×

Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow. (English) Zbl 1221.76217

Summary: We consider the two-dimensional fully-developed steady, viscous hydrodynamic flow of a deoxygenated biomagnetic micropolar fluid, in an \((X, Y)\) coordinate system. The momentum conservation equations with zero-pressure gradient are extended to incorporate the \(X\)- and \(Y\)-components of the biomagnetic body force term with appropriate boundary conditions. The equations are non-dimensionalized using a set of transformations. A finite element solution is obtained to the resulting non-dimensional model and the effects of biomagnetic number \((N_{H})\), micropolar microinertia parameter \((B)\) and micropolar viscosity ratio parameter \((R)\) on the \(X\)- and \(Y\)-direction velocity profiles and micro-rotation \((N)\) is studied in detail. Translational velocities \((U, V)\) are seen to be reduced with an increase in micropolarity \((R)\) and also biomagnetic effects \((N_{H})\). Conversely the velocities are increased with a rise in microinertia parameter \((B)\). Several special cases, e.g. Newtonian biomagnetic physiological flow, are also discussed. The model finds applications in blood flow in biomedical device technology (e.g. oxygenators), hemodynamics under strong external magnetic fields, magnetic drug carrier analysis, etc.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
92C35 Physiological flow
Full Text: DOI

References:

[1] Jarvinen E, Lyly M, Ruokolainen J, Raback P. Three-dimensional fluid-structure interaction modeling of blood flow in elastic arteries. ECCOMAS CFD, Swansea, 4-7 September; 2001.; Jarvinen E, Lyly M, Ruokolainen J, Raback P. Three-dimensional fluid-structure interaction modeling of blood flow in elastic arteries. ECCOMAS CFD, Swansea, 4-7 September; 2001.
[2] Dabiri Y, Fatouraee N, Katoozian H. Finite element simulation of blood flow in arteries. In: Proceedings: biomechanics symposium, vol. 485. Netherlands; 2005.; Dabiri Y, Fatouraee N, Katoozian H. Finite element simulation of blood flow in arteries. In: Proceedings: biomechanics symposium, vol. 485. Netherlands; 2005.
[3] Stuhne, G.; Steinman, D. A., Finite-element modeling of the hemodynamics of stented aneurysms, ASME J Biomech Eng, 126, 3, 382-387 (2004)
[4] Chen, J.; Lu, X.-L.; Wang, W., Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses, J Biomech, 39, 11, 1983-1995 (2006)
[5] Chien, S.; Usami, S.; Taylor, H. M.; Lundberg, J. L.; Gregersen, M. I., Effects of hematocrit and plasma proteins on human blood rheology at low shear rates, J Appl Physiol, 21, 81-87 (1966)
[6] Chien, S., Blood rheology in hypertension and cardiovascular diseases, Cardiovas Med, 2, 356-360 (1977)
[7] Chien S, Usami S, Jan K-M, Skalak R. Macrorheological and microrheological correlation of blood flow in the macrocirculation and microcirculation. In: Gabelnick HL, Litt M, editors. Rheology of biological systems, 12-48. Springfield, Illinois: Thomas Charles C; 1973.; Chien S, Usami S, Jan K-M, Skalak R. Macrorheological and microrheological correlation of blood flow in the macrocirculation and microcirculation. In: Gabelnick HL, Litt M, editors. Rheology of biological systems, 12-48. Springfield, Illinois: Thomas Charles C; 1973.
[8] Chien S, Usami S, Skalak R. Blood flow in small tubes, In: Renkin EM, Michel C, editors. Handbook of physiology, circulation [section on microcirculation]. Bethesda, MD: American Physiological Society; 1984. p. 217-49.; Chien S, Usami S, Skalak R. Blood flow in small tubes, In: Renkin EM, Michel C, editors. Handbook of physiology, circulation [section on microcirculation]. Bethesda, MD: American Physiological Society; 1984. p. 217-49.
