Abstract
The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations (Laplace and finite Hankel transforms). For the semianalytical solution, the inverse Laplace transform is found by means of Stehfest’s and Tzou’s algorithms. The numerical calculations were performed by using Mathcad software. The flow is significantly affected by Hartmann number, inclination angle, fractional parameter, permeability parameter, and pulsatile pressure gradient frequency, according to the findings. It is deduced that there exists a significant difference in the velocity of the flow at higher time when the magnitude of Reynolds number is small and large.
Highlights
The flow of blood into arteries is important in medical research
In the analysis that was carried out by Hatami et al [1], blood was considered as a third grade non-Newtonian fluid conveying gold nanoparticles through a hollow porous vessel, and it was revealed that increase in the magnitude of the MHD parameter corresponds to a decrease in the velocity profile
The inverse Laplace transform has been calculated by using numerical package though Mathcad because the velocity expressions of Laplace transform are in the complex form of modified Bessel functions
Summary
The flow of blood into arteries is important in medical research. Computational blood flow simulation across vessels is one tool for integrating and interpreting clinical results. The transient fluid dynamic equations of blood flow through stenosis geometry considering the non-Newtonian viscosity of blood and both magnetization and Lorentz forces was studied by Amlimohamadi et al [2]. The two-phase blood flow through a circular tube with magnetic properties has been studied by Zafar et al [21] He found the comparison of the analytical and semianalytical solutions of the classical model. Motivating by Shah et al [28], we have obtained the analytic and semianalytical solutions of unsteady MHD blood flow through an inclined porous tube that has been studied in the presence of peristaltic pressure gradient. The effect of pertinent physical parameters is discussed in detail
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