The present investigation deals with the application of Adomian's decomposition method to blood flow through a constricted artery in the presence of an external transverse magnetic field which is applied uniformly. The blood flowing through the tube is assumed to be Newtonian in character. The expressions for the two-term approximation to the solution of stream function, axial velocity component and wall shear stress are obtained in this analysis. The numerical solutions of the wall shear stress for different values of Reynold number and Hartmann number are shown graphically. The solution of this theoretical result for a particular Hartmann number is compared with the integral method solution of Morgan and Young .
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Adomian G.,Nonlinear Stochastic Operator Equations, Academic Press (1986).
Adomian G.,Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers (1989).
Adomian G.,Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers (1994).
Adomian G.,Application of the Decomposition Method to the Navier-Stokes Equations, Jr. Math. Anal. Appl. Vol.119, p. 340–360 (1986).
Adomian G.,Nonlinear Transport in moving fluids, Appl. Math. Lett. Vol.6, No. 5, p. 35–38 (1993).
Adomian G. and Rach R.,Analytic Solution of Nonlinear Boundary value Problems in several Dimensions, Jr. Math. Anal. Appl. Vol.174, No. 1, pp. 118–137 (1993).
Barnothy M. F. (ed),Biological effects of Magnetic fields Vols. 1 and 2, Plenum Press (1964–1969).
Gold, R. R.,Magnetohydrodynamics pipe flow, Part-1, J. Fluid Mech. Vol.13, p. 505–512 (1962).
Gupta S.C. and Bani Sinha,Unsteady magnetohydrodynamic flow in a circular pipe under a travsverse magnetic field, Phys. Fluids, Vol.13, p. 346–352 (1970).
Ramchandra Rao A. and Deshikachar K. S.,Physiological-type flow in a circular pipe in the presence of a transverse magnetic flow, Indian Inst. Sci. Vol.68, p. 247–260 (1988).
Sud V. K. and Sekhon G. S.,Blood flow through the human arterial system in the presence of a steady magnetic field, Phys. Med. Bio. Vol.34, p. 795–805 (1989).
Deshikachar K. S. and Ramchandra Rao A.,Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section, Int. J. Engng. Sci. Vol.23, p. 1121–1133 (1985).
Ramchandra Rao A. and Deshikachar K. S.,MHD Oscilatory flow of blood through channels of variable cross-section, Int. J. Engng. Sci. Vol.24, p. 1615–1628 (1986).
Mc Michacl J. M. and Deutsch S.,Magnetohydrodynamics of laminar flow in slowly varying tubes in an axial magnetic field, Phys. Fluids. Vol.27, p. 110–118 (1984).
Cherruault Y. Kybernetes,Convergence of Adomian's Method, Vol.18 No. 2, p. 31–39 (1989).
Cherruault Y.,New resulis for the convergence of Adominan's Method applied to integral equations, Math. Comp. Modelling, Vol.16, No. 2, p. 85–93 (1992).
Morgan B. E. and Young, D. F,An integral method for the analysis of flow in arterial stenoses, Jr. Math. Biol. Vol.36, p. 39–53 (1974).
K. Haldar: Dr. K. Haldar was born in West Bengal, India, in 1943. He recieved his B.Sc. Honours degree from Calcutta University. Then he got. M.Sc. and Ph.D. degrees from Jadavpur University in 1967 and 1974 respectively. He joined the departments of Mathematics and Mechanical Engineering of Jadavpur University in 1975 and 1978 to carry out his research works in Fluid Dynamics and Atmospheric Sciences respectively. In 1982 he joined the Electronics Unit of Indian Statistical Institute. Calcutta, India, as a Visiting Scientist and was absorbed there as a Lecturer afterwords. He is currently now a Professor in Mathematics of the same Institute. His research interests include Blood flow in Cardiovascular System, Viscous fluid flow through constricted straight and bent tubes, and Applications of Adomian's Decomposition method to Physics and Fluid Mechanics.
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Haldar, K. Application of Adomian's approximation to blood flow through arteries in the presence of a magnetic field. JAMC 12, 267–279 (2003). https://doi.org/10.1007/BF02936199
AMS Mathematics Subject Classification
Key words and phrases
- Constricted tube
- Newtonian blood
- magnetic field
- Navier-Stokes equations and decomposition method