[9] Merrill, E. W.; Cokelet, G. C.; Britten, A.; Wells, R. E., Non-Newtonian rheology of human blood- effect of fibrinogen deduced by “subtraction”, Circ Res, 13, 48-55 (1963)
[10] Wells, R. E.; Gawronski, T. H.; Cox, P. H.; Perera, R. D., Influence of fibrinogen on flow properties of erythrocyte suspensions, Am J Physiol, 207, 1035-1040 (1964)
[11] Johnston, B. M.; Johnston, P. R.; Corney, S.; Kilpatrick, D., Non-Newtonian blood flow in human right coronary arteries: steady state simulations, J Biomech, 37, 5, 709-720 (2004)
[12] Cheng, T.; Deville, M., Pulsatile flow of non-Newtonian fluids through arterial stenoses, J Biomech, 29, 7, 899-908 (1996)
[13] Misra, J. C.; Patra, M. K.; Misra, S. C., A non-Newtonian fluid model for blood flow through arteries under stenotic conditions, J Biomech, 26, 9, 1129-1141 (1993)
[14] Hlavacek, M., The role of synovial fluid filtration by cartilage in lubrication of synovial joints-IV: squeeze film lubrication: the central film thickness for normal and inflammatory synovial fluids for axial symmetry under high loading conditions, J Biomech, 28, 10, 1199-1205 (1995)
[15] Stoltz, J. F.; Gaillard, S.; Lucius, M., A study of the visco-elastic properties of blood in transient flow, J Biomech, 13, 4, 341-346 (1980)
[16] Torzilli, P. A.; Mow, V. C., On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function II: the analysis, solution and conclusions, J Biomech, 9, 9, 587-606 (1976)
[17] Murayama, M., Orientation of sickled erythrocytes in a magnetic field, Nature, 206, 420-422 (1965)
[18] Chen, I. I.H.; Saha, S., Analysis of an intensive magnetic field on blood flow, J Bioelectricity, 3, 293-298 (1984)
[19] Okazaki, M.; Maeda, N.; Shiga, T., Effect of an inhomogenous magnetic field on flowing erythrocytes, Eur J Biophys, 14, 139-145 (1987)
[20] Takeuchi, T.; Mizuno, T.; Higashi, T.; Yamagishi, A.; Date, M., Orientation of red blood cells in high magnetic field, J Magnetism Magn Mater, 140-144, 1462-1463 (1995)
[21] Ruuge, E. K.; Rusetski, A. N., Magnetic fluids as drug carriers: targeted transport of drugs by a magnetic field, J Magnetism Magn Mater, 122, 335-339 (1993)
[22] Selyama, A.; Maeda, N.; Shiga, T., Analysis of distribution of flowing erythrocytes in a model vessel under an inhomogenous magnetic field, Eur J Biophys, 25, 1-7 (1996)
[23] Srinivasacharya, D.; Radhakrishnamacharya, G.; Srinivasulu, Ch., Influence of wall properties on peristalsis in the presence of magnetic field, Int J Fluid Mech Res, 27, 4, 374-386 (2007)
[24] Bhargava, R.; Rawat, S.; Takhar, H. S.; Bég, O. A., Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel, Mecannica J, 42, 247-262 (2007) · Zbl 1162.76410
[25] Haik Y, Chen JC, Pai VM. Development of biomagnetic fluid dynamics. In: Proc. IX int. symp. on transport phenomena in thermal fluids engineering, Singapore, pacific centre in thermal fluids engineering, Hawaii USA, June; 1996. p. 25-8.; Haik Y, Chen JC, Pai VM. Development of biomagnetic fluid dynamics. In: Proc. IX int. symp. on transport phenomena in thermal fluids engineering, Singapore, pacific centre in thermal fluids engineering, Hawaii USA, June; 1996. p. 25-8.
