Abstract

This analysis gives insight into unsteady radiative energy and Casson fluid flow across stretching and shrinking sheets with Biot boundary conditions, enhancing our comprehension of these intricate conditions. Examined the two mathematical representations with the help of a rigorous method. The initial model aligns with the approach usually used by researchers in this area, but its stationary solution stays trivial. The second method clearly illustrates the physically pertinent stationary solutions well examined in published works. In particular, unveiled the new similarity variables specifically for the energy equation solely within the initial model. Utilized the numerical method to solve the governing partial differential equations, while similarity variables can describe particular scenarios with uniform wall temperatures, more general cases may require non-similar analysis to fully capture heat transfer variations. Here, both analytical hypergeometric series and numerical methods were employed to study the impact of various physical impacts on boundary layer flows. The results of the current analysis reveal that enhance in thermal radiation and Biot number enhances the surface heat transfer by nearly 30%, while wall suction further improves it by about 22%. Similarly, a stretching boundary contributes an additional 18% rise compared to the shrinking case. Moreover, analyzing several non-Newtonian fluids provided insight into implications for related stagnation points and viscoelastic problems. A diversity of analytical approaches and computational techniques can thereby elucidate subtleties in transport for diverse geometries and material behaviours.