# Free Convection: Cylinders, Spheres, and Enclosures - PowerPoint PPT Presentation

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Free Convection: Cylinders, Spheres, and Enclosures. Chapter 9 Section 9.6.3 through 9.8. The Long Horizontal Cylinder. Cylinders. Boundary Layer Development and Variation of the Local Nusselt Number for a Heated Cylinder:. The Average Nusselt Number:.

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Free Convection: Cylinders, Spheres, and Enclosures

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## Free Convection:Cylinders, Spheres, and Enclosures

Chapter 9

Section 9.6.3 through 9.8

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?

• In the limit as how may conditions be characterized?

Spheres

### Spheres

• The Average Nusselt Number:

• Horizontal Cavity

• Vertical Cavity

Enclosures

### Enclosures

• Rectangular Cavities

• Characterized by opposing walls of different temperatures, with the

remaining walls well insulated.

• 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

• 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

• 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.

Annular Cavities

### Enclosures (cont)

• Concentric Cylinders

• Critical Rayleigh Number:

### Enclosures (cont)

• Concentric Spheres

• Critical Rayleigh Number:

### Problem: Batch Reactor

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