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Journal of Applied Nonlinear Dynamics 12(1) (2023) 87--97 | DOI:10.5890/JAND.2023.03.006

V. Sitamahalakshmi$^1$, G. Venkata Ramana Reddy$^2$, Bidemi Olumide Falodun$^3$

$^1$ Department of Mathematics, PVP Siddhartha Institute of Technology, Kanur, India-520007

$^2$ Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, India-522502

$^3$ Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria

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Abstract

In this paper theoretical analysis of blood flow with heat along with mass transport under the influence of time-dependent magnetism with Casson fluid flow intensity has been elucidated. The unsteady nonlinear partial differential equations (PDEs) of blood flow considers time-dependent stretching velocity, the energy equation also accounts time-dependent temperature of the vessel wall and the concentration equation includes time-dependent blood concentration. The governing nonlinear equation of motion, energy as well as concentration were simplified into ordinary differential equations (ODE) using the approach of similarity transformations. Runge-Kutta Fehlberg method alongside shooting procedure was later used to solve the set of ODE. The effect of physical parameters viz., Casson fluid, permeability, unsteadiness, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter, and Schmidt number on flow variables viz., velocity flow of blood in the vessel, temperature and concentration of blood has been analyzed and discussed graphically. From the simulation study, the following important results are obtained: velocity of blood flow decreases with both increment of magnetic and unsteadiness parameter. The temperature of the blood decreases in the vessel wall as Prandtl number becomes large. The concentration of the blood degenerates as time-dependent chemical reaction parameter together with the Schmidt number increases.This study is unique because it explores unsteady blood flow extended to a penetrable slim vessel with the impact of time-dependent magnetism. We considered the blood flow in a slim vessel; hence the flow is two dimensional. We have taken the blood vessel to be stretched with a velocity and blood concentration. To the very best of our understanding, the problem of this type has not been elucidated in the past.

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