Conjugate natural convection from a discrete heat source on a conducting plate in a shallow enclosure

Abstract

Experiments were performed to characterize the conjugate heat transfer due to a square flush heat source mounted at the center of a square horizontal plate in a small horizontal enclosure. The plate area was six times larger than the heat source area. Three different plates with heat source facing upwards were considered: a 25mm balsa wood plate which provided a nearly adiabatic surface, a 1.57mm thick FR-4 plate with no copper, and a 1.57mm thick FR-4 plate with a single layer of 0.036mm thick copper cladding on source side. The back of the board was insulated for all cases. The experimental exploration included measurement of heat transfer coefficient over the heat source, plate surface temperature distribution and temperature distribution in the air volume above the plate. The heat transfer coefficients exhibited distinct behavior at high aspect ratios in which the dominant length scales were related to the source. At intermediate aspect ratios, length scales for both source and enclosure were relevant, and at small aspect ratios, a conduction limit was observed, which was dependent on board conductivity. The heat transfer coefficients at high aspect ratios exceeded by 14% the prior correlations for upward facing isolate plates, when the ratio of source area to perimeter was used as the significant length scale, and a stronger dependence than Ra1/4 was measured. Classical correlations for shallow differentially heated enclosure were not satisfactory in describing the dependence on enclosure height. With increasing board conductivity, board thermal spreading increased the effective source size so that the discretely heated board heat transfer coefficients tended towards the behavior of the classical uniformly heated board. New first-order thermal design formulae were derived for determining peak temperatures of sources on conducting substrates, and for determining the associated thermal "zone of influence" or "footprint." The board heat spreading was accounted for by using its effective "thermal footprint" radius and correlations for conjugate heat transfer based on this length scale were successful in describing the behavior of the average Nusselt number at large enclosure heights. Some qualitative flow visualization was also performed and representative results are shown.