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.

The Effects of Radiative Heat Transfer Upon the Melting and Solidification of Semitransparent Crystals

Employing the assumptions of one-dimensional energy transfer, equilibrium phase change, and negligible convection in liquid regions, the time-dependent conservation of energy equation is formulated for the general situation of n semitransparent contiguous liquid and solid phases. The dimensionless parameters governing phase change are identified and the effects of their variation are ascertained by a finite difference solution of the rigorously formulated energy and radiative transfer equations. The chief conclusions of this investigation are that for the range of parameters encountered in the melting and solidification of many optical materials, radiant transfer has a significant effect, and that during solidification, radiation can force the temperature profile within the liquid phase to assume a shape which leads to unstable interfacial growth.