Numerical Solution of Heat and Mass Transfer Problem in Oscillatory Flow of a Viscous Electrically Conducting Fluid Through a Porous Channel Subjected to a Magnetic Field: Applications to Blood Flow in Arteries in a Pathological State

A.Sinha; J.C.Misra

doi:10.3879/j.issn.1000-0887.2012.05.009

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A.Sinha, J.C.Misra. Numerical Solution of Heat and Mass Transfer Problem in Oscillatory Flow of a Viscous Electrically Conducting Fluid Through a Porous Channel Subjected to a Magnetic Field: Applications to Blood Flow in Arteries in a Pathological State[J]. Applied Mathematics and Mechanics, 2012, 33(5): 614-627. doi: 10.3879/j.issn.1000-0887.2012.05.009

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Numerical Solution of Heat and Mass Transfer Problem in Oscillatory Flow of a Viscous Electrically Conducting Fluid Through a Porous Channel Subjected to a Magnetic Field: Applications to Blood Flow in Arteries in a Pathological State

doi: 10.3879/j.issn.1000-0887.2012.05.009

A.Sinha¹,
J.C.Misra²

¹School of Medical Science and Technology, Indian Institute of Technology, Kharagpur 721302, India;²Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India

Received Date: 2011-03-09
Rev Recd Date: 2011-11-12
Publish Date: 2012-05-15

Abstract

Abstract

A problem was motivated towards studying heat and mass transfer in the unsteady MHD flow of blood through a porous vessel, when the lumen of the vessel had turned into a porous structure. Consideration of time-dependent permeability and oscillatory suction velocity had been made. The problem was solved numerically. The computational results are presented graphically for the velocity, temperature and concentration fields as well as the skin friction co-efficient, Nusselt number and Sherwood number for various values of the parameters involved in the analysis.It was revealed that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.
- mass transfer,
- radiation,
- suction velocity,
- skin friction

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References(46)

