CONJUGATE NATURAL-CONVECTION FROM AN ARRAY OF DISCRETE HEAT-SOURCES .2. A NUMERICAL PARAMETRIC STUDY

Coupled conduction and natural convection transport within a discretel y heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wal l and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equatio ns for the fluid and solid region are solved simultaneously using a co ntrol volume formulation, coupled with an additive correction multigri d procedure that increases the convergence rate of the solution. The f luid Prandtl number and heater/fluid thermal conductivity ratio are fi xed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modifie d Rayleigh number (10(4) less than or equal to Ra-Lz less than or equ al to 10(9)), the cavity flow becomes more boundary layer-like along t he vertical walls and multiple fluid cells develop in the central regi on. Thermal spreading in the substrate increases with decreasing modif ied Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10(-1) less than or equal to R(s) less tha n or equal to 10(3)). For large R(s), the discrete heat sources lose t heir thermal identity, and the streamlines and isotherms resemble thos e associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cav ity a nd on maximum surface temperatures.