Non-similar solution for natural convective boundary layer flow of a nanofluid past a vertical plate embedded in a doubly stratified porous medium

This article studies the effects of thermal and mass stratification on natural convection boundary layer flow over a vertical plate embedded in a porous medium saturated by a nanofluid. The plate is maintained at a uniform and constant wall temperature, concentration and nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and nonlinear partial differential equations are solved by the Keller-box method. The effect of the Brownian motion parameter, thermophoresis parameter, modified Dufour number, Dufour-solutal Lewis number, thermal and mass stratification parameters on the non-dimensional velocity, temperature, concentration, nanoparticle volume fraction, heat and mass transfer rates at the plate are discussed and displayed graphically.