Abstract
The present study is focused on the unsteady two-phase flow of blood in a cylindrical region. Blood is taken as a counter-example of Brinkman type fluid containing magnetic (dust) particles. The oscillating pressure gradient has been considered because for blood flow it is necessary to investigate in the form of a diastolic and systolic pressure. The transverse magnetic field has been applied externally to the cylindrical tube to study its impact on both fluids as well as particles. The system of derived governing equations based on Navier Stoke's, Maxwell and heat equations has been generalized using the well-known Caputo-Fabrizio (C-F) fractional derivative. The considered fractional model has been solved analytically using the joint Laplace and Hankel (L&H) transformations. The effect of various physical parameters such as fractional parameter, Gr, M and 7 on blood and magnetic particles has been shown graphically using the Mathcad software. The fluid behaviour is thinner in fractional order as compared to the classical one.