Emptying non-adiabatic filling boxes: the effects of heat transfers on the fluid dynamics of natural ventilation

A model for steady flow in a ventilated space containing a heat source is developed, taking account of the main heat transfers at the upper and lower boundaries. The space has an opening at low level, allowing cool ambient air to enter the space, and an opening near the ceiling, allowing warm air to leave the space. The flow is driven by the temperature contrast between the air inside and outside the space (natural ventilation). Conductive heat transfer through the ceiling and radiant heat transfer from the ceiling to the floor are incorporated into the model, to investigate how these heat transports affect the flow and temperature distribution within the space. In the steady state, a layer of warm air occupies the upper part of the space, with the lower part of the space filled with cooler air (although this is warmer than the ambient air when the radiant transfer from ceiling to floor is included). Suitable scales are derived for the heat transfers, so that their relative importance can be characterized. Explicit relationships are found between the height of the interface, the opening area and the relative size of the heat transfers. Increasing heat conduction leads to a lowering of the interface height, while the inclusion of the radiant transfer tends to increase the interface height. Both of these effects are relatively small, but the effect on the temperatures of the layers is significant. Conductive heat transfer through the upper boundary leads to a significant lowering of the temperature in the space as a proportion of the injected heat flux is taken out of the space by conduction rather than advection. Radiative transfer from the ceiling to floor results in the lower layer becoming warmer than the ambient air. The results of the model are compared with full-scale laboratory results and a more complex unsteady model, and are shown to give results that are much more accurate than models which ignore the heat transfers.