1. Free Convection: Cylinders, Spheres, and Enclosures 1

2. The Long Horizontal Cylinder Boundary Layer Development and Variation of the Local Nusselt Number for a Heated Cylinder: The Average Nusselt Number: How do conditions change for a cooled cylinder? 2

3. Spheres The Average Nusselt Number:  In the limit as how may conditions be characterized? Ra D  10 11 Pr  0,7 3

4. Enclosures Rectangular Cavities  Characterized by opposing walls of different temperatures, with the remaining walls well insulated.   Horizontal Cavity  Vertical Cavity 4

5. Horizontal Cavities  Heating from Below – Fluid layer is thermally stable. – Thermal instability yields a regular convection pattern in the form of roll cells. – Buoyancy drive flow is turbulent 5

6.  Heating from Above – Fluid layer is unconditionally stable. Vertical Cavities   – A primary cellular flow is established, as the core becomes progressively more quiescent, and secondary (corner) cells develop with increasing  6

7. Inclined Cavities  Relevant to flat plate solar collectors.  Heat transfer depends on the magnitude of relative to a critical angle, whose value depends on H/L (Table 9.4).  Heat transfer also depends on the magnitude of relative to a critical Rayleigh number of  Heat transfer correlations Eqs. (9.54) – (9.57). 7

8. Annular Cavities Concentric Cylinders    Critical Rayleigh Number: 8 K of a stationary fluid to transfer the same amount of heat as the moving fluid

9.   Concentric Spheres   Critical Rayleigh Number:   9

10. 6A