A Low Prandtl Number Haemodynamic Oscillatory Flow through a Cylindrical Channel using the Power Series Method

Abstract

This article details the use of the power series method to solve a haemodynamics problem in a cylindrical channel with a low Prandtl number. The process involves modifying the Navier-Stokes momentum equation and energy equation with radiation absorption to represent flow through a cylindrical channel; the governing models are made dimensionless with the help of some dimensionless quantities; and the flow is subjected to no-slip boundary conditions. It is true that the flow through biological vessels is thought to be oscillatory due to the pulsatile nature of the heart. The solutions were thought to be associated with an oscillatory frequency term. The dimensionless models were perturbed using the oscillatory term, and the partial differential equations were reduced to ordinary differential equations. Wolfram Mathematica, version 12, was used to code the analytical solutions, which included biophysical parameters such as the Prandtl number, oscillatory frequency parameter, Hartmann number, radiation absorption parameters, and dimensionless wall temperature. It was discovered that changes in biophysical parameters caused changes in both the velocity and temperature profiles, which is extremely important for scientists and clinicians. It is recommended that we pay attention to some of the parameters mentioned above in order to achieve the best results when studying blood flow through a vessel.