Spectral Quasi-Linearization Study of Variable Viscosity Casson Nanofluid Flow under Buoyancy and Magnetic Fields

The behavior of buoyancy-driven magnetohydrodynamic (MHD) nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling, nuclear reactors, and metallurgical processes. This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation, as it interacts with a vertically stretching sheet under dissipative conditions. To manage the inherent nonlinearities, Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms. These reduced equations are then solved via the Spectral Quasi-Linearization Method (SQLM), ensuring high accuracy and computational efficiency. The analysis comprehensively explores the impact of key parameters—including mixed convection intensity, magnetic field strength, Casson fluid properties, temperature-dependent viscosity, thermal radiation, and viscous dissipation (Eckert number)—on flow characteristics and heat transfer rates. Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport, while buoyancy effects enhance heat transfer but lower shear stress on the surface. This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids, advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.