Eur. Phys. J. Plus (2022) 137: 847
https://doi.org/10.1140/epjp/s13360-022-03035-5

Regular Article

Unsteady nonisothermal tangent hyperbolic fluid flow in a stenosed blood vessel with pulsatile pressure gradient and body acceleration

Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan

^a fahim131992@gmail.com

Received: 27 September 2021
Accepted: 4 July 2022
Published online: 21 July 2022

Abstract

This article presents a numerical solution to the time-dependent blood flow in a ω-shaped stenosed vessel influenced by the body acceleration and pulsatile pressure gradient. The tangent hyperbolic fluid model is used to describe the blood rheology. The model under consideration is one of the non-Newtonian models whose constitutive equation is valid at both high and low shear rates. It falls into the class of generalized Newtonian fluids and is capable of describing the shear-thinning behaviour very well. It is proven that this model is significantly sensitive to modest changes in zero shear-rate viscosity and mildly sensitive to fluctuations in infinite shear-rate viscosity. As an accurate predictor of shear-thinning, this model is well suited for the rheology of blood. Scale analysis is used to simplify the basic equations of fluid flow and heat transport for the moderate constriction model. The effects of the vessel’s wall are immobilized via radial coordinate transformation. The resultant nonlinear system of differential equations with specified boundary conditions is computed by utilizing an explicit finite difference approach. The numerical analysis of the dominant quantities such as resistive impendence, flow rate, wall shear stress, axial velocity, and temperature field is performed with variations in the relevant non-dimensional parameters. These findings are represented graphically and described briefly in the discussion. The flow rate and blood velocity rise with escalating the amplitude of body acceleration; however, the reverse response is observed when the stenosis height, Weissenberg number, and power-law exponent are increased. In addition, the Brinkman number and Prandtl number are found to have significant effects on the temperature field.