<p>The potential advancements in cancer diagnosis and treatment are significant, with nanoparticles showing promise as therapeutic agents when exposed to an applied magnetic field. This paper seeks to analyze the stability of blood flow, treating it as a non-Newtonian fluid. By augmenting the Navier-Stokes equations with energy considerations, a pair of eigenvalue equations governing flow stability is derived. Subsequently, a numerical approximation using the Chebyshev collocation scheme is employed. The study illustrates how various factors, including Hartmann number, wave number, magnetic field orientation, and Reynolds number, affect the stability of non-Newtonian blood flow at standard body temperature. Specifically, altering the magnetic field’s direction, which amplifies the Lorentz force, thereby influencing flow dynamics. These findings hold significant implications in medicine, offering potential non-surgical interventions for cancerous and arterial diseases. Such interventions could potentially reduce costs and mitigate post-surgical complications for patients.</p>