This study investigates unsteady two-dimensional magnetohydrodynamic (MHD) Casson nanofluid flow over a stretching sheet under sinusoidal boundary conditions. It incorporates variable viscosity, thermal conductivity, and chemical reactions to explore thermodynamic, chemical, and flow characteristics relevant to diverse engineering applications. The novelty lies in the integrated treatment of variable fluid properties, sinusoidal boundaries, and reactive effects within an MHD Casson nanofluid framework-an area scarcely addressed in existing literature. The model includes critical physical phenomena such as Brownian motion, thermophoresis, and thermal radiation, making it applicable to fields like energy systems, micro-manufacturing, biomedical engineering, and geophysical fluid mechanics. A similarity transformation is applied to reduce the governing equations to nonlinear ODEs, which are solved numerically. The simulations yield velocity, temperature, and concentration profiles, along with skin friction, Nusselt, and Sherwood numbers. A stability and convergence study confirms the model's reliability, showing convergence at Pr≥0.068 and Le≥0.023 for τ=0.0005, ΔX=0.80, and ΔY=0.40. Results indicate that skin friction rises with Grashof and Eckert numbers, while the Nusselt number decreases with higher thermal conductivity and radiation. Streamline and isotherm analyses further reveal key flow dynamics under variable thermal and chemical conditions.
Islam et al. (Wed,) studied this question.