Spectral analysis of nonlinear free convective flow of a casson fluid in a non-Darcy porous medium with convective boundary condition

This study explores the quadratic natural convective flow of a Casson fluid over an inclined plate embedded in a non-Darcy porous medium under the influence of a convective boundary condition. Such fluid flow models are significant in biomedical engineering, polymer processing, and geophysical fluid dynamics, where non-Newtonian fluids interact with porous structures. The governing equations, incorporating the Casson fluid model, Forchheimer drag, and convective heating, are highly nonlinear and are solved using the Spectral Quasilinearization Method, which ensures rapid convergence and computational efficiency. The impact of key physical parameters on velocity and temperature distributions is systematically analyzed. Results indicate that increasing the Non-Darcy Thermal parameter, Biot number, and Casson fluid parameter enhances the heat transfer rate. Conversely, higher inclination angles and Forchheimer numbers reduce heat transfer efficiency due to increased resistance in the porous medium. The findings provide insights into optimizing heat transfer in industrial and biomedical applications where Casson fluids, such as blood and polymeric suspensions, are encountered. Notably, the heat transfer rate increases significantly with higher Biot numbers, illustrating the model’s effectiveness for realistic porous flow configurations. • Nonlinear Casson flow analyzed in non-Darcy porous media with convective walls. • SQLM is used for the efficient solution of nonlinear boundary layer equations. • Velocity rises with Biot, NDT, and Casson parameters; falls with ℧, Fs. • Heat transfer rate improves with Biot, NDT, and Casson parameters. • Forchheimer and inclination reduce heat transfer and fluid velocity.