The onset of nanofluid natural convection inside a porous layer with rough boundaries

Smooth boundaries guarantee the infinitely stable flow when the linear stability analysis is implemented. Hence, the study on rough boundaries is essential when the laminar-turbulent transition is being considered. Because of the importance of rough boundaries, the present paper concentrates on the analysis of the onset of nanofluid natural convection (Rayleigh-Bénard convection) in a porous layer between two rough solid walls. The nanofluid surrounded between these surfaces contains the influence of both Brownian motion and thermodiffusion (thermophoresis). The non-negligible roughness boundary conditions are modeled according to the Saffman interface condition. For this purpose, the roughness is analogized as a shallow saturated fluid porous media. The simulation is performed under the isothermal condition and the zero nanoparticle flux condition for both surfaces. Then the governing equations are transported to an eigenvalue problem, and they are solved by a numerical method. The results prove that boundaries roughness and porosity parameters have a stabilizing influence on the onset of convective heat transfer while nanoparticle-concentration Rayleigh number, thermophoresis parameter, modified nanoparticle-density increment, and Lewis number have the destabilizing effects on the onset of Rayleigh-Bénard convection. For example, by increasing the roughness parameter from zero (i.e., stress-free boundary condition) to 100 (i.e., rigid solid walls with no-sleep condition), the critical convection Rayleigh number and the critical wave number increase around 145% and 41%, respectively.