Kh. S. Mekheimer, Mohamed H. Haroun, M. A. El Kot. Effects of Magnetic Field,Porosity and Wall Properties for Anisotropically Elastic Multi-Stenosis Arteries on the Characteristics of Blood Flow[J]. Applied Mathematics and Mechanics, 2011, 32(8): 981-997. doi: 10.3879/j.issn.1000-0887.2011.08.009
Citation: Kh. S. Mekheimer, Mohamed H. Haroun, M. A. El Kot. Effects of Magnetic Field,Porosity and Wall Properties for Anisotropically Elastic Multi-Stenosis Arteries on the Characteristics of Blood Flow[J]. Applied Mathematics and Mechanics, 2011, 32(8): 981-997. doi: 10.3879/j.issn.1000-0887.2011.08.009

Effects of Magnetic Field,Porosity and Wall Properties for Anisotropically Elastic Multi-Stenosis Arteries on the Characteristics of Blood Flow

doi: 10.3879/j.issn.1000-0887.2011.08.009
  • Received Date: 2010-09-16
  • Rev Recd Date: 2011-04-10
  • Publish Date: 2011-08-15
  • A mathematical model for blood flow through an elastic artery with multi-stenosis under effect of a magnetic field in a porous medium was presented.The arterial segment under consideration was simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood.The analysis was carried out for an artery with mild local narro wing in its lumen forming a stenosis.The effects of arterial wall parameters that represent the viscoelastic stresses components acting along the longitudinal and circumferential directions Tt and Tθ respectively,the degree of anisotropy of the vessel wall γ, the total mass of the vessel and the surrounding tissues M and the contributions of the viscous and elastic constraints to the total tethering C and K respectively on the resistance impedance, the wall shear stress distribution,the radial and axial velocities had been well illustrated.Also the effects of the stenosis shape m,the constant of permeability κ,the Hartmann number Ha and the maximum height of the stenosis size δ on the fluid flow characteristics were investigated.The obtained results show that the flow was appreciably influenced by the surrounding connective tissues of the motion of the arterial wall and the degree of aniso tropy of the vessel wall play an important role to determine the material of the artery.Further the wall shear stress distribution increases with increasing Tt and γ while it decreases with increasing Tθ,M,C and K.The transmission of the wall shear stress distribution and the resistance impedance at the wall surface through a tethered tube were substantially lower than those through the free tube while the shearing stress distribution at the stenosis throathad inverse character through to tally tethered and free tubes.The trapping bolus increases in size to ward the line center of the tube as the constant of permeability κ increases and it decreases by increasing Hartmann number Ha.Finally the trapping bolus appears gradually in the case of non-symmetric stenosis while it seems to disappear in the case of symmetric stenosis and the size of trapped bo lus for the stream lines in the free isotro pictube(means the tube which initially unstressed) was smaller than those in the tethered tube.
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