Heat and mass transfer effects on fluid past an exponentially accelerated vertical plate due to time-fractional MHD-free convection

This article focuses on the study of heat and mass transfer (HMT) fluid flow over an exponentially accelerated vertical plate, which is subjected to an applied magnetic field and viscous dissipation. The research has applications in various manufacturing processes such as wire/fiber drawing, hot rolling, continuous casting, and hot extrusion, where heat transfer to the ambient medium and the hot moving material are of utmost importance. The findings could also be relevant to aerospace engineering applications. The study investigates the time-fractional natural convection phenomenon and utilizes conservation laws to derive the flow guiding equations, which are then made nondimensional. Finite difference discretization is utilized to solve the dimensionless equations implicitly. Then the flow simulation results such as concentration, temperature, and velocity profiles are discussed based on the variation in parameters such as Prandtl number ($Pr$), thermal/mass Grashof number ($\mathit{Gr}/\mathit{Gc}$), Eckert number ($\mathit{Ec}$), magnetic parameter ($M$), time-fractional order ($\lambda$), and Schmidt number $\left(\mathit{Sc}\right)$. Also, the HMT rate is depicted using the Nusselt number and skin friction plots. It is noted that HMT increases when $\mathit{Sc}$ increases and $\lambda$ decreases. The change in time-fractional order affects the velocity profiles adjacent to the wall and is more significant in the case of lower values of the Prandtl number.