The onset of convection of power-law fluids in a shallow cavity heated from below by a constant heat flux

Numerical nonlinear analysis of subcritical Rayleigh-Bénard convection in a horizontal confined enclosure filled with non-Newtonian fluids

“…This result had recently been confirmed by Albaalbaki and Khayat 21 shear-thinning fluids obeying to the Carreau-Bird model. When the power law model was used by Alloui et al, 25 for shear-thinning, the authors found that the critical Rayleigh number was nil. This result was far from being real, due to the fact that the power law model does not represent the real behavior of shear-thinning fluids at very low shear rates.…”

“…Among the fluids considered, Maxwell fluids were shown to be unstable, whereas the Rivlin-Ericksen fluids were stable and behave like Newtonian fluids with a temperature dependent or constant viscosity. An analytical and numerical study of natural convection of a non-Newtonian fluid obeying the power law model was performed by Alloui et al 25 For shear thinning fluids, the onset of convection was found to be always subcritical. Inversely, for dilatant fluids, convection was always stationary due to the fact that the critical Rayleigh number for the onset of stationary convection was zero.…”

“…The present study was motivated by the recent research studies conducted by Alloui et al 25 to describe the physics of the fluid rheology effect on the onset of convection. The study was based on ideal rheological behavior of the fluid near criticality, where the power-law model was not valid for very low shear-rate.…”

Three dimensional simulation of natural convection and entropy generation in an air and MWCNT/water nanofluid filled cuboid as two immiscible fluids with emphasis on the nanofluid height ratio's effects

“…Their results show that the average Nusselt number obtained for the case of imposed heat flux on the hot wall is smaller than that corresponding to the case of imposed constant high temperature. Also, an analytical and numerical study of natural convection in a shallow rectangular cavity filled with a power-law fluid is carried out by Alloui et al [14].…”

“…The non-dimensional local volumetric entropy generation equation is defined in three dimensional form as follows: (14) Where is the irreversibility coefficient. The first and second terms of equation (14) represent heat transfer irreversibility and fluid friction irreversibility respectively.…”