Significances of exponential heating and Darcy's law for second grade fluid flow over oscillating plate by using Atangana-Baleanu fractional derivatives

The main aim of this study is to apply the recent definition of fractional derivative i.e. Atangana-Baleanu time-fractional derivative on second grade fluid flowing on an infinite plate under the MHD (magnetohydrodynamics) effect. The flow is studied under both Darcy's law and heat transfer. To find out the analytical solution, the Laplace transformation technique is utilized on the obtained non-dimensional governing equations momentum and heat equations with initial and boundary conditions. To enhance the innovation of this study, the graphical and numerical comparison of heat and momentum equation is analyzed with different parameters for different values. Main results and conclusions are accomplished at the end of this work. The increasing change in temperature profile is noticed with fractional parameter and Grashof number. The velocity profile increases with the Prandtl number while a reverse trend is noted for the temperature profile.