Effects of thermodiffusion on Darcy–Brinkman convection in a rotating binary nanofluid saturating a porous layer

In this study, the onset of convection in a rotating horizontal porous layer saturated by a binary nanofluid was theoretically investigated under the influence of thermodiffusion and nanoparticles. To study the onset of convection, the Darcy–Brinkman model was employed for the porous medium, and the thermal Rayleigh number was derived analytically using linear stability analysis. Water–ammonia-based silver, copper, and alumina, three binary nanofluids, were considered, and the effect of nanoparticles on the stability of the system was analysed using addition factor analysis. The Brinkman model for viscosity and Bruggeman model under the mean field approach for thermal conductivity were used to study the impact of nanoparticles. Heat transport was examined by calculating the heat transfer coefficient. The effects of nondimensional parameters involved in binary nanofluids on the onset of convective instabilities are depicted pictorially. The dependence of the size of the convection cells on nondimensional parameters is also discussed. The Darcy–Taylor number decreases the size of convection cells, whereas the Darcy number increases the size of convection cells. The size of the convection cells is independent of the porosity of the medium, Lewis number, volume fraction of nanoparticles, Soret effect of nanoparticles, and the solute in binary nanofluids. Furthermore, the Darcy–Taylor number and porosity have stabilising effects, whereas the Darcy number, volume fraction of nanoparticles, and Lewis number have destabilising effects on the system. Soret effects of nanoparticles and solutes exhibit dual consequences on stability. They stabilise the binary nanofluid layer if δ 4   –1. Their effect is immaterial if δ 4  = –1.