Conjugate natural convection from an array of protruding heat sources

Coupled conduction and natural convection heat transfer has been investigated numerically for protruding heat sources mounted to one vertical wall of a rectangular cavity. The heat sources simulate an array of computer chips mounted on a substrate of finite thermal conductivity. The back of the substrate and the horizontal walls of the cavity are assumed to be adiabatic, while the opposing vertical wall provides an isothermal heat sink. The fluid Prandtl number and the heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77, manufactured try 3M Company) and silicon chips. With increasing modified Rayleigh number (10(4) less than or equal to RaLz* less than or equal to 10(9)), the cavity flow approaches boundary layer behavior, and more fluid penetrates the regions between protrusions. The effect of contact resistance between the heater and substrate is shown to be small for R(th)'' less than or equal to 10 cm(2) degrees C/W. With decreasing substrate thermal conductivity [1.48 W/ (m K) less than or equal to k(s) less than or equal to 148 W/(m K)] fluid circulation decreases and the maximum heater temperatures increase.