Siddiqui, S. U.; Verma, N. K.; Mishra, Shailesh; Gupta, R. S. Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis. (English) Zbl 1159.92012 Appl. Math. Comput. 210, No. 1, 1-10 (2009). Summary: The effects of the non-Newtonian nature of blood and pulsatility on flow through a stenosed artery have been investigated. It is of interest to note that the thickness of the viscous flow region changes with the axial distance. An important result is that the mean and steady flow rates decrease as the yield stress increases. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Another important result of pulsatility is that the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for the pulsatile blood flow is equal to the steady wall shear stress. The velocity profiles and associated physiological characteristics involved in the analysis have been determined. Many standard results regarding Casson and Newtonian fluid flows, and uniform and steady flows in an artery can be obtained in the present analysis as special cases. Cited in 17 Documents MSC: 92C35 Physiological flow 76A05 Non-Newtonian fluids 76Z05 Physiological flows Keywords:non-Newtonian; wall shear stress; resistance to flow PDFBibTeX XMLCite \textit{S. U. Siddiqui} et al., Appl. Math. Comput. 210, No. 1, 1--10 (2009; Zbl 1159.92012) Full Text: DOI References: [1] Young, D. F., Fluid mechanics of arterial stenosis, J. Biomech., 101, 157-175 (1979) [2] Shim, E. B.; Kamm, R. D., Numerical analysis of blood flow through a stenosed artery using a coupled, multiscale simulation method, Comput. Cardiol., 27, 219-222 (2000) [3] Huang, H.; Virmani, R., The impact of calcification on the biomechanical stability of atherosclerotic plaques, Circulation, 103, 8, 1051-1056 (2001) [4] Huang, Y.; Doerschuk, C. M., Computational modeling of RBC and neutrophil transit through the pulmonary capillaries, J. Appl. Physiol., 90, 2, 545-564 (2001) [5] Huang, H.; Kamm, R. D., Receptor-based differences in human aortic smooth muscle cell membrane stiffness, Hypertension, 38, 5, 1158-1161 (2001) [6] Morris, J.; Ingenito, E. P., Dynamic behavior of lung surfactant, J. Biomech. Eng., 123, 1, 106-113 (2001) [7] Ozawa, E. T.; Bottom, K. E., Numerical simulation of enhanced external counterpulsation, Ann. Biomed. Eng., 29, 4, 284-297 (2001) [8] Swartz, M. A.; Tschumperlin, D. J., Mechanical stress is communicated between different cell types to elicit matrix remodeling, Proc. Natl. Acad. Sci. USA, 98, 11, 6180-6185 (2001) [9] Smith, F. T., The separation flow through a severity constricted symmetric tube, J. Fluid Mech., 90, 725-754 (1979) · Zbl 0399.76047 [10] Belardinelli, E.; Cavalcanti, S., A new non-linear two-dimensional model of blood motion in tapered and elastic vessels, Comput. Bio. Med., 21, 1-13 (1991) [11] Imeada, K.; Goodman, F. O., Analysis of non-linear pulsatile blood flow in arteries, J. Biomech., 13, 1007-1022 (1980) [12] Mishra, J. C.; Chakravarty, S., Flow in arteries in the presence of stenosis, J. Biomech., 19, 907-918 (1986) [13] Tu, C.; Deville, M.; Vanderschuren, L.; Dheur, L., Finite element simulation of pulsatile flow through arterial stenosis, J. Biomech., 25, 10, 1141-1152 (1992) [14] Zendehbudi, G. R.; Moayeri, M. S., Comparison of physiological and simple pulsatile flows through stenosed arteries, J. Biomech., 32, 959-965 (1999) [15] Haldar, K., Oscillatory flow of blood in a stenosed artery, Bull. Math. Bio., 49, 3, 279-287 (1987) · Zbl 0623.92015 [16] Chaturani, P.; Samy, R. P., Pulsatile flow of Casson’s fluid through stenosed arteries with application to blood flow, Biorheology, 23, 499-511 (1986) [17] Mishra, J. C.; Patra, M. K.; Mishra, S. C., A non-Newtonian fluid model for blood flow through arteries under stenotic condition, J. Biomech., 26, 1129-1141 (1993) [18] Nakamura, M.; Sawada, T., Numerical study of the unsteady flow on non-Newtonian fluid, J. Biomech. Engg. Trans. ASME, 112, 100-103 (1990) [19] Ookawara, S.; Ogowa, K., Flow properties of Newtonian and non-Newtonian fluid downstream of stenosis, J. Chem. Engg. Jpn., 33, 582-590 (2000) [20] Pak, B.; Young, Y. I.; Choi, S. U.S., Separation and re-attachment of non-Newtonian fluid flow in a sudden expansion pipe, J. Non-Newtonian Fluid Mech., 37, 175-199 (1990) [21] Shukla, J. B.; Parihar, R. S.; Rao, B. R.P., Effects of stenosis on non-Newtonian flow of the blood in an artery, Bull. Math. Bio., 42, 283-294 (1980) · Zbl 0428.92009 [22] Tu, C.; Deville, M., Pulsatile flow in non-Newtonian fluid through arterial stenosis, J. Biomech., 29, 899-908 (1996) [23] Chakravarty, S.; Sharifuddin Mandal, P. K., Unsteady flow of a two-layer blood stream past a tapered flexible artery under stenotic conditions, Comput. Methods Appl. Math., 4, 4, 391-409 (2004) · Zbl 1060.35145 [24] Gijsen, F. J.H.; van de Vosse, F. N.; Janssen, J. D., The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model, J. Biomech., 32, 601-608 (1999) [25] Johnston, B.; Johnston, P. R.; Corney, S.; Kilpatrick, D., Non-Newtonian blood flow in human right coronary arteries: steady state simulations, J. Biomech., 37, 709-720 (2004) [26] Leuprecht, A.; Perktold, K., Computer simulation of non-Newtonian effects on blood flows in large arteries, Comput. Methods Biomech. Biomed. Eng., 4, 149-163 (2004) [27] Neofytou, P.; Drikakis, D., Non-Newtonian flow instability in a channel with a sudden expansion, J. Non-Newtonian Fluid Mech., 111, 127-150 (2003) · Zbl 1042.76023 [28] K.K. Yeleswarapu, Evaluation of Continuum Models for Characterizing the Constitutive Behavior of Blood, Ph.D. Thesis Department of Mechanical Engineering, University of Pittsburgh, 1996.; K.K. Yeleswarapu, Evaluation of Continuum Models for Characterizing the Constitutive Behavior of Blood, Ph.D. Thesis Department of Mechanical Engineering, University of Pittsburgh, 1996. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.