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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.

The present study numerically investigates the unsteady natural convection in a triangular domain induced by ramped iso-flux cooling at the water surface. The simulations indicate that, although the ramped cooling does not alter the final state of the flow for a given steady state flux, it may change the developing path towards the final state as well as slow down the development of the flow. The ramped cooling delays or completely suppresses the onset of a Rayleigh-Benard type (RBT) instability during the developing process. As a consequence, a transitional stage characterized by the appearance and disappearance of the RBT instability at intermediate Rayleigh numbers does not occur if the ramp time is significantly long. Both qualitative and quantitative information is presented to demonstrate the effects of the ramp time on the transient behaviour of the flow at different Rayleigh numbers. A time scale for the onset time of the RBT instability under ramped cooling is also proposed and verified by the numerical results. The local instantaneous Rayleigh number at different parameters is calculated and its time history confirms the observed transient flow behaviours.

The unsteady natural convection flow adjacent to the finned sidewall of a differentially heated cavity is numerically investigated through comparisons between the cases with a conducting fin and an adiabatic fin. The results show that the flow and temperature structures in the transition to a periodic flow induced by a conducting fin are considerably different from those by an adiabatic fin. Based on the present numerical results, the temporal development and spatial structures of the flow adjacent to the finned sidewall are described, and instabilities are characterized. It is found that the conducting fin improves the transient convective flows in the cavity and enhances heat transfer across the cavity (by up to 52% in comparison with the case without a fin).

This work incorporates scaling analysis to characterise unsteady boundary-layer development for thermo-magnetic convection of paramagnetic fluids with Prandtl numbers (Pr ) greater than one. Under consideration is a square cavity with a quiescent isothermal, Newtonian fluid placed in a micro-gravity condition (g≈0g≈0), and under a uniform vertical gradient magnetic field. A distinct magnetic convection boundary layer is produced by the sudden imposition of a higher temperature on the left-hand side vertical sidewall due to the effect of the magnetic body force generated on the paramagnetic fluid. This magnetic force is proportional to the magnetic susceptibility and the gradient of the square of the magnetic induction. According to Curie’s law, the magnetic susceptibility of a paramagnetic fluid is inversely proportional to the absolute temperature. Thermal convection of a paramagnetic fluid can therefore take place even in zero-gravity environments as a direct consequence of temperature differences occurring within the fluid placed within a magnetic field gradient. Scaling predictions presented here are verified by numerical simulations It is shown that the transient flow behaviour of the resulting boundary layer can be described by three stages: a start-up stage, a transitional stage and a steady state. Special attention in this work is paid to the dependency of the flow development upon the Prandtl number, varied over the range of 5–100, thus representing various fluids. Also, the effect of the magnetic momentum parameter, m, and the quantity γRa, upon the flow development obtained in numerical simulations confirms the accuracy of new scaling predictions for paramagnetic fluids.

The unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity is visualized using a shadowgraph technique and measured using fast-response thermistors. Experiments show that the transition of the unsteady thermal flow around the fin from initiation by sudden heating to a quasi-steady state undergoes a number of stages including the formation of a horizontal gravity current under the fin and a starting plume bypassing the fin, entrainment into the downstream thermal boundary layer, and separation and oscillations of the thermal flow above the fin. We present a series of flow visualization images to describe the transition of the unsteady thermal flow, and obtain the unsteady velocity scales of the fronts of the lower intrusion and starting plume as functions of the time and Rayleigh number, which are verified by the results of the flow visualization experiments. In the transition to the quasi-steady state, separation and oscillations of the thermal flow above the fin are observed. It is demonstrated that these oscillations, which are sensitive to the geometry of the fin, trigger instability of the downstream thermal boundary layer flow and thus enhance convection. It is found that the frequency of the oscillations is a linear function of the Rayleigh number.

This study considers the unsteady natural convection in a triangular domain induced by a constant cooling at the water surface. The study consists of two parts: a scaling analysis and numerical simulations. The scaling analysis for small bottom slopes reveals that three laminar flow regimes, namely conductive, transitional and convective flow regimes are possible depending on the Rayleigh number. Proper scales have been established to quantify the transient flow development in each of these flow regimes. The numerical simulation has verified the scaling predictions.