<p>This study investigates the flow and thermal characteristics of a Jeffrey fluid in a horizontal channel under the influence of rotation and a magnetic field. Understanding the behavior of non-Newtonian fluids in magnetohydrodynamic environments is essential for advancing applications in energy systems, biomedical devices, and rotating machinery. The governing equations are derived through mathematical modeling, incorporating the effects of rotation, magnetic forces, and pressure gradients. These equations are then non dimensionalized to obtain a set of partial differential equations (PDEs) that describe the fluid dynamics and heat transfer. To solve these PDEs, a Radial Basis Function Pseudo-Spectral Method (RBF-PSM) is employed. Velocity and temperature profiles are analyzed for various dimensionless parameters, including the Coriolis frequency parameter, Hartmann number, and others. Additionally, the pumping power required to maintain the flow in the absence of any external pressure is calculated for different parameter values. The pumping power analysis highlights that rotational forces, magnetic fields, and fluid elasticity play a crucial role in reducing the energy required to transport the fluid. Further, the results reveal that an increase in the Hartmann number decreases both primary and secondary velocities due to the enhanced Lorentz force, while a higher Coriolis frequency parameter reduces primary velocity but amplifies secondary velocity. Additionally, the Hall parameter increases both velocities by weakening the Lorentz force’s opposition, and higher Eckert numbers lead to steeper temperature gradients due to increased viscous dissipation. The findings offer quantitative design guidance for optimizing flow control, energy efficiency, and thermal management in rotating machinery, MHD pumps, and heat exchanger systems used in power generation, aerospace, and chemical processing industries.</p>