Natural convection of nanofluids in a square enclosure with different shapes of inner geometry

We develop a model to study the natural convection of a nanofluid between a square enclosure and a circular, an elliptical, or a rectangular cylinder. Using super elliptic functions, the dimensionless governing equations of two-dimensional rectangular coordinates have been transformed into a system of equations valid for the above geometry. The resulting equations are then solved utilizing finite difference technique. We illustrate the flow and heat transfer characteristics of nanofluids with streamlines and isotherms as well as the Nusselt number at the inner and outer cylinders. It is found that the intensity of streamlines becomes stronger with the increase in the volume fraction of nanoparticles and the Rayleigh number. The Nusselt number at the inner and outer cylinders is almost linearly increased for higher values of the volume fraction of nanoparticles while an exponentially increasing tendency is observed with the increase in the Rayleigh number. The distinct findings are that the intensity of the streamlines increases with rectangular, circular, and elliptical inner shapes. Moreover, the Nusselt number at the inner and outer cylinders diminishes with circular, elliptical, and rectangular inner shapes. The acquired knowledge from the results could be used to augment or control the heat transfer of nanofluids and for the advancement of existing technology. Moreover, the present concept of introducing super elliptic functions might be useful to formulate a model for more complex geometry. Published by AIP Publishing.