Analytical study of the magnetohydrodynamic natural convection of a nanofluid filled horizontal shallow cavity with internal heat generation

An analytical study is presented of the laminar, steady-state two-dimensional MHD natural convection of a nanofluid filled shallow cavity, which is driven by volumetrically internal heat sources and is subject to an external uniform vertical magnetic field. All walls are electrically insulated, with the horizontal ones being adiabatic, while the vertical ones are isothermal. The working nanofluid is water partially filled with copper nanoparticles. The method of the matched asymptotic expansions is used to obtain solutions of the flow and heat transfer problem in the core region of the horizontal cavity taking into account the Brownian motion of the nanoparticles. Overall, the results indicate that convective phenomena are intensified by increasing the internal heating. It is found that in the hydrodynamic regime adding more nanoparticles slightly enhances heat transfer, whereas in the presence of an external magnetic field results in the deterioration of it. In the latter magnetohydrodynamic regime, the nanofluid flow is decelerated, and thus heat conduction dominates over convection as the magnitude of the magnetic field increases or smaller size of nanoparticles are employed. Finally, heat transfer enhancement is observed by ignoring the Brownian motion part of the effective thermal conductivity. (C) 2018 Elsevier Ltd. All rights reserved.