Heat and mass diffusion to williamson fluid streaming through a tube with multiple stenoses while subjected to periodic body acceleration

Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

^* Corresponding author: fahim.muh1@gmail.com

Received: 17 October 2022
Accepted: 28 June 2023

Abstract

This article examines a mathematical framework that describes the versatile behavior of heat and mass exchange in blood flowing through a narrowed vessel having multiple stenoses. The geometry of a channel having multiple stenoses with an asymmetrical axial axis and a symmetrical radial axis can be visualized by applying a suitable mathematical expression. The geometry of the chosen model considers the height and shape of stenoses. The modification in shape parameter is used to capture variations in the shape of the stenoses in the artery. The blood is supposed to be isochoric (incompressible), while its rheological behavior is characterized by Williamson’s fluid model. The transfer of momentum is analyzed using the equation of motion in cooperation with the continuity equation. In addition, the equations of heat conduction and diffusion are utilized, respectively, to illustrate the distributions of heat and mass. Simplified forms of momentum, mass, and heat transport equations are achieved by incorporating dimensionless quantities and moderate stenosis conditions. A well-known explicit finite difference approach is utilized to solve the emergent non-linear system of governing equations numerically. The influence of different evolving parameters on the flow field along with mass and heat distributions is illustrated through various plots.