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In the present work, the influence of the amplitude ratio, phase deviation, and undulation number on natural convection in a wavy-walled enclosures differentially heated and filled with a water based nanofluid is studied. The upper and bottom walls are wavy with several undulations. The sinusoidal distribution of temperature is imposed at the vertical walls. The flow, heat, and mass transfer are calculated by solving governing equations for embody the conservation of total mass, momentum, thermal energy, and nanoparticles, taking into account the Darcy-Boussinesq-Buongiorno approximation with second order finite difference method in “stream function-temperature-concentration” formulation. Results are presented in the form of streamlines, isotherm, and isoconcentration contours, and distributions of the average Nusselt number for the different values of the amplitude ratio of the sinusoidal temperature on the right side wall to that on the left side wall (γ = 0-1), phase deviation (φ = 0-π), and undulation number (κ = 1-4). It has been found that variations of the undulation number allow to control the heat and mass transfer rates. Moreover, an increase in the undulation number leads to an extension of the non-homogeneous zones

Free convection in wavy porous enclosures with non-uniform temperature boundary conditions filled with a nanofluid: Buongiorno’s mathematical model