Convective instability of nanofluids in vertical circular porous microchannels

Abstract

• Convective instability of nanofluids in a vertical circular microchannel was considered • Dependence of the critical Rayleigh number of different parameters was obtained • An increase in the Knudsen number causes a decrease in the critical Rayleigh number • A decrease in the Prandtl number causes a decrease in the critical Rayleigh number The article presents an analysis of the convective instability of a nanofluid in a vertical porous cylindrical microchannel with slip boundary conditions on the wall. The microchannel is surrounded by a continuous medium. For the calculation, the Galerkin method with a different order of approximation was used. The influence of the Darcy, Knudsen and Prandtl numbers, the ratio of the thermal conductivities of the fluid and the wall, the intensity of sliding along the wall, as well as the properties of nanoparticles on the Rayleigh number at which instability occurs, is analyzed. It was shown that an increase in the porosity of the medium promotes stabilization. It has been determined that the conditions for the onset of convection are decisively influenced by the thermal conductivity of nanoparticles (Lewis number), whereas the slippage effects (Knudsen number) are of lesser importance.