Analysis of free convection flow of viscous fluid with damped thermal and mass fluxes

Abstract

In this article, we have studied the convective flows of a linearly viscous fluid near a vertical isothermal plate. The heat transfer process is modeled with a generalized fractional constitutive equation which provides a damped thermal and mass flux. To do this, we used the time-fractional derivative with power-law singular kernel introduced by Caputo. Using the Laplace transform, we have obtained the closed forms solutions for the non-dimensional temperature, concentration and velocity fields, expressed with the Wright functions and the Mittag-Leffler function. The Nusselt number, Sherwood number and the skin friction coefficient have been also determined. The solutions for the ordinary fluid have been obtained as particular case of the solutions for the fractional model when the memory parameter (the fractional derivative order) tends to 1. The behavior of the fluid with thermal and mass memory, described by the fractional model and the behavior of the ordinary fluid described by the ordinary differential equations is analyzed by numerical simulations and graphical representations.