On the Natural Convection in a Cavity With a Cooled Top Wall and Multiple Protruding Heaters

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Abstract
Natural convection in rectangular enclosures with multiple protruding heaters mounted on one side wall is of relevance to the cooling of electronic equipment. In some configurations, the top wall behaves as the heat sink while the opposing vertical wall and the bottom wall are insulated. The present work examines the peculiarities introduced in the natural convection process for such configurations. The enclosure considered had five protrusions, cavity width to heater length ratio of 1.2 and cavity height to heater length ratio of 11. It is shown that for such configurations, a stable flow exists only at lower Rayleigh numbers and that above a certain critical Rayleigh number, only quasi-steady solutions exist. At low Rayleigh numbers(Ra* ≤ 1.5 × 107), the flow is stable and characterized by the presence of a primary flow cell and a counter-rotating secondary cell at the top of the enclosure. At higher Rayleigh numbers (Ra* ≥ 3 × 108), however, the isothermal top wall causes a periodic flow pattern to develop within the enclosure. Several interesting characteristics of the flow and temperature fields are presented. Results compared with previous experimental and numerical work are found to be in good agreement.