Paper Title
Thermal Effects on Rayleigh-Marangoni Instability in a Layer of Nanofluid

These instructions give you guidelines for A linear stability analysis for the onset of Rayleigh-Marangoni convection in a horizontal layer of a nanofluid heated from below is investigated. The model employed for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The lower boundary of the layer is assumed to be a rigid surface at fixed temperature while the top boundary is assumed to be a non-deformable free surface cooled by convection to an exterior region at a fixed temperature. The boundaries of the layer are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The linear analysis uses spectral methods based on the expansion of eigenfunctions as Chebyshev series. Stability boundaries for temperature and nanofraction Marangoni numbers and Rayleigh number are obtained for several nanofluids. Index Terms- Brownian motion, nanofluid, Rayleigh Marangoni stability, thermophoresis.