Mildly zigzag heat transfer affected by aspect ratios for recirculating flows in rectangular enclosures

In past decades, although buoyancy-driven recirculating flows in rectangular enclosures (left hot wall, right cold wall, insulated top and bottom) have been intensively studied as a benchmark problem, there exist interesting Nusselt-number characteristics that have been unreported in the literature. As the enclosure widens, the average Nusselt number exhibits mildly zigzag behaviors, namely, decreasing first, reaching a local minimum, then rising, reaching a local maximum, and finally decreasing again. The first extremum is associated with the competition between heat convection and heat conduction, as well as the former's victory in terms of the magnitude of the slope (the derivative of the heat transfer as a function of the aspect ratio), whereas the second extremum occurs when the heat convection dominates the overall heat conduction. Our study may shed the light on various thermal-system designs that desire either maximal insulation (e.g., storm windows and energy storage) or maximal cooling (e.g., LED and other electronic devices).