Combined effect of radiation and natural convection in a square cavity differentially heated with a periodic temperature

The coupling between natural convection and surface radiation in a square cavity with its vertical walls submitted to different heating models is studied numerically using a finite-difference procedure. The temperature of the left vertical surface (hot temperature) is varied sinusoidally with time, while that of the opposite surface (cold temperature) is maintained constant. The remaining horizontal walls are considered adiabatic. The parameters governing the problem are the emissivity of the walls (0 <=epsilon <= 1), the amplitude (0 <= a <= 1) and the period (0.001 <=tau <= 1) of the variable temperature, the Rayleigh number (Ra=10(6)), and the Prandtl number (Pr=0.72). The effect of these parameters on heat transfer and fluid flow within the cavity is examined. Streamlines, isotherms, and total Nusselt numbers are presented for various typical combinations of the governing parameters. The results obtained show that the heat transfer could be significantly enhanced, with respect to the case of a constant heating temperature, by a proper choice of the parameters related to the periodic temperature and the emissivity of the walls.