Linear stability analysis of mixed convection flow in a horizontal channel filled with nanofluids

Abstract

The convective instability driven by buoyancy in the Poiseuille-Rayleigh-Bénard flow through two infinite parallel horizontal plates filled with nanofluids is investigated using linear stability analysis. We considered water-based nanofluids with different volume fractions of aluminum (Al O 2 3 ) and silver (Ag) nanoparticles. A spectral collocation method founded on Chebyshev polynomials is implemented and the obtained algebraic eigenvalue problem is solved. In this study, we have numerically determined the critical Rayleigh number of the onset of longitudinal and transversal rolls and the results are represented in the form of marginal stability curves. Critical wave numbers that describe the size of convective cells in the flow are also presented, analyzed, and compared with those of the Poiseuille-Rayleigh-Bénard flow without nanoparticles. The effects of the type and nanoparticle volume fractions on the onset of both longitudinal and transversal rolls are investigated. K E Y W O R D S mixed convection, nanofluids, Poiseuille-Rayleigh-Bénard, thermoconvective instabilities

Linear stability analysis of shear flows with thermal effects

“…Their study also showed that the maximum transient growth occurred for streamwise uniform modes. More recently, Babajani et al (2017) and Bammou et al (2020) studied the stability of PRB flows under the influence of nanoparticles. They found that the presence of the nanoparticles can stabilize or destabilize the flow toward longitudinal rolls depending on the type and volume fraction of the nanoparticles.…”