LAUSR

Abstract The present analytical study deals with the laminar steady-state two-dimensional magnetohydrodynamic natural convection within a shallow enclosure. The latter is filled with an Al2O3-water nanofluid, which is determined by volumetrically internal heat sources subject to an externally applied uniform vertical magnetic field. The analytical model incorporates the role of a nanolayer, which is adjacent to the solid particle, in order to comprehend the anomalous heat conducting properties of nanofluids. Besides, the effects of the nanoparticle volume fraction and its size are examined on the cooling process. All the aforementioned factors seem to play a key role on the heat transfer. In brief, via shrinking the nanoparticles, increasing their volume fraction as well as enlarging the nanolayer thickness results (especially for comparable nanoparticle radii and nanolayer thicknesses) in deceleration of the nanofluid motion and, thus, in deterioration of the heat transfer. Finally, the analytical results are expected to be of particular importance regarding the comprehension of the versatile problem of magnetohydrodynamic natural convection of nanofluids given the fast-growing interest in this scientific field.