Rayleigh–Bénard instability in nanofluids: a comprehensive review

Abstract

The extraordinary enhancement in heat transfer efficiency of nanofluids at extremely low volume fractions has attracted a lot of attention in identifying the governing mechanisms. The nanoscale effects, Brownian motion (random motion of particles inside the base fluid) and thermophoresis (diffusion of particles due to temperature gradient) are found to be important slip mechanisms in nanofluids. Based on these findings, a set of partial differential equations for conservation laws for nanofluids was formed. Since then, a large number of mathematical studies on convective heat transfer in nanofluids became feasible. The present paper summarizes the studies pertaining to instability of a horizontal nanofluid layer under the impact of various parameters such as rotation, magnetic field, Hall currents and LTNE effects in both porous and non-porous medium. Initially, investigations were made using the model considering fixed initial and boundary conditions on the layer, gradually the model was revised in the light of more practical boundary conditions and recently it has been modified to get new and more interesting results. The exhaustive analysis of instability problems is presented in the paper and prospects for future research are also identified.

The onset of natural convection in a horizontal nanofluid layer heated from below

“…Only the recent work 37 had performed a preliminary observation for the formation of Bénard cell in a nanofluid layer with a free surface. As the review report 38 suggested, further experimental investigations are necessary to verify the results of theoretical works and this subject needs more interdisciplinary research in the future.…”

“…They also derived an analytic expression for the thermal Rayleigh number with free–free boundary conditions to validate the experimental results. A comprehensive review of Rayleigh–Bénard instability in nanofluids was presented by Ahuja and Sharma 38 in which a large number of theoretical studies pertaining to the instability of a horizontal nanofluid layer were introduced. The presence of nanoparticles was found to hasten the onset of instability generally in numerous studies.…”

A revised work on the Rayleigh-Bénard instability of nanofluid in a porous medium layer

“…Equation ( 20) is then substituted into equation ( 19) to give , (21) and the general solution of can be derived by integrating Eq. ( 20) to give…”

“…17 Recently, a comprehensive review has been proposed to summarize all the studies related to the Rayleigh-Bénard instability problems in nanofluids for both porous and non-porous media. 21 Although the study 13 has provided an initiatory exploration for the thermal instability characteristics of nanofluid in a horizontal porous medium layer, a potential contradiction exists when thermophoresis effect is pronounced. As elucidated in the recent works, 18,22 the thermophoretic diffusion coefficient is actually dependent upon the nanoparticle volume fraction.…”

Impact of volume fraction and fluid layer thickness on heat transfer effectiveness of water‐based nanofluids

“…The efficacy of nanofluids as the medium of heat transfer is greatly reliant on Rayleigh numbers of base fluid as well as nanofluid. The number points to the relative magnitude of viscous and buoyancy forces in the fluid 29,30 which are given by Equations (1) and (2) respectively. …”