Investigation of Hall Effect on Hydromagnetic Blood Flow in an Inclined Stretching Permeable Vessel of Patients

Abstract

The present work provides a computational analysis with applications to magnetohydrodynamic (MHD) blood flow that goes beyond standard models by incorporating Hall currents, ion-slip phenomena, and various other fundamental factors that are deeply interrelated within the context of blood flow in a permeable and extending blood vessel. At the heart of this research is its novel fundamental mathematical model that combines within one overarching theoretical construction of the fundamentals of porous medium flow resistance, buoyancy forces caused by purely thermal as well as solutal processes, and viscous dissipation. Notably, such an integrated research model fills an absolutely fundamental gap in current research findings that have treated these phenomena one by one. The partial differential equations that are dominant are made nondimensional and transformed into a set of nonlinear ordinary differential equations that are solved to a high degree of accuracy by the bvp4c solver function in MATLAB. Validation results indicate that the present numerical solution compares perfectly with existing benchmark solutions with no error (maximum relative error ¡ 0.02%). What is perhaps most enlightening is the sensitivity analysis indicating complex, even counterintuitive, dependencies with key parameters in electromagnetic phenomena. For example, the Hartmann number (Ha) has a DOUBLE role; that is, with increasing values of (Ha) from 0.1 to 1.0, there is a 42% reduction in the main flow but, due to the coupling with Hall currents, there is an impressive 300% enhancement in secondary flow. A more dramatic effect is found with the Hall parameter (m), wherein an increase from 0.5 to 5.0 leads to an impressive 400% increase in secondary flow speeds with 35% less electromagnetic braking. These findings not only deepen our fundamental understanding of MHD biofluid dynamics but also highlight practical pathways for controlling blood flow in applications such as magnetic drug delivery, targeting and lab-on-a-chip diagnostics where fine tuned electromagnetic tuning could replace invasive mechanical interventions.