Convective heat transport by longitudinal rolls in dilute nanoliquid layer of finite depth

The paper investigates the thermal stability of a horizontal layer of a Newtonian nanofluid in the linear and non-linear regimes. A finite depth of fluid layer is considered which incorporates the effect of Brownian motion and thermophoresis slip mechanism along with no nanoparticle flux boundary conditions. For the linear stability a normal mode analysis is performed whereas a two term Fourier series analysis has been used for the nonlinear analysis. In case of linear stability, analytic expression for thermal Rayleigh number (Ra) in terms of various pertinent parameters are obtained. The graphs are presented to visualize the effect of these parameters on the critical value of the thermal Rayleigh number (Racr). Thermal Nusselt number in nonlinear analysis has also been plotted and discussed.