A numerical study is performed to investigate the magnetohydrodynamic viscous steady biofluid flow through a curved pipe with circular cross section under various conditions. A spectral method is applied as the principal tool for the numerical simulation with Fourier series, Chebyshev polynomials, collocation methods and an iteration method as secondary tools. The combined effects of Dean number, Dn, magnetic parameter, Mg, and tube curvature, δ, are studied. The flow patterns have been shown graphically for large Dean numbers as well as magnetic parameter and a wide range of curvatures, 0.01 ≤δ≤ 0.2. Two-vortex solutions have been found. Axial velocity has been found to increase with an increase of Dean number, whereas it is suppressed with greater curvature and magnetic parameters. For high magnetic parameter and Dean number and low curvature, almost all the fluid vortex strengths are weak. The study is relevant to magnetohydrodynamic blood flow in the cardiovascular system.
TripathiDBégOA. A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Proc IMechE, Part H: J Engineering in Medicine2012; 226: 631–644.
6.
RashidiMMKeimaneshMBégOA. Magneto-hydrodynamic biorheological transport phenomena in a porous medium: a simulation of magnetic blood flow control and filtration. Int J Numer Method Biomed Eng2011; 27: 805–821.
7.
RamamurthyGShankerB. Magnetohydrodynamic effects on blood flow through a porous channel. Med Biol Eng Comput1994; 32: 655–659.
8.
TakharHSBhargavaRRawatS. Biomagnetic hydrodynamics in a two-dimensional non-Darcian porous medium: finite element study. J Theor Appl Mech2007; 37: 59–76.
9.
BhargavaRSharmaSBégOA. Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow. Commun Nonlinear Sci2010; 15: 1210–1233.
10.
BégOAGhoshSKAhmedS. Mathematical modelling of oscillatory magneto-convection of a couple stress biofluid in an inclined rotating channel. J Mech Med Biol2012; 12: 1250050.1–1250050.35.
11.
BégOARashidiMMBégTA. Homotopy analysis of transient magneto-bio-fluid dynamics of micropolar squeeze film in a porous medium: a model for magneto-bio-rheological lubrication. J Mech Med Biol2012; 12: 1250051.1–1250051.21.
12.
SudYKSuriPKMishraRK. Laminar flow of blood in an elastic tube in the presence of magnetic field. Stud Biophys1978; 69: 175–185.
13.
PandeySKTripathiD. Influence of magnetic field on peristaltic flow of viscous fluid through a finite length cylindrical tube. Appl Bionic Biomech2010; 7: 169–176.
14.
KainzWGuagJBenklerS. Development and validation of a magneto-hydrodynamic solver for blood flow analysis. Phys Med Biol2010; 55: 7253–7273.
15.
DeanWR. Note on the motion of fluid in a curved pipe. Philos Mag1927; 4: 208–223.
16.
ReidWH. On stability of viscous flow in curved channel. P Roy Soc A: Math Phy1958; 244: 186–198.
17.
BrewsterDBGrosbergPNissanAH. The stability of viscous flow between horizontal concentric cylinders. P Roy Soc A: Math Phy1959; 251: 76–91.
18.
ItoH. Theory on laminar flows through curved pipes of elliptic and rectangular cross-section. Reports of Institute of High Speed Mechanics, Tohoku University, Japan, May1951, pp.1–16.
19.
CumingHG. The secondary flow in curved pipes. Aeronautical Research Council Reports and Memoranda. No. 2880, Cleveland, USA, July1952. NACA Publications.
20.
ChengKCAkiyamaM. Graetz problem in curved pipes with uniform wall heat flux. Appl Sci Res1974; 29: 401–418.
21.
ChengKCLinROuJW. Graetz problem in curved square channels. J Heat Trans: T ASME1975; 97: 244–248.
22.
MasliyahJH. On laminar flow in curved semi-circular ducts. J Fluid Mech1980; 99: 469–479.
23.
NandakumarKMasliyahJH. Swirling flow and heat transfer in coiled and twisted pipes. Adv Transport1986; 4: 49–112.
24.
