Numerical study of flow and heat transfer during oscillatory blood flow in diseased arteries in presence of magnetic fields

doi:10.1007/s10483-012-1577-8

摘要/Abstract

摘要：

A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic (MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure. The time-dependent permeability and the oscillatory suction velocity are considered. The computational results are presented graphically for the velocity, the temperature, and the concentration fields for various values of skin friction coefficients, Nusselt numbers, and Sherwood numbers. The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.

Abstract:

中图分类号:

O357

A. SINHA;J. C. MISRA. Numerical study of flow and heat transfer during oscillatory blood flow in diseased arteries in presence of magnetic fields[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 649-662.

参考文献

[1] Misra, J. C., Sinha, A., and Shit, G. C. Flow of a biomagnetic viscoelastic fluid: application to estimationof blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure forcancer treatment. Appl. Math. Mech. -Engl. Ed., 31(11), 1405-1420 (2010) DOI 10.1007/s10483-010-1371-6

[2] Misra, J. C., Sinha, A., and Shit, G. C. Theoretical analysis of blood flow through an arterialsegment having multiple stenoses. J. Mech. Med. Biol., 8, 265-279 (2008)

[3] Misra, J. C. and Kar, B. K. Momentum integral method for studying flow characteristics of bloodthrough a stenosed vessel. Biorheology, 26, 23-25 (1989)

[4] Misra, J. C., Pal, B., and Gupta, A. S. Hydrodynamic flow of a second-grade fluid in a channel—some applications to physiological systems. Math. Model. Meth. Appl. Sci., 8, 1323-1342 (1998)

[5] Misra, J. C., Patra, M. K., and Misra, S. C. A non-Newtonian fluid model for blood flow througharteries under the stenotic conditions. J. Biomech., 26, 1129-1141 (1993)

[6] Misra, J. C. and Roychoudhuri, K. A study on the stability of blood vessels. Rheol. Acta., 21,341-346 (1982)

[7] Misra, J. C. and Roychoudhuri, K. Effect of initial stresses on the wave propagation in arteries.J. Math. Biol., 18, 53-67 (1983)

[8] Misra, J. C. and Shit, G. C. Blood flow through arteries in a pathological state. Int. J. Eng. Sci.,44, 662-671 (2006)

[9] Misra, J. C. and Shit, G. C. Role of slip velocity in blood flow through stenosed arteries: anon-Newtonian model. J. Mech. Med. Biol., 7, 337-353 (2007)

[10] Misra, J. C. and Shit, G. C. Biomagnetic viscoelastic fluid flow over a stretching sheet. Appl.Math. Comput., 210, 350-361 (2009)

[11] Misra, J. C., Shit, G. C., and Rath, H. J. Flow and heat transfer of an MHD viscoelastic fluid ina channel with stretching walls: some applications to hemodynamics. Comput. Fluids, 37, 1-11(2008)

[12] Misra, J. C. and Singh, S. I. A study on the nonlinear flow of blood through arteries. Bull. Math.Biol., 49, 257-277 (1987)

[13] Misra, J. C. and Shit, G. C. Flow of a biomagnetic viscoelastic fluid in a channel with stretchingwalls. J. Appl. Mech., 76, 061006-061014 (2009)

[14] Misra, J. C., Shit, G. C., Chandra, S., and Kundu, P. K. Electro-osmotic flow of a viscoelastic fluidin a channel: application to physiological fluid mechanics. Appl. Math. Comput., 217, 7932-7939(2011)

[15] Misra, J. C. and Chakravarty, S. Dynamic response of arterial walls in vivo. J. Biomech., 15,317-324 (1982)

[16] Misra, J. C. and Singh, S. I. Pulse wave velocities in the aorta. Bull. Math. Biol., 46, 103-114(1984)

[17] Mortimer, R. G. and Eyring, H. Elementary transition state theory of the Soret and Dufour effects.Proc. Nat. Acad. Sci., 77, 1728-1731 (1980)

[18] Ramamurthy, G. and Shanker, B. Magnetohydrodynamic effects on blood flow through a porouschannel. Med. Biol. Eng. Comput., 32, 655-659 (1994)

[19] Mustapha, M., Amin, N., Chakravarty, S., and Mandal, P. K. Unsteady magnetohydrodynamicblood flow through irregular multistenosed arteries. Comput. Biol. Med., 39, 896-906 (2009)

[20] Mekheimer, K. S. Peristaltic flow of blood under effect of magnetic field in a non-uniform channel.Appl. Math. Comput., 153, 763-777 (2004)

[21] Vardanyan, V. A. Effect of magnetic field on blood flow. Biofizika, 18, 491-496 (1973)

[22] Barnothy, M. F. Biological Effects of Magnetic Fields, Plenum Press, New York, 1964-1969 (1964)

