Effect of Unsteadiness On Blood Flow
Through A Stenosed Artery Using A Third
Grade Fluid Model With Slip Conditions

Jimoh; A

doi:https://doi.org/10.14445/22315373/IJMTT-V66I4P522

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P522

Effect of Unsteadiness On Blood Flow Through A Stenosed Artery Using A Third Grade Fluid Model With Slip Conditions

Jimoh, A

Abstract

Effect of unsteadiness on blood flow through a stenosed artery using a third grade fluid model with slip conditions was investigated in this paper. Externally applied magnetic field was also taken into consideration. The solutions of the steady and unsteady non-linear dimensionless momentum equations are obtained using Galerkin’s Weighted residual, Newton Raphson and Fourth order Runge- Kutta methods. Comparative analysis as regards effects of slip velocity, magnetic field, shear thinning, pressure gradient and Reynold number on the flow characteristics of steady and unsteady third grade blood flow models were carried out and the results were presented graphically. It was reveals from the graphs that, slip velocity and shear thinning increases with velocity profiles, flow rate but reduces resistance to fluid flow for both steady and unsteady blood flow models. Also, magnetic field parameter increases with resistance to fluid flow but reduces velocity profiles and shear stress for both steady and unsteady blood flow models. Other parameters that can influences both steady and unsteady blood flow are pressure gradient and Reynold number. Finally, for the constant values of the parameters such as slip velocity, magnetic field, shear thinning, pressure gradient and Reynold number, the velocity profile of unsteady blood model is higher than that of the steady blood flow model.

Keywords

Steady blood flow, unsteady blood flow, magnetic field, slip conditions, stenosed artery, shear thinning, shear thickening, third grade fluid models and Galerkin’s Weighted residual methods.

References

[1] Shanthi, M., Pekka, P. and Norrving, B. (2011). Global Atlas on Cardiovascular Disease Prevention and Control. World Health Organization in Collaboration with the World Heart Federation and The World Stoke Organization. Pp. 3-18.
[2] Young, D. F and Tsai, F. Y (1973).Flow Characteristics in Model of Arterial Stenosis Steady Flow. Journal of Biomechanics, 6, 395-410.
[3] Miller, J, D. (2013). Cardiovascular Calcification: Orbicular Origins. Nature Material 12, 476-478.
[4] Biswas, D and Chakraborty. U. S (2010). Pulsatile Blood Flow through a catheterized Artery with an Axially Nonsymmetrical Stenosis. AppliedMathematical Sciences. 4(58), 2865-2880.
[5] Narendra, K. V, Shailesh, M, Shafi, U. S. and Ram, S. G. (2011). Effect of Slip Velocity on Blood Flow through a Catheterized Artery. Applied Mathematics, 2, 746-700.
[6] Devajyoti, B and Uday, S.C (2010). Two Layered Blood Flow in Stenosed Artery with a Body Acceleration and Slip at Wall. International journal of Application and Applied Mathematics, 5(2): 313-320.
[7] Devajyoti, B, and Razial, B. L (2011). Steady Flow of Blood through a Stenosed Artery: A Non- Newtonian Fluid Model. Assan University Journal of Science and Technology. Vol. 7, No 11, Pp. 144-153.
[8] Mallik, B. B., Nanda, S., Das B., Saha, D., Das, D. S. and Paul, K. (2013). A Non-Newtonian Fluid Model for Blood Flow using Power Law through Atherosclerotic Arterial Segment having Slip Velocity. International Journal of Pharmaceutical, Chemical and Biological Sciences, 3(3): 752-760.
[9] Tian, F. B., Zhu, L, Fok, P. U., and Lu, X. Y (2013). Simulation of a Pulsatile Non- Newtonian Blood Flow past a Stenosed 2D Artery with Artherosclerosis, Computer in Biological and Medicine, 43, Pp. 1098-1113.
[10] Misra, J. C. and Shit, G. C. (2007). Role of Slip Velocity in Blood Flow through Stenosed Arteries: A Non-Newtonian Model. Journal of Mechanical in Medicine and Biology, 7: 337-353.
[11] Venkateswarlu, K., and Rao, J. A. (2004). Numerical Solution of Unsteady Blood Flow through an Indented Tube with Atherosclerosis. Indian Journal of Biochemistry and Biophysics, Vol. 41, Pp. 241-245.
[12] Geeta, A. and Siddique, S. U. (2016). Analysis of Unsteady Blood Flow through a Stenosed Artery with Slip Effect. International Journal of Bio-Science and Bio-Technology, 8(5): 43-54.
[13] Srikanth, D. S., Ramana, R. S. and Jain, A. K (2015). Unsteady Polar Fluid Model of Blood Flow through Tapered X-Shape Stenosed Artery. Effect of Catheter and Velocity Slip. Ain Shams Engineering Journal, 6: 1093 – 1104.
[14] Ikbal, M. A, Chakravarty, S, Wong, K. K and Mandal, P. K (2009). Unsteady Response of Non-Newtonian Blood Flow through a Stenosed Artery in Magnetic Field.Journal of Computational and Applied Mathematics. 230: 243-259.
[15] Islam, M. E. (2012). Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source. World Journal of Mechanics, 2(3), 2012.
[16] Mandal, P. K. (2005). An Unsteady Analysis of Non-Newtonian Blood Flow through Tapered Arteries with a Stenosis. International Journal of Non-Linear Mechanics, 40: 151-164.
[17] Jimoh, A, Okedayo, G.T, and Ikpakyegh, L. N. (2019). Computational Analysis of Unsteady Flow of Blood and Heat Transfer throug a Stenosed Artery in a third Grade Fluid Model with Slip Conditions. International OF Applied Mathematics and Statistical Sciences. Vol. 8, Issue 5, Pp. 11-36.
[18] Mohammed, A. A. (2011). Analytical Solution for MHD Unsteady Flow of a Third Grade Fluid with Constant Viscosity. M.Sc. Thesis, Department of Mathematics, university of Baghdad. Pp. 1-104.
[19] Young, D. F. (1979). Effect of Time Dependent Stenosis on Flow through a Tube. Journal of Engineering, 90: 248-254.
[20] Biswas, D. (2000). Blood Flow Model: A Comparative Study. New Delhi:Mittal Publication. P. 15.
[21] Cirillo, M, Lourenzi, M, Trevisern, M and Stamler, L. (1992). Hematocrit, Blood Pressure and Hypertensions: The Gubbio Population Study, Hypertension. 20, 319-326.

Citation :

Jimoh, A, "Effect of Unsteadiness On Blood Flow Through A Stenosed Artery Using A Third Grade Fluid Model With Slip Conditions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 177-202, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P522