Maxwell fluid flow between vertical plates with damped shear and thermal flux: Free convection

In this article, we studied free convection flow of Maxwell fluid between two parallel plates a distance d apart from each other. The Caputo time-fractional derivative is used in model and the model is fractionalized through mechanical laws (generalized shear stress constitutive equation and generalized Fourier's law). Closed form solutions are found by means of Laplace and sine-Fourier transforms which are suitable for our boundary conditions. The solutions are expressed in the form of Mittag-Leffler function and generalized G-function of Lorenzo and Hartley. The viscous fractional and ordinary Maxwell and fractional model are presented as special cases. The effects of fractional and physical parameters are graphically illustrated.