Numerical Simulation of Magnetized Blood Flow in Cylindrical Vessel via Caputo-Fabrizio Time-Fractional Derivative

Abstract

The mathematical modelling of blood flow is a fundamental aspect of bio-fluid mechanics, offering a critical insight into human circulatory system and the development of targeted medical therapies. This research aimed to make a numerical simulation based on a blood flow problem transverse magnetic field and pressure gradient in an axisymmetric circular cylindrical vessel without singular kernel using the Caputo-Fabrizio Time Fractional Derivative. There are several governing equations that been used for achieving the mathematical model such as, Laplace transform on the time variables and Fourier transform on spatial variables to define a non-local system which could elucidate the material properties and changes of different stages. Therefore, the flow motion, magnetic particle motion and magnetic field are governed by Navier-Stokes equations, Newton’s second law of motion and Maxwell’s equations, respectively. Hence, the new fractional time derivative NFDt is obtained by changing the kernel, and with its associated initial and boundary conditions. The mathematical model is then transformed into a dimensionless form to identify key physical parameters, including the Hartmann number, Reynold number, and particle concentration.