Fractional modeling of unsteady flow of Jeffrey fluid using active and passive control strategies

The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Jeffrey nanofluid flows across a vertical plate because of these possible uses. Free convection, magnetic effect, and thermo-diffusion properties are all applied to the flow considered here. The modeling also takes into account the passive and active control of the Jeffrey nanofluid. The constant proportional Caputo fractional operator which was recently introduced is used in this work together with generalized Fick's and Fourier's law. Using suitable nondimensional variables, ordinary differential equations are obtained from the modeling equations, and the Laplace transform method is used to solve these modeled equations. The concentration and temperature profiles are rising functions of the fractional and thermophoresis parameters, and they drop more quickly as the values of the Schmidt, Prandtl, and Nb (Brownian motion parameters) rise. The constant proportional Caputo (CPC) fractional derivative is the best choice for achieving more stable concentration, temperature, and velocity than conventional fields. Raising the values of alpha will increase the rate of heat transfer and skin friction coefficient. Additionally, as compared to the classical model, the constant proportional Caputo derivative model shows more decay nature. Consequently, compared to the classical model, the constant proportional Caputo differential model has a superior memory function.