DennisSCRNgM. Dual solutions for steady laminar flow through a curved tube. Q J Mech Appl Math1982; 35: 305–324.
25.
YanaseSGotoNYamamotoK. Dual solutions of the flow through a curved tube. Fluid Dyn Res1989; 5: 191–201.
26.
ShanthiniWNandakumarK. Bifurcation phenomena of generalized Newtonian fluids in curved rectangular ducts. J Non-Newton Fluid1986; 22: 35–59.
27.
WintersKH. A bifurcation study of laminar flow in a curved tube of rectangular cross-section. J Fluid Mech1987; 180: 343–369.
28.
DaskopoulosPLenhoffAM. Flow in curved ducts: bifurcation structure for stationary ducts. J Fluid Mech1989; 203: 125–148.
29.
YangTWangL. Solution structure and stability of viscous flow in curved square ducts. J Fluid Eng: T ASME2001; 123: 863–868.
30.
FinlayWH. Perturbation expansion and weakly nonlinear analysis for two-dimensional vortices in curved or rotating channels. Phys Fluids A: Fluid1989; 1: 854–860.
31.
FinlayWHNandakumarK. Onset of two-dimensional cellular flow in finite curved channels of large aspect ratio. Phys Fluids A: Fluid1990; 7: 1163–1174.
32.
SinghSN. Magnetohydrodynamic flow in a curved pipe. Appl Sci Res1965; 12: 405–423.
33.
IssacciFGhoniemNMCattonI. Magnetohydrodynamic flow in a curved pipe. Phys Fluids1988; 31: 65–71.
34.
HayatTNoreenSAlsaediA. Effect of an induced magnetic field on peristaltic flow of non-Newtonian fluid in a curved channel. J Mech Med Biol2012; 2: 1250058 (26 pp.).
35.
MathieuJ-BMartelS. Magnetic microparticle steering within the constraints of an MRI system: proof of concept of a novel targeting approach. Biomed Microdevices2007; 9: 801–808.
36.
VoltairasPAFotiadisDIMichalisLK. Hydrodynamics of magnetic drug targeting. J Biomech2002; 35: 813–821.
37.
FrewerRA. The electrical conductivity of flowing blood. Biomed Eng1974; 23: 552–554.
38.
BégOAGhoshSKBégTA. Applied magnetofluid dynamics: modelling and computation. Saarbrücken: Lambert Academic Publishing, 2011, 443 pp.
39.
GottliebDOrszagSA. Numerical analysis of spectral methods: theory and applications (CBMS-NSF regional conference series in applied mathematics no. 26). Philadelphia, PA: SIAM, 1977.
40.
ShihYD. MHD flow in curved pipes. PhD Thesis, State University of New York (SUNY), Buffalo, NY, 1981.
41.
ShihYDLiuCSYuCP. Fully developed magnetohydrodynamic flow in a curved rectangular channel. In: ASME Winter Annual Meeting (Fluids Engineering Division, FED), Phoenix, AZ, 14 November 1982, New York: ASME.
42.
PapadopoulosPKTzirtzilakisEE. Biomagnetic flow in a curved square duct under the influence of an applied magnetic field. Phys Fluids2004; 16: 2952–2962.
43.
KinouchiYYamaguchiHTenfordeTS. Theoretical analysis of magnetic field interactions with aortic blood flow. Bioelectromagnetics1996; 17: 21–32.
44.
MorrisLDelassusPCallananA. 3-D numerical simulation of blood flow through models of the human aorta. J Biomech Eng: T ASME2005; 127: 767–775.
45.
TripathiDBégOA. A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium. Transport Porous Med2012; 95: 337–348.
46.
BégOAHameedMBégTA. Chebyschev spectral collocation simulation of nonlinear boundary value problems in electrohydrodynamics (EHD). Int J Comput Meth Eng Sci Mech2013; 14: 104–115.
47.
BégOAWahiduzzamanMAlamMA. Spectral numerical study of non-isothermal physiological flow through a rotating rectangular cross-section duct. ZAMM- J. Appl. Math. Mechanics2013, in press.
