Mechanics of blood flow through narrow artery using Prandtl viscoelastic model

Abstract

Background

The mechanics of blood flow via converging diverging conduits is an intriguing phenomenon that involves multiple fundamental principles of fluid dynamics. Blood arteries can diverge, which means they expand, or converge, which means they contract down. This specific structure is essential for controlling blood flow and preserving adequate circulation across the body. The theory of fluid mechanics is significant concept related to blood flow along converging/divergent channels. Elevated shear strains near the narrower artery throat can stimulate platelets, causing thrombosis that can completely or partially stop blood supply to the human brain or heart. This communication addresses the blood flow in convergent and diverging artery using fundamental concept of fluid mechanics. The Prandtl fluid model is considered as a blood, because of its viscoelastic nature. The influence of heat source, frictional dissipations and a chemical reaction are included.

Methods

The Jaffrey-Hamel flow in a converging and diverging conduits is generalized to Prandtl fluid model considering the purely radial flow through cylindrical pipe like artery with an arbitrary cross section. The governing equations are solved computationally using the Runge–Kutta-Fehlberg (RKF-4) method.

Significant finding

The rheological parameters ε and δ of blood show opposite tendencies for blood circulation. The Brownian and thermophoresis parameters has a significant effect on heat and mass transport rate. The presence of slip (semi blockage) produces flow reversal and higher drag forces at the arterial wall. Significant flow dynamics and heat-mass transport was reveled for diverging (wider) artery β > 0. The non-uniform heat source show similar trends for thermal profile and heat transfer rate.