Thermal convection in slender laterally-heated cavities
Two-dimensional convective flows in shallow and tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical end walls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. As the Rayleigh number increases, nonlinearity first affects the flow structure in the turning regions near the ends of the cavity. These `end-zone problems' have been investigated by a combined computational and analytical approach. Numerical solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are obtained by both analytical and computational methods. A numerical scheme for finding thermal convective flows in a finite laterally heated cavity is described in detail in Chapter 2. The end-zone problems for tall cavities with conducting and adiabatic horizontal boundaries are considered in Chapters 3 and 4 respectively. For shallow cavities, the end-zone problems for these two thermal boundary conditions are considered in Chapters 5 and 6. Finally, timedependent shallow cavity flows for insulated horizontal boundaries are investigated using both analytical and computational methods in Chapter 7.