Unsteady Free Convection Flow of Fractionalized Maxwell Fluid over an Inclined Vertical Plate with Heat and Mass Transfer

Abstract

Abstract: This study examines the unsteady motion of a fractional Maxwell fluid over an inclined vertical surface, considering the effects of thermo-diffusion and slip conditions. The model is further developed using Fick’s and Fourier’s laws, introducing a novel fractional formulation for mass diffusion and thermal diffusivity. The flow model is formulated with the CPC fractional derivative, and the governing equations are transformed into a non-dimensional form, and the resulting governing equations are solved using the Laplace transform method. The effects of key flow parameters—including the Grashof number, chemical reaction rate, Prandtl number, fractional parameters, and Schmidt number—are analyzed graphically. The results indicate that the fractional model provides a more accurate and flexible description of flow behavior than the classical model. Specifically, the magnetic field suppresses fluid motion, while thermo-diffusion enhances it.

Keywords: Free convection, Maxwell fluid, Slip condition, Soret effect, CPC fractional derivative.