[23] Ritman, E. L. and Lerman, A. Role of vasa vasorum in arterial disease: a re-emerging factor.Current Cardiology Reviews, 3, 43-55 (2007)

[24] Khaled, A. R. A. and Vafai, K. The role of porous media in modeling flow and heat transfer inbiological tissues. Int. J. Heat Mass Trans., 46, 4989-5003 (2003)

[25] Jha, B. K. and Prasad, R. Effects of applied magnetic field on transient free convective flow in avertical channel. J. Math. Phys. Sci., 26, 1-8 (1992)

[26] Lai, F. C. Coupled heat and mass transfer by mixed convection from a vertical plate in a saturatedporous medium. Int. Comm. Heat Mass Trans., 18, 93-106 (1991)

[27] Singh, A. K., Singh, A. K., and Singh, N. P. Heat and mass transfer in MHD flow of a viscousfluid past a vertical plate under oscillatory suction velocity. Ind. J. Pure Appl. Math., 34, 429-442(2003)

[28] Leitao, A., Li, M., and Rodrigues, A. The role of intraparticle convection in protein absorption byliquid chromatography using porous 20 HQ/M articles. Biochem. Eng. J., 11(2-3), 33-48 (2002)

[29] Darcy, H. R. P. G. Les Fontaines Publiques de la Voll de Dijan, Vector Dalmout, Paris (1856)

[30] Preziosi, L. and Farina, A. On Darcy's law for growing porous media. Int. J. Nonlin. Mech., 37,485-491 (2002)

[31] Dash, R. K., Mehta, K. N., and Jayaraman, G. Casson fluid flow in a pipe filled with homogeneousporous medium. Int. J. Eng. Sci., 34, 1146-1156 (1996)

[32] Acharya, M., Dash, G. C., and Singh, L. P. Magnetic field effects on the free convection and masstransfer flow through porous medium with constant suction and constant heat flux. Ind. J. PureAppl. Math., 31(1), 1-18 (2000)

[33] Kumar, A., Chand, B., and Kaushik, A. On unsteady oscillatory laminar free convection flowof an electrically conducting fluid through porous medium along a porous hot plate with timedependent suction in the presence of heat source/sink. J. Acad. Math., 24, 339-354 (2002)

[34] Takhar, H. S., Chamkha, A. J., and Nath, G. Unsteady laminar MHD flow and heat transfer in thestagnation region of an impulsively spinning and translating sphere in the presence of buoyancyforces. Heat Mass Trans., 37, 397-402 (2001)

[35] Prasad, K. V. and Vajravelu, K. Heat transfer in the MHD flow of a power law fluid over anon-isothermal stretching sheet. Int. J. Heat Mass Trans., 52, 4956-4965 (2009)

[36] Ganesan, P. and Palani, G. Finite difference analysis of unsteady natural convection MHD flowpast an inclined plate with variable surface heat and mass flux. Int. J. Heat Mass Trans., 47,4449-4457 (2004)

[37] Pal, B., Misra, J. C., and Gupta, A. S. Steady hydromagnetic flow in a slowly varying channel.Proc. Natl. Inst. Sci. Ind. Part A, 66, 247-262 (1996)

[38] Misra, J. C., Pal, B., Pal, A., and Gupta, A. S. Oscillatory entry flow in a plane channel withpulsating walls. Int. J. Nonlin. Mech., 36, 731-741 (2001)

[39] Misra, J. C. and Shit, G. C. Effect of magnetic field on blood flow through an artery: a numericalmodel. J. Comput. Tech., 12, 3-16 (2007)

[40] Yin, F. and Fung, Y. C. Peristaltic waves in circular cylindrical tubes. J. Appl. Mech., 36, 679-687(1969)

[41] Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L. Peristaltic pumping with long wavelength atlow Reynolds number. J. Fluid Mech., 37, 799-825 (1969)

[42] Takabatake, S., Ayukawa, K., and Mori, A. Peristaltic pumping in circular cylindrical tubes: anumerical study of fluid transport and its efficiency. J. Fluid Mech., 193, 267-283 (1988)

[43] Olugu, A. and Amos, E. Modeling pulsatile blood flow within a homogeneous porous bed in thepresence of a uniform magnetic field and time dependent suction. Int. Comm. Heat Mass Trans.,34, 989-995 (2007)

[44] Brewster, M. Q. Thermal Radiative Transfer Properties, John Wiley and Sons, New York (1992)

[45] Olugu, A. and Amos, E. Asymptotic approximations for the flow field in a free convective flow ofa non-Newtonian fluid past a vertical porous plate. Int. Comm. Heat Mass Trans., 32, 974-982(2005)

[46] Chaudhary, R. C. and Jha, A. K. Effect of chemical reactions on MHD micropolar fluid flow pasta vertical plate in slip-flow regime. Appl. Math. Mech. -Engl. Ed., 29(9), 1179-1194 (2008) DOI10.1007/s10483-008-0907-x