Wall slip and non-integer order derivative effects on the heat transfer flow of Maxwell fluid over an oscillating vertical plate with new definition of fractional Caputo-Fabrizio derivatives

Abstract

This article is focused on natural convection of unsteady flow of generalized Maxwell fluid over an oscillating vertical flat plate with constant temperature at the boundary. The Maxwell fluid with classical derivatives, describing one dimensional flow has been generalized to non-integer order derivatives known as fractional derivative with term of buoyancy. A modern definition of fractional derivative, recently introduced by Caputo and Fabrizio has been used to formulate the considered problem. Semi analytical solutions of the dimensionless problem have been obtained by using the Laplace transform. The solutions for temperature, velocity and shear stress are obtained with numerical inversion techniques of Laplace transform namely, Stehfest’s and Tzou’s algorithms. At the end, graphical illustrations for temperature, velocity, Nusselt number and shear stress are plotted. We have studied especially the influence of fractional parameter on temperature, velocity and shear stress respectively. We have observed that temperature can be enhanced for increasing the fractional parameter α while velocity and shear stress can be increased by decreasing the value of fractional parameter α.