Free convection flows over a vertical plate that applies shear stress to a fractional viscous fluid

Abstract

Free convection flow of a fractional viscous fluid over an infinite vertical plate with exponential heating is studied using a fractional derivative with non-singular kernel. Fluid motion is induced by the plate that applies an arbitrary time-dependent shear stress to the fluid. Closed-form solutions for the dimensionless velocity and temperature fields and Nusselt number are established under the usual Boussinesq approximation. The obtained results can generate exact solutions for any motion with technical relevance of this type. Moreover, fluid’s velocity is presented as a sum of its mechanical and thermal components. A semi analytical solution based on the Stehfest’s formula for the inverse Laplace transform is also obtained. Finally, the influence of fractional parameter on the fluid motion as well as the contributions of mechanical and thermal components of velocity are graphically underlined and discussed. Keywords: Free convection flow, Viscous fluid, Exponential heating, Caputo-Fabrizio fractional derivative, Stehfest’s formula