Analysis of heat and mass transfer in nanofluid flow over a stretching surface in a porous medium considering thermophoretic and Darcy effects

The main purpose of this study is to investigate the interactions among convection, magnetic field, Darcy effect, thermal radiation, Brownian diffusion, and thermophoresis when a nanofluid containing carbon nanotubes in a water-base fluid flows over a stretching horizontal plate through a porous medium. Governing equations are solved using a numerical method to analyze the impact of the Darcy effect on boundary layer development. This work concurrently accounts for Darcy effect, Brownian diffusion, thermophoresis, and nanoparticle volume fraction, offering a more complete description of carbon nanotubes (CNTs) – water nanofluid transport. The combined consideration of Brownian motion and thermophoresis further clarifies their roles in nanoparticle distribution and mass transfer phenomena. The results reveal that a higher Darcy number results in lower flow velocity and thus in the boundary layer having a higher temperature and concentration. Increasing nanoparticle volume fraction corresponds to an increase in the boundary layer of temperature and a decrease in nanoparticle concentration at the wall. A higher Brownian motion parameter reduces the surface heat transfer rate, while increasing the mass transfer rate near the wall and producing a larger concentration gradient. In addition, a higher Schmidt number results in the accumulation of more nanoparticles near the wall. The local Nusselt number and Sherwood number are lower when the Darcy number is higher. A higher Brownian motion parameter results in a lower local Nusselt number but higher Sherwood number. Sherwood number is lower when the thermophoretic parameter is higher; whereas it is higher when volume fraction is higher as well.