Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R=0 to r/R=1 and it follows a concave pattern when we move from r/R=0 to r/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature

Investigation on numerical solution for a robot arm problem

The aim of this article is focused on providing numerical solutions for a Robot arm problem using the Runge-Kutta sixth-order algorithm. The parameters involved in problem of a Robot control have also been discussed through RKsixth-order algorithm. The précised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Experimental results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. The stability polynomial for the test equation ( is a complex Number) using RK-Butcher algorithm obtained by Murugesan et. al. [Murugesan K., Sekar S., Murugesh V., Park J.Y., "Numerical solution of an Industrial Robot arm Control Problem using the RK-Butcher Algorithm", International Journal of Computer Applications in Technology, vol.19, no. 2, 2004, pp. 132-138] is not correct and the stability regions for RK-fourth order (RKAM) and RK-Butcher methods have been presented incorrectly. They have made a mistake in determining the range for real parts of (h is a step size) involved in the test equation for RKAM and RK-Butcher algorithms. In the present paper, a corrective measure has been taken to obtain the stability polynomial for the case of RK-Butcher algorithm, the ranges for the real part of and to present graphically the stability regions of the RKAM and the RK-Butcher methods. The stability polynomial and stability region of RK-Sixth order are also reported. Based on the numerical results it is observed that the error involved in the numerical solution obtained by RK-Sixth order is less in comparison with that obtained by the RK-Fifth order and RK-Fourth order respectively

Tracer dispersion due to pulsatile casson reactive flow in a circular tube modulated by electrical and magnetic fields

The present article describes a detailed mathematical investigation of electro-magneto-hydrodynamic dispersion in the pulsatile flow of a Casson viscoplastic fluid in a tube packed with a porous medium. Using appropriate transformations, the model is rendered non-dimensional. Via the generalized dispersion method and finite Hankel transforms, analytical solutions for the solute concentration dispersion and convection coefficients have been obtained. The impact of the Hartmann (magnetic) number, Debye–Hückel(electrokinetic) parameter, Darcy number, and chemical reaction parameter with regard to dispersion phenomena has been studied. The evolution in velocity and concentration profiles are investigated graphically for realistic ranges of the various physical parameters. The present investigation, highlights the dual nature of the Debye–Hückel parameter in the dispersion process. Increment in the lower or higher magnitudes of Debye–Hückel parameter induces or decreases the magnitudes of effective dispersion coefficient, whereas it induces a reverse dual mechanism in the zenith of the average concentration profile. The present simulations are relevant to enhancing the performance of diagnostic tools in biochemical engineering, pumping of intelligent rheological working fluids in biomedicine, and also soft robotics