Linear stability analysis of Marangoni mixed convection flow for nanofluids in a horizontal open channel

This paper presents the linear stability analysis of laminar mixed convection flow combined to thermocapillary effect in a horizontal infinite channel heated uniformly from below. Pure water and water-based nanofluid containing various volume fractions of Al2O3 and Ag nanoparticles are considered. The results are presented for volume fractions up to 3%. A spectral collocation method based on Chebyshev polynomials is implemented and the obtained algebraic eigenvalue problem is solved. In this study, the thresholds of the onset of the convective instability in the form of longitudinal and transverse rolls are determined numerically. The comparison between the pure water and the nanofluid flows allows to investigate the nanoparticles effects on the critical parameters for the onset of convective rolls. The combination of buoyancy and thermocapillary effects on the flow instability is studied and showing the competition between these two effects to make the flow more unstable in pure water and nanofluids. Critical wave numbers that describe the size of convective cells, in nanofluid flow are also presented, analysed, and compared with those of the pure water flow without nanoparticles. Besides, the effects of the type and the volume fraction of nanoparticles on the stability of the system are investigated.