Stability analysis of Fe₂O₃-enhanced magnetohydrodynamic blood flow in cylindrical vessels using Chebyshev collocation methods

• Computational models are used to simulate blood flow dynamics. • investigated the temporal advancement of slight disorder in arterial blood flow. • Solution for the resultant eigenvalue problem, the Chebyshev collocation method is executed in MATLAB software. • Applying magnetic field to the transverse of fluid flowing. • The linear stability was analyzed using nanoparticles named Ferro-Oxide (Fe 2 O 3 ) in the blood. • The influence of stability rises in the viscosity of the blood flow in the way of arterial middle area. The Navier Stocks and continuity equations were used in our work. The stability of blood flow is a crucial aspect of physiological health, and researchers study it in various contexts to better understand its implications for human well-being. Computational models are used to simulate blood flow dynamics. With advancements in imaging techniques and computational modeling, researchers are significantly able to quantify blood flow stability. In this task, we investigated the temporal advancement of slight disorder in an arterial blood flow as well as the effect of nanoparticle and magnetic field. The Navier-Stokes and continuity equations were used in our work. To obtain numerical results we have utilized Chebyshev collocation scheme for the approximation of the resultant eigenvalue problem. We have applied a magnetic field transverse to the fluid flowing. It is assumed that blood is Casson non-Newtonian, steady, fully developed, and incompressible fluid. Consider the vessel as a cylindrical rigid tube having the z-axis along the fluid flowing, whereas the r-axis is normal to the z-axis, and the radius of the tube is R. Solution for the resultant eigenvalue problem, the Chebyshev collocation method is executed in MATLAB software. The linear stability was analyzed using nanoparticles named Ferro-Oxide (Fe 2 O 3 ) in the blood. It is noticed that the influence of stability increases in the viscosity of the blood flow along the way of arterial centerline. It has been seen in our analysis that a powerful magnetic field and low wave number play a vital role in the stabilization of blood flow.