A theoretical model for the magnetohydrodynamic natural convection of a CNT-water nanofluid incorporating a renovated Hamilton-Crosser model

•Analytical solutions with emphasis on the role of interfacial nanolayers.•Detailed study of nanofluid volume fraction, thermal and shape properties effects.•Nanoparticles shape importance for the cooling due to higher thermal conductivity.•Nanolayer thickness ratio over the particle radius on heat transfer enhancement. The present study pertains to the laminar two-dimensional magnetohydrodynamic natural convection in a shallow cavity utilizing a Carbon Nanotube (CNT)-water nanofluid which is internally heated by volumetrically heat sources. The theoretical model comprehends the effect of the nanoparticle volume fraction and its size. Furthermore, the role of an interfacial nanolayer, which is adjacent to the solid particles, is taken into account as well as the shape of the latter. In a nutshell, increasing the concentration of the CNTs results in deceleration of the fluid flow and, thus, in deterioration of the heat transfer. Besides, the shape of the solid nanoparticles seems to be of great importance regarding the cooling process, since the elongation of them leads to bigger thermal conductivities that promotes conduction over convection heat transfer. Finally, the ratio of the nanolayer thickness over the radius of the particle influences the heat in the nanofluid and, as a consequence, the entire heat transfer. The asymptotic results appear to be particularly helpful for the understanding of such an interesting and fundamental problem which emerges in a lot of industrial applications.