Eur. Phys. J. Special Topics 228, 2511–2530 (2019)
https://doi.org/10.1140/epjst/e2019-900074-1

Regular Article

A study of Rayleigh–Bénard convection in hybrid nanoliquids with physically realistic boundaries

¹ GuiZhou University, State Laboratory of Public Big Data, Guizhou, Guiyang 550025, P.R. China
² College of Science, Harbin Institute of Technology, Shenzhen, University Town, Nanshan District, Guangdong Province, Shenzhen - 518055, P.R. China
³ Department of Mathematics, Bangalore University, Jnanabharathi Campus, Bangalore 560056, India

^a e-mail: zhao.yi@hit.edu.cn

Received: 22 April 2019
Received in final form: 6 June 2019
Published online: 6 December 2019

Abstract

Linear and weakly nonlinear stability analyses of Rayleigh–Bénard convection in water–copper–alumina hybrid nanoliquid bounded by rigid isothermal boundaries is studied analytically. A single-phase description is used for the nanoliquid. Using a minimal Fourier series representation and an appropriate scaling a classical Lorenz model for rigid isothermal boundaries is derived. The Lorenz model is transformed to the Ginzburg–Landau model using the renormalization group method. The solution of the Ginzburg–Landau model is used to arrive at the expression of the Nusselt number. The study shows that the presence of two nanoparticles in water is to increase the coefficient of friction, advance the onset of convection and enhance the heat transfer. Further, it is shown that compared to a single nanoparticle the combined influence of two nanoparticles is more effective on heat transfer. The percentage of heat transfer enhancement in water due to Al₂O₃-Cu hybrid nanoparticles is almost twice that of Al₂O₃ nanopartcles. It is found that the hybrid nanoparticles of Al₂O₃-Cu intensify convection in water more than the mono nanoparticles of Al₂O₃ and the plots of stream function and isotherm point to this fact. The effect of the physically realistic rigid boundaries is to inhibit the onset of convection when compared with that of free boundaries.