Fractional model for Casson fluid flow with thermal radiation effects in a convectively heated channel

This research investigates the effect of thermal radiation on the unsteady fractional-order flow of a Casson fluid in a convectively heated Couette tube. The Caputo-Fabrizio and Atangana-Baleanu fractional derivatives are used to represent non-Newtonian behavior, whereas the Rosseland approximation describes radiative heat transfer. Exact solutions to the fractional momentum and energy equations are achieved using the Laplace transform and Riemann sum approximation techniques. The impacts of essential factors, such as fractional order, Casson parameter, Biot number, and radiation parameter, are visually and mathematically evaluated. The results reveal that increasing thermal radiation increases fluid temperature and velocity, whereas higher Casson parameters increase flow resistance and decrease velocity. The Nusselt number and wall shear stress are also evaluated, and validation against existing literature supports the model's correctness. The results apply to engineering, biomedical, and thermal energy applications.