Mechanical and thermal energies transport flow of a second grade fluid with novel fractional derivative

In this study, an unsteady natural convection flow of second-grade fluid over a vertical plate with Newtonian heating by constant proportional Caputo non-integer order derivative is presented. After developing a dimensionless flow model, the set of governing equations are solved with the help of integral transform, namely the Laplace transform and closed solutions are obtained. Also, some graphs of temperature and velocity field are drawn to see the subjectively of fractional parameter (Formula presented.) and other involved parameters of interest. It also shows dual nature for small and large time behavior due to the power-law kernel. Further, a comparative analysis between the temperature as well as the velocity fields with existing literature has been presented. Further, as a result, it is concluded that constant proportional Caputo derivative shows more decaying nature of the fluid flow properties than classical Caputo and Caputo-Fabrizio fractional derivatives.