Abstract
In this paper, the third grade non-Newtonian MHD blood flow in the porous arteries subjected to the periodic pressure gradient was studied using the Caputo-Fabrizio (NFDt ) time fractional order derivative. The time fractional model was solved by taking the Laplace and the finite Hankel transforms. Results were compared with those reported in the previous studies and good agreement was found. The Mathematica software was used to simulate the velocity profile and the Bessel functions with zero order and first order of first kind. The correlations between the flow velocity and the third grade non-Newtonian fluid parameter, the magnetic field and the porosity were negative. Nevertheless, the flow velocity increased with respect to the Womersely number.
Highlights
Blood flows inside human arteries consist of red blood cells (RBCs), white blood cells (WBCs), platelets and other nutrients
RBC is rich in iron; its behavior is sensitive to the magnetic field
According to Akbar [2], for symmetric stenosis, the resistance caused by impedance reaches to its maximum value, and due to high flow rate in the diverging tapered artery it was smaller than as compared to the converging tapered artery case and size of the trapping bolus was increased by increasing the height of the stenosis and n, while the number and size of the trapped bolus was decreased in the non-tapered artery = 0 and converging tapered artery 0 than as compared to the diverging tapered artery 0
Summary
Blood flows inside human arteries consist of red blood cells (RBCs), white blood cells (WBCs), platelets and other nutrients. According to Abdullah et al [1], the velocities of blood and magnetic particles were low in the presence of external magnetic field Both velocities increased when the Reynolds number decreased. Eldesoky [8] reported that both channel temperature and axial blood flow velocity increased with respect to the Prandtl number and the heating source parameter. These parameters decreased as, the decay’s parameter increased. In the presence of strong external magnetic field, the momentum of the boundary layer diminished and the thermal boundary layer thickened Factors such as Schmidt, Hartmann, Grashof, Eckert numbers and the chemical reaction parameters had no significant effects on the temperature profiles as reported by Ram et al [15]. The results are beneficial to the understandings of magnetic drug transportation in arteries, complex bio-waste fluids deliveries, irregularities of gastro intestinal regulated by magnetic field, magneto endoscopy and surgeries in bleeding control
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