References

[1]	Ramamurthy G, Shanker B. Magnetohydrodynamic effects on blood through a porous channel[J]. Med Biol Eng Comput, 1994, 32(6):655-659.
[2]	Mustapha M, Amin N, Chakravarty S, Mandal P K. Unsteady magnetohydrodynamic blood flow through irregular multistenosed arteries[J].Computers in Biology and Medicine, 2009, 39(10):896-906.
[3]	Mekheimer Kh S. Peristaltic flow of blood under effect of magnetic field in a non-uniform channel[J]. Appl Math Comput, 2004, 153(3):763-777.
[4]	密斯让 J C，辛哈 A，斯特 G C. 生物磁粘弹性流体的流动：应用动脉电磁过热评估血液的流动，癌症治疗进程[J]. 应用数学和力学, 2010, 31(11):1330-1343. (Misra J C, Sinha A, Shit G C. Flow of a biomagnetic viscoelastic fluid: application to estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(11): 1405-1420.)
[5]	Misra J C, Sinha A, Shit G C. Theoretical analysis of blood flow through an arterial segment having multiple stenoses[J]. J Mech Med Biol, 2008, 8(2):265-279.
[6]	Misra J C, Kar B K. Momentum integral method for studying flow characteristics of blood through a stenosed vessel[J]. Biorheol, 1989, 26(1):23-25.
[7]	Misra J C, Pal B, Gupta A S. Hydrodynamic flow of a second-grade fluid in a channel-some applications to physiological systems[J]. Math Model Meth Appl Sci, 1998, 8:1323-1342.
[8]	Misra J C, Patra M K, Misra S C. A non-Newtonian fluid model for blood flow through arteries under the stenotic conditions[J].J Biomech, 1993, 26(9):1129-1141.
[9]	Misra J C, Roychoudhuri K. A study on the stability of blood vessels[J].Rheol Acta, 1982, 21(3):341-346.
[10]	Misra J C, Roychoudhuri K. Effect of initial stresses on the wave propagation in arteries[J].J Math Biol, 1983, 18(1):53-67.
[11]	Misra J C, Shit G C. Blood flow through arteries in a pathological state[J].Int J Eng Sci, 2006, 44(10): 662-671.
[12]	Misra J C, Shit G C. Role of slip velocity in blood flow through stenosed arteries: a non-Newtonian model[J].J Mech Med Biol, 2007, 7(3):337-353.
[13]	Misra J C, Shit G C.Biomagnetic viscoelastic fluid flow over a stretching sheet[J].Appl Math Comput, 2009, 210(2):350-361.
[14]	Misra J C, Shit G C, Rath H J. Flow and heat transfer of an MHD viscoelastic fluid in a channel with stretching walls: some applications to hemodynamics[J].Comp Fluids, 2008, 37(1):1-11.
[15]	Misra J C, Sinha S I. A study on the nonlinear flow of blood through arteries[J].Bull Math Biol, 1987, 49(3):257-277.
[16]	Misra J C, Shit G C. Flow of a biomagnetic viscoelastic fluid in a channel with stretching walls[J]. ASME J Appl Mech, 2009, 76(6):1006-1014.
[17]	Misra J C, Shit G C, Chandra S, Kundu P K. Electro-osmotic flow of a viscoelastic fluid in a channel: application to physiological fluid mechanics[J].Appl Math Comput, 2011, 217(20):7932-7939.
[18]	Misra J C, Chakravarty S. Dynamic response of arterial walls in vivo[J].J Biomech, 1982, 15(4):317-324.
[19]	Misra J C, Singh S I. Pulse wave velocities in the aorta[J].Bull Math Biol, 1984, 46(1):103-114.
[20]	Vardanyan V A. Effect of magnetic field on blood flow[J].Biofizika, 1973, 18(3):491-496.
[21]	Barnothy M F. Biological Effects of Magnetic Fields[M]. Vols 1 and 2. New York:Plenum Press, 1964 and 1969.
[22]	Ritman E L, Lerman A. Role of vasa vasorum in arterial disease: a re-emerging factor[J].Current Cardiology Reviews, 2007, 3(1):43-55.
[23]	Khaled A R A, Vafai K. The role of porous media in modeling flow and heat transfer in biological tissues[J].Int J Heat Mass Trans, 2003, 46(26):4989-5003.
[24]	Jha B K, Prasad R. Effects of applied magnetic field on transient free convective flow in a vertical channel[J]. J Math Phys Sci, 1992, 26(1):1-8.
[25]	Lai F C. Coupled heat and mass transfer by mixed convection from a vertical plate in a saturated porous medium[J].Int Comm Heat Mass Trans, 1991, 18(1):93-106.
[26]	Singh A K, Singh A K, Singh N P. Heat and mass transfer in MHD flow of a viscous fluid past a vertical plate under oscillatory suction velocity[J].Ind J Pure Appl Math, 2003, 34(3):429-442.
[27]	Leitao A, Li M, Rodrigues A. The role of intraparticle convection in protein absorption by liquid chromatography using porous 20 HQ/M articles[J].Biochem Eng J, 2002, 11(1):33-48.
[28]	Darcy H R P G. Les Fontaines Publiques de la voll de Dijan[M]. Paris:Vector Dalmout, 1856.
[29]	Preziosi L, Farina A. On Darcy’s law for growing porous media[J].Int J Non-Linear Mech, 2002, 37(3): 485-491.
[30]	Dash R K, Mehta K N, Jayaraman G. Casson fluid flow in a pipe filled with homogeneous porous medium[J]. Int J Eng Sci, 1996, 34(10):1146-1156.
[31]	Acharya M, Dash G C, Singh L P. Magnetic field effects on the free convection and mass transfer flow through porous medium with constant suction and constant heat flux[J].Ind J Pure Appl Math, 2000, 31(1):1-18.
[32]	Kumar A, Chand B, Kaushik A.On unsteady oscillatory laminar free convection flow of an electrically conducting fluid through porous medium along a porous hot plate with time dependent suction in the presence of heat source/sink[J].J Acad Math, 2002, 24:339-354.
[33]	Takhar H S, Chamkha A J, Nath G. Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces[J].Heat Mass Trans, 2001, 37(4):397-402.
[34]	Prasad K V, Vajravelu K. Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet[J]. Int J Heat Mass Trans, 2009, 52(21/22):4956-4965.
[35]	Ganesan P, Palani G. Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux[J].Int J Heat Mass Trans, 2004, 47(19/20):4449-4457.
[36]	Pal B, Misra J C, Gupta A S. Steady hydromagnetic flow in a slowly varying channel[J].Proc Natl Inst Sci Ind Part A, 1996, 66:247-262.
[37]	Misra J C, Pal B, Pal A, Gupta A S. Oscillatory entry flow in a plane channel with pulsating walls[J]. Int J Non-Linear Mech, 2001, 36(5): 731-741.
[38]	Misra J C, Shit G C. Flow and heat transfer of an MHD viscoelastic fluid in a channel with stretching walls: some applications to hemodynamics[J].Computers and Fluids, 2008, 37(1):1-11.
[39]	Yin F, Fung Y C. Peristaltic waves in circular cylindrical tubes[J]. J Appl Mech, 1969, 36(3):679-687.
[40]	Shapiro A H, Jaffrin M Y, Weinberg S. L. Peristaltic pumping with long wavelength at low Reynolds number[J].J Fluid Mech, 1969, 37(4):799-825.
[41]	Takabatake S, Ayukawa K, Mori A. Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency[J].J Fluid Mech, 1988, 193:267-283.
[42]	Olugu A, Amos E. Modeling pulsatile blood flow within a homogeneous porous bed in the presence of a uniform magnetic field and time dependent suction[J].Int Comm Heat Mass Trans, 2007, 34(8): 989-995.
[43]	Mortimer R G, Eyring H. Elementary transition state theory of the Soret and Dufour effects[J].Proc Nat Acad Sci, 1980, 77(4):1728-1731.
[44]	Brewster M Q. Thermal Radiative Transfer Properties[M]. New York :John Wiley and Sons, 1992.
[45]	Olugu A, Amos E. Asymptotic approximations for the flow field in a free convective flow of a non-Newtonian fluid past a vertical porous plate[J], Int Comm Heat Mass Trans, 2005, 32(7):974-982.
[46]	乔德哈瑞 R C, 吉哈 A K. 化学反应对竖直平板边界磁流体动力学微极流体滑流的影响[J].应用数学和力学, 2008, 29(9):1069-1082.(Chaudhary R C, Jha A K. Effect of chemical reactions on MHD micropolar fluid