A Study of a Thermally-Vigorous Rayleigh-Bénard Convection in a Hybrid Nanofluid Using Non-Classical Boundary Condition

Abstract

A linear stability analysis of a thermally-vigorous Rayleigh-Bénard convection in a mono and a hybrid nanofluid is carried out using the single-phase model. We make use of non-classical boundary condition on velocity (rough boundary condition) and temperature (third-type boundary condition) instead of a specific boundary condition (free-free isothermal, rigid-rigid isothermal, etc.) which is traditionally considered. The thermophysical properties are calculated using phenomenological laws and mixture theory. A unique and novel combination of a single-term Galerkin technique and the Maclaurin series expansion is used to solve the boundary-eigen-value problem obtained in the problem. The critical value of the wave number and the Rayleigh number that are calculated using the procedure are quite accurate up to 5 and 3 decimal places respectively. A comparative study on the instability in two types of nanofluids is carried out so as to infer which type of nanofluid suits best for thermally vigorous systems. This paper aims to provide a theoretical basis to ease the selection process pertaining to the making of a choice from different types of nanofluids. To validate the study sixteen limiting cases have been obtained. To visualize the flow behavior physically, streamlines have been plotted.