Non-equilibrium natural convection in a differentially- heated nanofluid cavity partially filled with a porous medium Mikhail A. Sheremet Laboratory on Convective Heat and Mass Transfer, Tomsk State University, Tomsk, Russia Ioan Pop Department of Applied Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania, and A. Cihat Baytas Faculty of Aeronautics and Astronautics, Istanbul Technical University, Istanbul, Turkey Abstract Purpose – This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non- equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach – Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings – It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value – The results of this paper are new and original with many practical applications of nanofluids in the modern industry. Keywords Natural convection, Nanofluid, Numerical results, Non-Darcy flow, Non-equilibrium model, Porous layer Paper type Research paper Nomenclature c = specific heat (J kg 1 K 1 ); Da = Darcy number; This work of M.A. Sheremet was conducted as a government task of the Ministry of Education and Science of the Russian Federation (Project Number 13.6542.2017/6.7). The work of I. Pop has been supported from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania. The authors also wish to express their thank to the very competent Reviewers for the valuable comments and suggestions. HFF 29,8 2524 Received 9 August 2018 Revised 8 October 2018 Accepted 30 October 2018 International Journal of Numerical Methods for Heat & Fluid Flow Vol. 29 No. 8, 2019 pp. 2524-2544 © Emerald Publishing Limited 0961-5539 DOI 10.1108/HFF-08-2018-0433 The current issue and full text archive of this journal is available on Emerald Insight at: www.emeraldinsight.com/0961-5539.htm