Significance of Thermal Dispersion and Biot Number on Non‐Darcy Flow of a Casson Fluid Over an Inclined Vertical Plate

Heat transfer enhancement in non‐Newtonian fluids flowing through porous structures is crucial in various engineering applications such as geothermal energy systems, polymer processing, and thermal coating technologies. In this study, the mixed convective boundary‐layer flow of a Casson fluid over an inclined vertical plate in a non‐Darcy porous medium is analyzed by incorporating nonlinear thermal convection effects, along with thermal dispersion, convective surface heating (Biot number), and nonlinear density variation with temperature. The novelty of the present work lies in analyzing these coupled effects within a non‐similar framework, which has not been sufficiently explored in earlier studies. The governing nonlinear partial differential equations are transformed into dimensionless form using appropriate non‐similar transformations and solved numerically via the Spectral Quasi‐Linearization Method (SQLM). The results reveal that an increase in the thermal dispersion parameter significantly enhances the fluid velocity and heat transfer rate while reducing the temperature distribution within the boundary layer. Higher Biot numbers intensify the convective heat exchange at the surface, leading to increased temperature, skin friction, and Nusselt number. It is also observed that increasing the inclination angle weakens the buoyancy force, resulting in a reduction in both velocity and heat transfer rate. These findings provide important physical insights into the control of heat and momentum transport in Casson‐type fluids within porous media, with direct relevance to industrial processes such as high‐temperature coating systems, geothermal heat extraction, and chemical thermal processing applications.