Thermal radiation and <scp>MHD</scp> effects on thermosolutal convection of Casson fluid in a quadrant domain

Abstract This paper examines the characteristics of thermo‐solutal convection of Casson incompressible flow in a quadrant‐shaped enclosure in the presence of magnetohydrodynamics (MHD). Unlike classical rectangular configurations, the present study considers a quadrant‐shaped enclosure, introducing geometric curvature effects on double‐diffusive convection. The coupled interaction between Casson rheology, MHD forces, and thermal radiation is systematically examined to identify the dominant parameters controlling dual convection patterns and transport rates. The governing equations are formulated under the Boussinesq approximation and solved using a finite‐difference stream function–vorticity approach. The effects of key dimensionless parameters, including the Rayleigh number (Ra), Hartmann number (Ha), Casson parameter ( β ), Lewis number (Le), buoyancy ratio (Nr), and radiation parameter (Rd), are systematically analyzed. Results reveal that increasing the Hartmann number significantly suppresses vortex strength due to electromagnetic damping, reducing both heat and mass transfer rates. In contrast, higher Casson parameter values (approaching Newtonian behaviour) enhance convective circulation and increase the mean Nusselt and Sherwood numbers. Thermal radiation modifies temperature stratification and influences buoyancy‐driven instability, particularly at higher Rayleigh numbers. The quadrant geometry introduces asymmetric vortex formation compared to classical rectangular cavities. These findings provide useful insights for the design and optimization of magnetically controlled non‐Newtonian fluid systems in microfluidic devices, cooling technologies, and biomedical transport applications involving curved geometries.