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Abstract

Buoyancy driven flows in enclosures, due to temperature gradients, have been studied since the eighteenth century for both scientific and practical reasons alike. Thus numerous analytical, numerical and experimental studies of two-dimensional rectangular cavities have been undertaken. A simple generic problem has been studied in order to make progress in understanding the physical nature of these motions. In such cavity flows, three parameters are found to be important, a Rayleigh number R based on the height of the cavity and the temperature difference across the end walls, the Prandtl number σ of the fluid and the aspect ratio (length/height).

Thermal convection in a shallow laterally heated cavity with conducting boundaries is considered in Chapter 2. The companion problem for adiabatic boundaries is studied in Chapter 3. Chapters 4-7 are concerned with the boundary-layer structure that emerges near the ends of the cavity as the Rayleigh number increases. On the horizontal walls two stages of development are identified, a horizontal boundary layer where the flow is independent of the temperature field and a longer scale on which buoyancy becomes significant. The horizontal boundary layer is considered in Chapters 4 and 5 and the horizontal buoyancy layer is studied in Chapters 6 and 7.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	Doctoral Theses School of Science & Technology > School of Science & Technology Doctoral Theses School of Science & Technology > Mathematics

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