CF and AB fractional models on MHD rotating flow through a vertical porous channel with chemical reaction and heat source

Abstract

The influence of the heat source through the fractional time-derivative, with the impact of dynamic and static slips on transient magnetohydrodynamic (MHD) free convective rotating flow in a vertical channel/duct under invariable isoflux and isothermal heating, has been determined. Chemical reaction and heat source consequences are considered. The presentation of the Laplace transformations of Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional time-derivative models is used to transform the governing equations from the time domain into the Laplace domain. The semi-analytical resolutions are obtained for the velocity, temperature and concentration over the transformed solutions with the numerical application of ‘Riemann sum approximation’. Using the MATHEMATICA programme, the impacts of the governing parameters on the velocity, temperature and concentration are graphically demonstrated, and numerical computations for skin friction, Nusselt and Sherwood numbers are presented in tabular format. Remarkably, the static slip and relaxation parameters supported the convective movement of the fluids and the spreading of heat and concentration, while the fractional order parameters and dynamic slip did otherwise. Also, the circulation of heat and the movement of the fluid are considerably enhanced with the heat source compared with the chemical reaction. Additionally, the CF model produced higher temperature, velocity and skin friction compared with the AB model. Notably, it is observable that the heat source amplified the heat, while the fractional time parameter reduced the temperature.