Volume 35 | Number 3 | Year 2016 | Article Id. IJMTT-V35P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P522

Blood flow is responsible for nutrient and waste transport within the closed loop i.e. cardiovascular networks. A common problem of the cardiovascular network is the narrowing of arteries due to the development of atherosclerotic plagues or other types of abnormal tissue development. As this growth project into the lumen of the artery, the flow is distributed and develops a potential coupling between the growth of the stenosis and the blood flow through the artery. It is noted that very small growths leading to mild stenotic obstructions, may be important in triggering biological mechanism such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section, through which a Newtonian fluid is steadily flowing, is made through this work. This chapter is based on a simplified model in which the connective acceleration terms in the Nervier-Stokes equations are neglected. Finally the governing equations are then solved numerically and obtain the expression for pressure gradient and impedance ratio with respect to stenosis height.

[1] D. F. Young, “Effect of a time dependent stenosis on flow through a tube,” J. of Engg. for Industry, 90(1), 248-254, 1968.

[2] J.B. Shukla, R. S. Parihar, and S. P. Gupta, “Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis,” Bull. of Math. Bio., 42, 797-805, 1980.

[3] J. Perkkio, and R. Keskinen, “Effect of the concentration profile of red cells on blood flow in the artery with stenosis,” Bull. of Math. Biol., 45, 259-267, 1983.

[4] C. M. Rodkiewicz, S. Tokarzewski, J. S. Kennody, and J. Nielubowicz, “Flow characteristics of the renal artery transplant-model studies,” J. Biomech., 21 (2), 97-105, 1988.

[5] G. Pontrelli, “Blood flow through an axisymmetric stenosis,” Proc. Inst. Mech. Eng, Part H, Eng Med, 215(1), 1-10, 2001.

[6] A. S. Most, N. A. Ruocco, and H. Gewirtz, “Effects of a reduction in blood viscosity on maximal myocardial oxygen delivery distal to a moderate coronary stenosis,” Medline Circulation, 74(5), 1085-1092, 2003.

[7] D. Tang, S. Yang, S. Kobayashi, J. Zheng, and R. P. Vito, “ Effect of stenosis asymmetry on blood flow and artery compression: a threedimensional fluid-structure interaction model,” Ann. Biomed. Engg., 31(10), 1182-1193, 2003.

[8] N. Padmanabhan, and R. Devanathan, “A Mathematical model of an arterial stenosis allowing for tethering,” J. Med. & Bio. Engg. & Comp., 19, 385-390, 2006.

[9] S. Kumar, and S. Kumar, “Numerical study of the axi-symmetric blood flow in a catheterised rigid tube,” Int. Rev. of Pure & Appl. Math., 2(2), 99-109, 2007.

[10] P. K. Mandal, S. Chakravarty, and A. Mandal, “ Numerical study of the unsteady flow of non-Newtonian fluid through differently shaped arterial stenosis,” Int. J. Comp. Math., 84(7), 1059-1077, 2007.

[11] O. K. Matar, and S. Kumar, “dynamics and stability of flow down a flexible inclined tube,” J. Engg. Math., 57(2), 145-147, 2007.

[12] A. Qiao, and Y. Liu, “Numerical study of hemodynamics comparison between small and large femoral bypass graft,” Comm. in Numr. Methods in Engg. , 24(11), 1067-1078, 2007.

[13] S. Kumar, and A. Dixit, “Mathematical model for the effect of micropolar parameter in stenotic artery,” Int. Tans. Appl. Science 1(4), 621- 628, 2009.

[14] D. S. Sankar, and U. Lee, “Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries,” Comm. Nonlinear Sc. & Num. Sim., 14(7), 2971-2981, 2009.

[15] S. Kumar, and S. Chandra, “Effects of multi-stenosis and poststenosis dilations in small artery,” . Jnanabha, 40, pp 97-104, 2010.

[16] S. Kumar, and A. Dixit, “ A study of the magnetic effects on the blood flow in an inclined artery with stenosis,” Int. Transactions in Applied Sciences , 2(1), 37-47, 2010.

[17] S. Kumar, R. S. Chandel, S. Kumar, and H. Kumar, “A mathematical model for blood flow and cross sectional area of an artery,” Math. Mod. & Appl. to Indus. Prob. (MMIP-2011), 211-220, 2011.

[18] S. Kumar, and C. S. Diwakar, “A biomagentic fluid dynamic model for the MHD Couette flow between two infinite horizontal parallel porous plates,” Int. J. of Phy. Sci. Vol. 24(3)B, 483-488, 2012.

[19] S. Kumar, and C. S. Diwakar, “A mathematical model for Newtonian blood flow in the presence of applied magnetic field,” Aryabhatta J. of Math & Infomatics, Vol. 4, 265-278, 2012.

[20] D. Biswas, and P. Moumita, “Study of blood flow inside an inclined non-uniform stenosed artery,” Int. J. of Mathematical Archive-4(5), pp. 33-42, 2013.

[21] A. R. Sankar, S. R. Gunakala, and D. M.G. Comissiong, “ Twolayered blood flow through a composite stenosis in the presence of a magnetic field,” Int. J. of Application or Innovation in Engineering & Management, -2(12), pp. 33-42, Dec. 2013.

[22] A. Bhatnagar, and R. K. Shrivastav, “Analysis of mhd flow of blood through a multiple stenosed artery in the presence of slip velocity,” Int. J. of Innovative Research in Advanced Engineering,-1(10), pp. 250- 257, Nov. 2014.

[23] G. C. Hazarika, and B. Sharma, “Magnetic field effect on oscillatory flow of blood in a stenosed artery,” Int. Conf. on Frontiers in Mathematics, March 26-28, 2015, Gauha ti University, Guwahati, Assam, India, pp.69-73, 2015.

[24] R. Bali, N. Gupta and S. Mishra, “ Study of transport of nanoparticles with power law fluid model for blood rheology in capillaries,” Journal of Progressive Research in Mathematics(JPRM), 7(3), pp. 1053-1062, 2016.

Chandrashekhar Diwakar, Sanjeev Kumar, "Effects of Axially Symmetric Stenosis on the Blood Flow in an Artery Having Mild Stenosis," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 35, no. 3, pp. 163-167, 2016. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V35P522