Power Law Nanofluid through Tapered Artery based on a ‎Consistent Couple Stress Theory

Document Type : Research Paper


1 Department of Mechanical Engineering, Lorestan University, Khoramabad, Iran

2 Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran


Based on couple stress theory, this study investigated non-Newtonian power-law nanofluid flows in converging, non-tapered, and diverging arteries. In addition to excluding gravity effects artery, geometry included mild stenosis. The momentum equation is solved via the Galerkin method, and the results are compared with experimental and classical findings. Although the power-law couple stress theory’s relations are first used in the analysis of non-Newtonian blood flow, the results of this theory are far more consistent with experimental results than classical results. Comparison of the results of the study of blood flow velocity profiles in a non-tapered artery without stenosis by the mentioned theory with experimental and classical theory results shows the difference in velocity at the center of the artery between the experimental results and the results of the classical theory is 36%, while this value has been reduced to 14% for the results of the couple stress theory. The variations in velocity profile with the power-law index (n=0.8 and n=0.85) and the dimensionless Darcy number (Da=10-10 and Da=10-7) in all three geometries indicated a flat velocity distribution with the increase in the power-law index while increasing the velocity profile with increased Darcy number. Mass transfer and energy equations are solved using the extended Kantorovich method. The solution convergence is evaluated, and the influence of parameters such as Prandtl number, Schmidt number, and dimensionless thermospheric and Brownian parameters on concentration and temperature profiles is obtained.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Ross, R., Atherosclerosis — an Inflammatory Disease, New England Journal of Medicine, 340(2), 1999, 115-126.
[2] Haldar, K., Effects of the shape of stenosis on the resistance to blood flow through an artery, Bulletin of Mathematical Biology, 47(4), 1985, 545-550.
[3] Nadeem, S. Akbar, N.S., Hendi, A.A., Hayat, T., Power law fluid model for blood flow through a tapered artery with a stenosis, Applied Mathematics and Computation, 217(17), 2011, 7108-7116.
[4] Liu, G.T., Wang, X.J. Ai, B.Q., Liu, L.G., Numerical Study of Pulsating Flow Through a Tapered Artery with Stenosis, Chinese Journal of Physics, 42(4), 2004, 401-409.
[5] Shukla, J.B., Parihar, R.S., Rao, B.R.P., Effects of stenosis on non-Newtonian flow of the blood in an artery, Bulletin of Mathematical Biology, 42(3), 1980, 283-294.
[6] Johnston, B.M., Johnston, P.R., Corney, S., Kilpatrick, D., Non-Newtonian blood flow in human right coronary arteries: steady state simulations, Journal of Biomechanics, 37(5), 2004, 709-720.
[7] Liu, B., Tang, D., Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries, Molecular & Cellular Biomechanics: MCB, 8(1), 2011, 73-90.
[8] Chen, J., Lu, X.Y., Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch, Journal of Biomechanics, 37(12), 2004, 1899-911.
[9] Mekheimer, K.S., Effect of the induced magnetic field on peristaltic flow of a couple stress fluid, Physics Letters A, 372(23), 2008, 4271-4278.
[10] Srinivasacharya, D., Srikanth, D., Effect of couple stresses on the flow in a constricted annulus, Archive of Applied Mechanics, 78(4), 2008, 251-257.
[11] Valanis, K.C., Sun, C.T., Poiseuille flow of a fluid with couple stress with applications to blood flow, Bio Rheology, 6(2), 1969, 85-97.
[12] Srivastava, L.M., Flow of couple stress fluid through stenotic blood vessels, Journal of Biomechanics, 18(7), 1985, 479-485.
[13] Srinivasacharya, D., Rao, G.M. Pulsatile flow of couple stress fluid through a bifurcated artery, Ain Shams Engineering Journal, 9(4), 2018, 883-893.
[14] Stokes, V.K., Couple Stresses in Fluids, Physics of Fluids, 9(9), 1966, 1709-1715.
