Theoretical modeling of unsteady buoyancy-driven natural ventilation

A modified theoretical model is developed to examine the unsteady natural ventilation produced by a localized inner heat source at the floor of a room. The model is validated by using experimental results in the literature. The main difference between this model and previous models is that the buoyant layer is regarded as composed of a middle layer and a near-ceiling layer rather than being well-mixed. This model is therefore named the three-layer model and then used to investigate the unsteady process. Three characteristic times are defined to predict the time taken for the stratification interface to reach three particular positions during the transient process. When the dimensionless effective vent area is smaller, the steady-state depths of the near-ceiling layer and the middle layer are smaller and larger, respectively. The dimensionless buoyancies of the near-ceiling layer and the middle layer increase gradually over time while the plume buoyancy at the lower interface increases rapidly to its maximum and then decreases slowly. The temperature difference between the near-ceiling layer and the middle layer is small, but it is not negligible comparing to the temperature difference between the middle layer and the lower layer. The variations of the layer buoyancy and ventilation flow rate with time are both dependent on the source buoyancy flux, the floor area, the effective vent area and the enclosure height.