Sud, V. K. and Sekhon, G. S. Blood flow through the human arterial system in the presence of a steady magnetic field. Phys. Med. Biol.Vol. 34, No. 7, pp. 795-805,1989.

[17] Chester, W. The effect of a magnetic field on Stokes flow in a conducting fluid. J. Fluid Mech,.Vol. 3, pp. 304-308, 1957.

[18] Jauchem, J.R. Exposure to extremely-low-frequency electromagnetic fields and radiofrequency radiation: cardiovascular effects in humans,Review Int Arch Occup Environ Health, Vol. 70, pp. 9-21.1997.

[19] Kolin.A, Electromagnetic flow meter: principle of method and its applications to blood flow measurement. Proc. Soc. Exptl. Biol. Med. 35, 53 (1936).

[20] Korchevskii E.M and Marochnik L.S., Magneto hydrodynamic version of movement of blood. Biofizica, 10(2), 371-373 (1965).

[21] Mathews, P., Fracture healing by pulsating electromagnetic fields- a study. M.S.Dessertation G.U.G. (Nov. 1988).

[22] Bathnagar and Rakesh, Non-Newtonian fluid flow between co-axial rotating disks: effects of an externally applied magnetic field. Mat-Apl Compt. 2, 171-191 (1983).

[23] Ramachandrarao and Deshikachar K.S., Physiological type flows in a circular pipe in the presence of a transverse magnetic field. Indian Insti. Sci., 68, 247-260, (july-Aug 1988).

[24] Shastri, D.V.S and Seetaramaswamy R, MHD dustry viscous flow through a circular pipe. Indian J. Pure Appl. Math, 13:7, 811-817 (July 1982).

[25] Debnath and Ghosh, On unsteady hydromagnetic flows of a dusty fluid between two oscillating plates. Appl. Sc., Res., 45(4), 353-365 (1988).

[26] Kaur and Sharma: Unsteady MHD flow of a dusty viscous fluid in an annulus bounded by two co-axial cylinders under the influence of exponential pressure gradient when the outer cylinder is moving with time dependent velocity. J. Maulana Azad College Tech, 18, 73-82,(1985).

[27] V. P.Rathod and Shakera Tanveer Pulsatile Flow of Couple Stress Fluid through a Porous medium with Periodic Body Acceleration and Magnetic Field. Bull. Malays. Math. Sci. Soc. (2) 3 2(2) 245- 259,(2009).

[28] Kinouchi, Y., Yamaguchi, H., and Tenforde, T.S. Theoretical analysis of magnetic field interactions with aortic blood flow. Bioelectromagnetics, Vol. 17, pp. 21-32, 1996.

[29] Womersely, J.R, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol., 127, 553-563.

[30] Chaturani P and Rathod V.P., A theoretical model for pulsatile blood flow with application to cerebrovascular diseases. Jour. Neurological research, 3, 289-303, (1981).

[31] V. P. Rathod and Gayatri, , Effect of magnetic field on two layer model of Pulsatile blood flow with micro-organisms, Bull. Pure Appl. Sci. Sect. E Math. Stat. 19 no. 1 1–13, (2000).

[32] Bugliarello, G. and Sevilla, J. “Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes”. Biorheology, 7, 85-107 (1970).

[33] Bugliarello, G. and Hayden, J.W. “High speed micro cinematographic studies of blood flow in vitro”. Science, 138, 981-983(1962).

**Keywords**

Stenosis, Couple Stress fluid, Transverse magnetic field, Micro-organisms.