[15] Pordanjani, A.H., Aghakhani, S., Afrand, M., Sharifpur, M., Meyer, J.P., Xu, H., Nanofluids: Physical phenomena, applications in thermal systems and the environment effects- a critical review, Journal of Cleaner Production, 320, 2021, 128573.
[16] Abidi, A., Ahmadi, A., Enayati, M., Sajadi, S.M., Yarmand, H., Ahmed, A., Cheraghian, G.A., Review of the Methods of Modeling Multi-Phase Flows within Different Microchannels Shapes and Their Applications, Micromachines, 12(9), 2021, 1113.
[17] Rostami, S., Aghakhani, S., Hajatzadeh Pordanjani, A., Afrand, M., Cheraghian, G., Oztop, H.F., Shadloo, M.S., A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid, Processes, 8(9), 2020, 1011.
[18] Sheikhpour, M., Arabi, M., Kasaeian, A., Rokn Rabei, A., Taherian, Z., Role of Nanofluids in Drug Delivery and Biomedical Technology: Methods and Applications, Nanotechnology, Science and Applications, 13, 2020, 47-59.
[19] Cao, Q.L., Massoudi, M., Liao, W.H., Feng, F., Wu, W.T., Flow Characteristics of Water-HPC Gel in Converging Tubes and Tapered Injectors, Energies, 12(9), 2019, 1643.
[20] Karami, F., Ahmadi Nadooshan, A., Tadi Beni, Y., Development of the Couple Stress Relationships for the Power Law Fluid and the Solution of Flow in CeramicTape Casting Process, Journal of Applied Fluid Mechanics, 11(5), 2018, 1239-1246.
[21] Ellahi, R., Rahman, S.U., Nadeem, S., Blood flow of Jeffrey fluid in a catherized tapered artery with the suspension of nanoparticles, Physics Letters A, 378(40), 2014, 2973-2980.
[22] Rahman, S.U., Ellahi, R., Nadeem, S., Zia, Q.M.Z., Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis, Journal of Molecular Liquids, 218, 2016, 484-493.
[23] Akbar, N.S., Rahman, S.U., Ellahi, R., Nadeem, S., Nano fluid flow in tapering stenosed arteries with permeable walls, International Journal of Thermal Sciences, 85, 2014, 54-61.
[24] Reddy, J.V.R., Srikanth, D., The Polar Fluid Model for Blood Flow through a Tapered Artery with Overlapping Stenosis: Effects of Catheter and Velocity Slip, Applied Bionics and Biomechanics, 2015, 12.
[25] Akbar, N.S., Non-Newtonian model study for blood flow through a tapered artery with a stenosis, Alexandria Engineering Journal, 55(1), 2016, 321-329.
[26] Chakravarty, S., Mandal, P.K., Two-dimensional blood flow through tapered arteries under stenotic conditions, International Journal of Non-Linear Mechanics, 35(5), 2000, 779-793.
[27] Srivastava, V.P., Saxena, M., Suspension model for blood flow through stenotic arteries with a cell-free plasma layer, Mathematical Biosciences, 139(2), 1997, 79-102.
[28] Beavers, G.S., Joseph, D.D., Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, 30(1), 2006, 197-207.
[29] Qiuyang, D., Numerical Solutions of the Radiosity Equation by the Galerkin Method for the Spherical Pyramid (Mars Project), Bachelor Thesis, Mathematics Department, Roger Williams University, Rhode Island, 2017.
[30] Suri, P.K., Suri, P.R., Effect of static magnetic field on blood flow in a branch, Indian Journal of Pure and Applied Mathematics, 12(7), 1931, 907-918.
[31] Belardinelli, E., Cavalcanti, S., A new nonlinear two-dimensional model of blood motion in tapered and elastic vessels, Computers in Biology and Medicine, 21(1), 1991, 1-13.
[32] Bugliarello, G., Sevilla, J., Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, 7(2), 1970, 85-107.
[33] Roe, E., Wells, Jr., E.W., Merrill, Influence of flow properties of blood upon viscosity-hematocrit relationships, The Journal of Clinical Investigation, 41(8), 1962, 1591-1598.
[34] Hadjesfandiari, A.R., Hajesfandiari, A., Dargush, G.F., Skew-symmetric couple-stress fluid mechanics, Acta Mechanica, 226(3), 2015, 871-895.
[35] Ai, L., Vafai, K., A coupling model for macromolecule transport in a stenosed arterial wall, International Journal of Heat and Mass Transfer, 49(9), 2006, 1568-1591.
[36] Murphy, J.D., Rabinovitch, M., Goldstein, J.D., Reid, L.M., The structural basis of persistent pulmonary hypertension of the newborn infant, The Journal of Pediatrics, 98(6), 1981, 962-967.
[37] Geddes, J., Carr, R., Karst, N., Wu, F., The Onset of Oscillations in Microvascular Blood Flow, SIAM Journal on Applied Dynamical Systems, 6(4), 2007, 694-727.