Natural convection heat transfer in a nanofluid-filled cavity with double sinusoidal wavy walls of various phase deviations

In the present study, a new 2D quarter-circular enclosure with two sinusoidal wavy walls and two straight walls was proposed. Natural convection heat transfer in such cavities filled with various kinds of nanofluids was investigated and the phase deviation between two sinusoidal wavy walls was paid special attention. With the given shape of inner wall, the effect of shape regulation of the outer wavy wall was studied by a combined Finite volume method (FVM) and response surface method (RSM) method. Sinusoidal amplitude of outer wall (A) and phase deviation (γ) between the inner and outer walls were found to have significant effects on surface heat transfer coefficient h. The isothermal lines deform and fluctuate much more intensively with the increase of γ. RSM optimization manifested that the highest h appears at A = 0.11 and γ = 1.77 rad for water-Ag nanofluid. In the optimal enclosure, the surface heat transfer coefficient increases as the volume fraction of nanofluid increases. With the increasing of Ra, mass flow rate increases greatly. Water-Ag, water-CuO, water-Al₂O₃, water-TiO₂ nanofluids have been studied and it shows that water-Ag nanofluid has higher surface heat transfer coefficient than the others. For the cavity with double sinusoidal wavy walls, a periodical fluctuation of local Nusselt number at different locations of the outer wavy wall has been found and the net result is that the outer wall Nusselt number is evidently larger than that with only single sinusoidal wavy wall.