Fractional model for blood flow under MHD influence in porous and non-porous media

In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grünwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a non-porous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow.