Fractional Study for Transient Free Convection Flow in a Channel with Mittag-Leffler Memory

Abstract

Fractional-order convective transient flow of viscous and incompressible fluids transiting through two infinite hot parallel upright plates is investigated analytically in the presence of chemical reaction, radiative heat flux, and mass diffusion at the boundary. A physical model for transient incompressible unsteady flow is developed with a comparatively new fractional derivative, namely, Atangana–Baleanu with nonsingular, nonlocal kernel. The developed fractional model is studied with means of an integral transform, i.e., Laplace transform method. Results obtained for the concentration, velocity, and temperature are expressed in the form of generalized $M_q^p\left(y\right)$ function. The impact of various physical parameters like fractional and flow parametric quantities is demonstrated diagrammatically. At last, we envisioned that for the fractional model, temperature and concentration could be enhanced for smaller fractional parameter $\alpha$ values while velocity for larger values of $\alpha$ , respectively. The proposed model gives the better results in the presence of memory effect besides the Caputo and Caputo–Fabrizio model when compared with the existing literature.