Porosity and Slip Velocity Effects on MHD Pulsatile Casson Fluid in a Cylinder

Abstract

Numerous researchers have extensively numerically investigated Casson fluid flow in a slip cylinder, resembling blood flow in human arteries. However, no study has successfully derived an analytical solution to validate the accuracy of the complex mathematical models obtained through numerical methods. This study focuses on utilizing Casson fluid to model blood flow in arteries with diameters ranging from 130 to 1300μm by analytical approach. The considered slip velocity is significant, closely mimicking challenges in real-world blood flow applications. Additionally, this research addresses the influence of magnetohydrodynamics (MHD), a porous medium simulating cholesterol plaque, and pulsatile pressure gradients simulating the rhythmic contraction of the heart. The problem is tackled using dual methods, incorporating Laplace and finite Hankel transform techniques. These techniques leverage versatile integral transformations to analytically resolve boundary value problems associated with time and cylindrical domains. The noteworthy outcomes emphasize that blood flow escalates with increasing slip velocity and pulsatile pressure gradient. This phenomenon is attributed to the increased velocity gradient between blood particles and the solid boundary as slip velocity rises. Furthermore, an elevated pressure gradient in blood flow leads to an increased force within blood vessels, directly accelerating blood flow. These findings are essential for addressing mathematical challenges related to blood diseases.