Natural Convection Liquid Cooling of a Substrate-Mounted Protrusion in a Square Enclosure: A Parametric Study

The coupled conduction and natural convection transport from a substrate-mounted heat generating protrusion in a liquid-filled square enclosure is numerically examined. The governing steady two-dimensional equations are solved using a finite-difference method for a wide range of Rayleigh numbers, protrusion thermal conductivities and widths, substrate heights, and enclosure boundary conditions. The results presented apply to liquids with 10≤Pr≤1000. It was established that in many situations it may be inappropriate to specify simple boundary conditions on the solid surface and decouple the conduction within the substrate or the protrusion. Higher Rayleigh numbers, protrusion thermal conductivities, and widths enhanced cooling. A variation in the substrate height did not affect the maximum protrusion temperature; however, the flow behavior was considerably altered. An empirical correlation for the maximum protrusion temperature was developed for a wide range of parametric values. The enclosure thermal boundary conditions changed the heat transfer in the solid region to only a small extent. Immersion cooling in common dielectric liquids was shown to be advantageous over air cooling only if the thermal conductivity of the protrusion was larger than that of the liquid.