Magneto-Hydrodynamic (MHD) Slip Blood Flow Past an Inclined Porous Vessel with Pressure Gradient, Heat and Chemical Reaction Effect: Mathematical Modeling and Treatment for Hypotension

This study investigates Magneto-hydrodynamic $(MHD)$ blood slip flow past a porous blood vessel, inclined and influenced by a pressure gradient, a magnetic field, heat transfer, and chemical reaction effects. The blood considered is a non-Newtonian, electrically conducting fluid with a slip boundary condition, accounting for the interaction between the porous wall and the fluid flowing through an inclined, tiny porous vessel under an applied magnetic field in the perpendicular direction. The governing equations were formulated using magneto-hydrodynamic principles and fluid transport phenomena with porosity, with the Hartmann number effect embedded. The governing equations in dimensional form are converted to dimensionless form, and analytical solutions are applied using the George Frobenius power series to obtain the solution for the velocity, temperature, and concentration profiles. Results showed the effect of chemical reaction, magnetic field, heat source, and various parameters on the blood flow through the porous, tiny blood vessels. The increase in chemical reaction $(Kn)$ increased mass diffusion and improved blood flow, while an increase in the heat source $Q_{T}$ increased the temperature and the flow of blood. An increase in suction/injection $(A)$ and porosity $(k)$ decreased the blood flow, while an increase in Schmidt $(Sc)$ number increased the mass diffusion. An increase in the Hartmann number $(Hn)$ increased the overall blood flow, and an increase in the inclination of the porous artery improved blood flow direction, which serves as a therapeutic approach for the treatment of hypotension in patients.