Spectral Relaxation Analysis of Rotating Magnetohydrodynamic Viscous Flow and Heat Transfer Past a Stretching Sheet

This work presents a high-accuracy spectral relaxation analysis of steady rotating magnetohydrodynamic (MHD) viscous flow and heat transfer over a linearly stretching sheet under the influence of a transverse magnetic field. The governing nonlinear boundary-layer equations for mass, momentum, and energy conservation are formulated in a rotating frame and reduced to a coupled system of ordinary differential equations via similarity transformations. The resulting system is solved using the Spectral Relaxation Method (SRM) combined with Chebyshev spectral collocation, which ensures exponential convergence for smooth solutions. Numerical stability and accuracy are verified through residual convergence diagnostics, grid-independence analysis, and comparison with benchmark solutions obtained from Homotopy Perturbation and finitedifference methods, yielding agreement up to 10 − 6 . Parametric analysis demonstrates that the rotation parameter ( K r ) intensifies secondary flow through Coriolis coupling while attenuating primary velocity and surface heat transfer. The magnetic parameter ( M ) suppresses momentum via Lorentz damping and elevates thermal energy due to Joule heating, leading to increased wall shear stress and reduced Nusselt number. Increasing the Reynolds number ( R ) enhances convective heat removal by thinning the boundary layer, whereas higher Prandtl numbers ( Pr ) reduce thermal diffusivity and produce sharper temperature gradients at the wall. The Eckert number ( Ec ) amplifies viscous dissipation, raising fluid temperature and diminishing cooling efficiency. The results confirm that the Spectral Relaxation Method provides a robust, rapidly convergent, and spectrally accurate framework for strongly coupled nonlinear rotating MHD boundarylayer systems. The novelty of this study lies in the application of the Spectral Relaxation Method (SRM) to a rotating MHD boundary-layer system incorporating simultaneous Coriolis effects, Lorentz damping, viscous dissipation, and Joule heating, with detailed convergence diagnostics and benchmark-level accuracy not previously reported. The generated benchmark data and physical insights are directly applicable to rotating machinery cooling, electromagnetic flow regulation, and high temperature polymer processing technologies.