Free Convection: Cylinders, Spheres, and Enclosures

1. Free Convection:Cylinders, Spheres, and Enclosures Chapter 9 Section 9.6.3 through 9.8

2. The Long Horizontal Cylinder Cylinders • 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?

3. In the limit as how may conditions be characterized? Spheres Spheres • The Average Nusselt Number:

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

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

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

7. 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). Enclosures (cont) • Inclined Cavities • Relevant to flat plate solar collectors.

8. Annular Cavities Enclosures (cont) • Concentric Cylinders • Critical Rayleigh Number:

9. Enclosures (cont) • Concentric Spheres • Critical Rayleigh Number:

10. Problem: Batch Reactor Problem 9.74: Use of saturated steam to heat a pharmaceutical in a batch reactor.

11. Problem: Batch Reactor (cont)

12. Problem: Batch Reactor (cont)

13. Problem: Batch Reactor (cont)

14. Problem: Batch Reactor (cont)