Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives

Natural convection flow of differential type fluid with non-integer order Caputo-fractional derivatives is investigated in this study. The non-dimensional temperature, concentration, and velocity fields are solved by using the Laplace transform method. There is no such result regarding second grade fluid with non-integer order Caputo fractional derivatives established. The obtained solutions are expressed in terms of G-function, Mittage-Leffler function, Robotnov-Hartley and Wright's function. Some known solutions from literature are recovered as a limiting case. Expression for Nusselt and Sherwood numbers with non-integer and integer order, respectively, are also determined. Numerical computations and graphical discussion were made to observe influence of Caputo-time fractional parameter α and second grade parameter α2 on the fluid flow. A comparison for second grade and viscous fluid for non-integer and integer order is also depicted. It is also observed that ordinary fluids have greater velocities than fractional fluids. This shows that how non-integer order fractional parameter affects the fluid flow.