Abstract

Blood can be assumed as a suspension of magnetic particles in non-magnetic plasma, due to presence of hemoglobin in red blood cells. The hemodynamic and rheological property of blood could help us to diagnose and perceive the pathological condition of stenosis. Stenosis is an abnormal and unnatural growth that is due to the deposits of atherosclerotic plaques, cholesterol, lipids, fats etc. inside the lumen of artery in a cardiovascular system. The governing equation of flowing fluid is solved numerically with the help of Frobenius method. The Einstein equation, dependent on hematocrit concentration of blood also helps to develop this model. The hematocrit is the proportion, by volume, of the blood that consists of red blood cells. The essential theoretical results such as axial velocity profile, pressure gradient and wall shear stress have been calculated numerically using MATLAB. From these results we conclude that the axial velocity decreases for increasing Hartmann number while pressure gradient and wall shear stress increases with increase of it. The variation of the solutions of these theoretical results with regard to different parameters has been shown from the graphical representation and it has been observed that the flow pattern is significantly controlled by the magnetic field.

Keywords

References

[1] A. Bhatnagar, R .K. Srivastav and A.K. Singh, ―A Numerical analysis for the effect of slip velocity & stenosis shape on Non-newtonian flow of blood‖, IJE Trans.C., Vol. 28, No. 3, pp. 440-446, 2015.
[2] A. Kolin, ―An electromagnetic flow meter: Principle of the method and its application to blood flow measurements‖, in Proceedings of Society for Experimental Biology and Medicine (New York), Royal Society of Medicine, Vol. 35, pp.53-56, 1936.
[3] A. Ramachandra Rao and K. S. Deshikachar, Journal of Indian Inst. Sci., Vol. 68, pp. 247-60, 1988.
[4] D. A. McDonald, Blood Flow in Arteries, Arnold, London, 1960, 1974.
[5] D. C. Sanyal and A. K. Maiti, ―On pulsatile flow of blood through a stenosed artery‖, Ind. J. Maths, Vol. 40, No.2, pp. 199-213, 1998.
[6] D. F. Young and F.Y. Tsai, ―Flow Characteristic in model of Arterial Stenosis-Steady Flow‖, J. Biomechanics, Vol. 6, No. 4, pp. 95-410, 1973.
[7] D. F. Young, ―Effects of time dependent Stenosis of Flow through a tube, J. Engg. for Industry, Vol. 90, No. 1, pp.248-254, 1968.
[8] D. Sut, ―Study of blood Flow with effects of slip in arterial stenosis due to presence of transverse magnetic field‖, International Journal of Mathematical Archive, Vol.3, No. 3, pp. 983-993, 2012.
[9] E. M. Korchevsky, and L.S. Marochnik, ―Magneto-hydrodynamic version of movement of blood, Biophysics, Vol.10, pp.411- 413, 1965.
[10] G. Awgichew, G. Radhakrishnamacharya, and B. Shreesha, ― Effect of slip condition on couple stress fluid flow in a channel with mild stenosis in the uniform magnetic field‖, AAM: International journal, Vol. 9, Issue 1, pp. 54-67, 2014.
[11] H. P. Mazumdar, U. N. Ganguly, S. Ghorai, and D. C. Dalal, ―On the distribution of axial velocity and pressure gradient in a pulsatile flow of blood through a constricted artery‖, Ind. J. of pure and Appl. Maths. Vol. 27, pp.1137-1150, 1996.
[12] J. Singh, and R. Rathee, ―Analysis of non-Newtonian blood flow through stenosed vessel in porous medium under the effect of magnetic field‖, International Journal of the Physical Sciences, Vol. 6, No.10, pp. 2497-2506, 2011.
[13] J.R. Keltner, M.S. Roos, P.R. Brakeman and T. F. Budinger, ―Magnetohydrodynamic of blood flow‖, Mag. Reson. Med. Journal, Vol.16, No. 1, pp. 139-149, 1990.
[14] K. Halder, and S.N. Ghosh, ―Effects of a magnetic field on blood flow through an intended tube in the presence of erythrocytes‖, Ind. Jr. Pure and Appl. Math, 25, No. 3, pp. 345-352, 1994.
[15] M. F. Barnothy(ed.), Biological Effects of Magnetic Fields, Vols. (1, 2), Plenum Press. 1964, 1969.
[16] M. Jain, G. C. Sharma and R. Singh, ―Mathematical modeling of blood flow in a stenosed artery under MHD effect through porous medium‖, I. J. Engg., Transactions B, Vol. 23, No. (3,4), pp. 243–251, 2010.
[17] M. K. Sharma, K. Bansal, and S. Bansal, ―Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field‖, Korea-Australia Rheology Journal, Vol. 24, No. 3, pp.181-189, 2012.
[18] M. Zamir, The Physics of Coronary Blood Flow, Springer, 2005.
[19] R. Agarwal and N. K. Varshney, ― Slip velocity effect on MHD oscillatory blood flow through stenosed artery‖, Pelagia Research Library, Advances in Applied Science Research, Vol. 5, No. 1, pp.84-90, 2014
[20] R. Bali and U. Awasthi, ―A Casson Fluid Model for Multiple Stenosed Artery in the Presence of Magnetic Field‖, Applied Mathematics, Scientific Research, Vol. 3, No. 5, pp. 436-441. (2012),
[21] R. K. Dash, K. N. Mehta and G. Jayarman, ―Casson flow in a pipe filled with a homogenous porous medium‖, Int. J. Eng. Sci., Vol. 34, pp.1145-1156, 1996.
[22] S. Verma and A. Srivastava, ―Effect of magnetic field on steady blood flow through an inclined circular tube‖, International Journal of Engineering Research and Applications, Vol. 3, No. 4, pp. 428-432, 2013.
[23] Y. C. Fung, Biodynamics circulation, Springer-Verlag, New York. 29, 1984.