Natural convection in a 2D enclosure with sinusoidal upper wall temperature

Natural convection in a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated. The applied sinusoidal temperature is symmetric with respect to the midplane of the enclosure. Numerical calculations are produced for Rayleigh numbers in the range 10(2) to 10(8), and results are presented in the form of streamlines, isotherm contours, and distributions of local Nusselt number. The circulation patterns are shown to increase in intensity, and their centers to move toward the upper wall corners with increasing Rayleigh number. As a result, the thermal boundary layer is confined near the upper wall regions. The values of the maximum and the minimum local Nusselt number at the upper wall are shown to increase with increasing Rayleigh number. Finally, an increase in the enclosure aspect ratio produces an analogous increase of the fluid circulation intensity.