Rheological behavior of Casson fluid in pressure-driven flow through a wavy curved channel under Rosseland's approximation

The rheological and thermal behavior of magnetohydrodynamic non-Newtonian fluids in pressure-driven flows has attracted significant attention due to its relevance in advanced energy and thermal management systems. Among various non-Newtonian models, the Casson fluid model is of particular importance owing to its extensive applications in industrial processing, biomedical devices, and energy-related technologies. A comprehensive understanding of its flow and heat transfer characteristics in complex geometrical configurations is, therefore, essential for efficient system design and optimization. In this study, the rheological and thermal characteristics of Casson fluid flow through a wavy curved channel under the influence of a transverse magnetic field are investigated. The channel walls exhibit sinusoidal and periodic waviness. The energy equation accounts for the combined effects of thermal radiation as well as internal heat generation and absorption. The governing equations are formulated in curvilinear coordinates and solved analytically using a regular perturbation technique, yielding closed-form expressions for the velocity field, temperature distribution, volumetric flow rate, skin-friction coefficient, and Nusselt number. The results reveal that an increase in the Casson parameter enhances the fluid velocity, whereas stronger magnetic effects suppress the flow. Additionally, the fluid temperature rises with increasing heat generation/absorption parameter intensity and decreases with increasing curvature of the channel.