Impact of fractional derivative on the distribution of concentration injected from the walls in diverging channel

This study examines the influence of fractional derivatives on the concentration distribution in the flow of a Newtonian fluid within a divergent channel with wall injection. The governing equations, originally formulated with integer derivatives in the radial direction, were modified using Caputo fractional derivatives. These transformed equations were converted into ordinary differential equations through similarity transformations and solved using the Adaptive Fraction Method (AFM) and numerical techniques. Key parameters, including the Reynolds number (Re), Peclet number (Pe), and fractional derivative orders$\beta$and$\xi$, were analyzed to assess their effects on flow dynamics and concentration profiles. The results indicate that increasing Re and$\beta$enhances the dimensionless radial velocity and velocity at the channel center while reducing them near the walls. As Re increases, the dimensionless concentration significantly decreases at the center, showing a minor rise near the walls. A surge in$\xi$ causes a slight decrease in concentration across the channel, whereas increasing $\mathrm{Pe}$reduces concentration in a localized central region with minimal impact elsewhere. Additionally, higher$\xi$values enhance concentration throughout the channel. These findings provide insights for optimizing fluid systems in mass transfer, heat transfer, and flow control by leveraging fractional derivatives to model non-local and memory effects in fluid flow phenomena.