A scaling investigation of the laminar convective flow in a solar chimney for natural ventilation

The flow behavior due to natural convection of air (with a Prandtl number less than 1) inside a solar chimney with an imposed heat flux on a vertical absorber wall is investigated by a scaling analysis and a corresponding numerical simulation. Three distinct flow regimes are identified, one with a distinct thermal boundary layer and the other two without a distinct thermal boundary layer, depending on the Rayleigh number. The two regimes without a distinct thermal boundary layer are further classified into low and medium Rayleigh number sub-regimes respectively. These sub-regimes are characterized by conduction dominance in which the thermal boundary layer grows to encompass the entire width of the channel before convection becomes important. Flow development in each of these flow regimes and sub-regimes is characterized through transient scaling, and scaling correlations are developed to describe the temperature, flow velocity and mass flow rate, which characterize the ventilation performance of the solar chimney. The scaling arguments are validated by the corresponding numerical data.