[26] Okazaki, M.; Maeda, N.; Shiga, T., Drift of an erythrocyte flow line due to magnetic field, Bioelectromagn J, 17, 4, 335-338 (1996)
[27] Haik, Y.; Pai, V.; Chen, C.-J., Apparent viscosity of human blood in a high static magnetic field, J Magnetism Magn Mater, 225, 1/2, 180-186 (2001)
[28] Tzirtzilakis, E. E.; Tanoudis, G. B., Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer, Int J Numer Methods Heat Fluid Flow, 13, 7, 830-848 (2003) · Zbl 1183.76940
[29] Louckopoulos, V. C.; Tzirtzilakis, E. E., Biomagnetic channel flow in spatially varying magnetic field, Int J Eng Sci, 42, 571-590 (2004) · Zbl 1211.76163
[30] Tzirtzilakis, E. E.; Sakalis, V. D.; Kafoussias, N. G.; Hatzikonstantinou, P. M., Biomagnetic flow in a 3D rectangular duct, Int J Numer Methods Fluids, 44, 1279-1298 (2004) · Zbl 1085.76569
[31] Tzirtzilakis, E. E., A mathematical model for blood flow in magnetic field, Phys Fluids, 17, 7, 077103-077115 (2005) · Zbl 1187.76532
[32] Eringen, A. C., Theory of micropolar fluids, J Math Mech, 16, 1, 909-923 (1966) · Zbl 0145.21302
[33] Eringen, A. C.; Kang, C. K., The effect of microstructure on the rheological properties of blood, Bull Math Biol, 38, 2, 135-159 (1976) · Zbl 0326.92009
[34] Laskowski, L. K.; Wronski, S., On pulsatile flow of micropolar fluid, Arch Mech, 28, 615-624 (1976) · Zbl 0355.76008
[35] Devanathan, R.; Parvathamma, S., Flow of micropolar fluid through a tube with stenosis, Med Biol Eng Comput, 21, 438-445 (1983)
[36] Bég OA, Bhargava R, Sughanda Rawat S, Takhar HS, Bég TA. Peristaltic pumping of a micropolar fluid in porous channel, 5th world congress in biomechanics, Munich, Germany, July; 2006.; Bég OA, Bhargava R, Sughanda Rawat S, Takhar HS, Bég TA. Peristaltic pumping of a micropolar fluid in porous channel, 5th world congress in biomechanics, Munich, Germany, July; 2006.
[37] Stokes, V. K., Theories of fluids with microstructure (1984), Springer Verlag: Springer Verlag New York
[38] Bég, O. A.; Takhar, H. S.; Bhargava, R.; Sharma, S.; Hung, T.-K., Mathematical modelling of biomagnetic flow in a micropolar fluid-saturated Darcian porous medium, Int J Fluid Mech Res, 34, 5, 403-424 (2007)
[39] Bég, O. A.; Bhargava, R.; Rawat, S.; Halim, K.; Takhar, H. S., Computational modeling of biomagnetic micropolar blood flow and heat transfer in a two-dimensional non-Darcian porous medium, Meccanica, 43, 391-410 (2008) · Zbl 1163.76454
[40] Rosensweig, R. E., Ferrohydrodynamics (1985), Dover: Dover New York
[41] Gorla, R. S.R.; Takhar, H. S., Boundary-layer flow of micropolar fluid on rotating axisymmetric surfaces with a concentrated heat source, Acta Mech, 105, 1-10 (1994) · Zbl 0814.76004
[42] Takhar, H. S.; Bhargava, R.; Rawat, S.; Bég, T. A.; Bég, O. A., Finite element modelling of third grade viscoelastic fluid flow in a Darcy-Forchheimer porous medium with suction effects, Int J Appl Mech Eng, 12, 215-233 (2007)
[43] Takhar, H. S.; Bhargava, R.; Rawat, S.; Bég, O. A.; Bég, T. A.; Hung, T.-K., Biomagnetic hydrodynamics in a 2-dimensional non-Darcian porous medium: finite element study, J Theor Appl Mech, 37, 2, 59-76 (2007)
[44] Bég, O. A.; Bhargava, R.; Rawat, S.; Takhar, H. S.; Bég, T. A., A study of buoyancy-driven dissipative micropolar free convection heat and mass transfer in a Darcian porous medium with chemical reaction, Nonlinear Anal Model Control J, 12, 2, 157-180 (2007) · Zbl 1288.35467
[45] Bég, O. A.; Takhar, H. S.; Bhargava, R.; Rawat, S.; Prasad, V. R., Numerical study of heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects, Phys Scripta, 77, 1-11 (2008) · Zbl 1162.76052
[46] Bég, O. A.; Bhargava, R.; Rawat, S.; Kahya, E., Numerical study of micropolar convective heat and mass transfer in a non-Darcy porous regime with Soret and Dufour diffusion effects, Emirates J Eng Res, 13, 2, 51-66 (2008)
[47] Bég, O. A.; Takhar, H. S.; Bég, T. A.; Bhargava, R.; Rawat, S., Nonlinear magneto-heat transfer in a fluid-particle suspension flowing in a non-Darcian channel with heat source and buoyancy effects: numerical study, J King Abdul Aziz Univ. Eng. Sci., 19, 1, 63-88 (2008)
[48] Bathe, K. J., Finite element procedures (1996), Prentice-Hall: Prentice-Hall New Jersey, USA
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.