Generalized magnetic blood flow in a cylindrical tube with magnetite dusty particles.

• Magnetic blood flow with MPD in a cylindrical tube is considered. • The two-phase Brinkman type fluid model is considered. • The fractional problem with physical condition is formulated. • Joint Laplace and Hankel transform are used for exact solutions. • Magnetic field influenced significantly blood and MPD velocities. This article deals with the magnetic blood flow in a cylindrical tube with uniformly distributed magnetite dusty particles (MDP). The two-phase Brinkman type fluid model is considered. The fractional governing equations are model in the cylindrical coordinate system taking into consideration the magnetization of the fluid due to the applied magnetic field. The fractional governing equations are subjected to physical initial and boundary conditions. The joint Laplace and Hankel transform are employed to develop exact analytical solutions. The obtained solutions are computed numerically and plotted in different graphs. It is noticed that for a long time τ = 0.4 the blood and MDP velocities increase with increasing values of the fractional parameter. In contrast, this effect reverses for a shorter time τ = 0.02. The magnetic field significantly influences the blood and MPD velocities due to Lorentz forces. Both velocities are decreased with increasing values of the magnetic parameter. [ABSTRACT FROM AUTHOR]