Indoor thermal stratification and its statistical distribution

Thermal stratification is established when warmer air rises and cooler air descends under thermal buoyancy. It occurs in indoor environment situations including large warehouse-type buildings, buoyancy-driven ventilated spaces with displacement, underfloor ventilation, and/or natural ventilation, and enclosure fires with hot smoke layer on top of cold air layer. This paper reports a recent study that thermal stratification of indoor environment follows the statistical Beta distribution so the vertical temperature distribution is the Cumulative Distribution Function of the Beta distribution defined by two shape parameters, Alpha (α) and Beta (β), despite ventilation types, heat source and other details. It is then possible to estimate a complete vertical temperature profile under thermal stratification by four temperature points (ie, 4-point Beta distribution), or as few as two points (ie, 2-point Beta distribution) with a slight loss of accuracy. The study was confirmed by the field measurement data of five warehouse-type buildings, and eleven thermal stratification studies from the literature. A few applications were demonstrated including quantitative characterization of thermal stratification; estimation of mean and spatial temperature uniformities and other key parameters. The dimensionless nature of the methodology may also be potentially applied to other indoor stratification phenomena.