Spectral Quasilinearization Analysis of Casson Fluid Flow over a Convectively Heated Inclined Plate Considering Thermal Dispersion and Nonlinear Thermal Convection

The present study investigates the influence of the thermal dispersion on natural convective flow of a Casson fluid along an inclined plate embedded in a non-Darcy porous medium. The governing equations, representing momentum and energy conservation, are transformed into non-dimensional form using similarity transformations. To address the complexity of the resulting equations, a bivariate spectral quasilinearisation method is employed. The effects of relevant parameters—including thermal dispersion, Casson parameter, Biot number, Forchheimer number, inclination angle, and nonlinear thermal convection parameter—are thoroughly examined. The results show that the drag coefficient and heat transfer rate increase with the nonlinear thermal convection parameter, Casson parameter, and Biot number. In contrast, they decrease as the Forchheimer number and inclination angle increase. The velocity near the inclined plate’s surface increases with the Biot number, Casson parameter, and nonlinear thermal convection parameter. However, it decreases farther from the plate. Additionally, the temperature of the Casson fluid increases with most parameters, except the Casson and nonlinear thermal convection parameters.