Linear Stability and Control in MHD Poiseuille Nanoparticle Flow

This study examines the linear stability of magnetohydrodynamic Poiseuille flow of nanoparticle based nanofluids under an applied magnetic field. Small perturbations are introduced to analyze flow stability, and the governing equations are nondimensionalized in terms of the Reynolds number R e , Hartmann number H a , Prandtl number P r , wave number k, and nanoparticle volume fraction ϕ . The resulting eigenvalue problem is solved using the Chebyshev collocation method together with the Qualitat and Zuverlassigkeit (QZ) algorithm. Stability characteristics are investigated through the Orr–Sommerfeld formulation, and the complex growth rate ω , wave number k, and Reynolds number R e are evaluated numerically. The results show that increasing the magnetic parameter H a significantly reduces the growth rate ω and shifts R e toward higher values, indicating enhanced flow stability due to Lorentz force damping. It is observed that higher wave numbers k suppress instability, while increasing R e promotes disturbance amplification and destabilizes the flow. Variations in P r strongly influence thermal stability by altering the balance between thermal diffusion and momentum transport. These quantitative findings demonstrate effective magnetic control of instability and are relevant to thermal management systems, electrical cooling technologies, targeted drug delivery, and advanced heat transfer applications.