Natural convection heat transfer in rectangular cavities partially heated from below

Natural convection in an enclosed cavity with localized heating from below has been investigated by a finite difference procedure. The upper surface is cooled at a constant temperature and a portion of the bottom surface is isothermally heated while the rest of the bottom surface and the vertical walls are adiabatic. Parameters of the problem are the cavity aspect ratio (A = 1 and 2), dimensionless length (B = 0.06 to 1.0) and position of the heat source with respect to the vertical symmetry line of the cavity (e = -0.6 to 0.7), the Prandtl number and the Rayleigh number (Ra = 0 to 5 x 10 6). The effects of the thermophysical and geometrical parameters on the fluid flow and temperature fields have been studied. The existence of multiple steady-state solutions and the oscillatory behavior for a given set of the governing parameters are demonstrated. Nomenclature A = aspect ratio, L'lH' B = dimensionless length of heat source, t'/L' g = acceleration due to gravity, m/s2 H' = cavity height, m h = local heat transfer coefficient, W/m2-K h = average heat transfer coefficient, W/m2-K k = thermal conductivity of fluid, W/m-K L' = cavity width, m €' = length of heat source, m m, n = wave numbers of initial disturbance, Eq. (15) Nu = Nusselt number based on cavity height, hH'/K Pr = Prandtl number,'via p'_ = pressure, Pa