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Free Convection: Cylinders, Spheres, and EnclosuresPowerPoint Presentation

Free Convection: Cylinders, Spheres, and Enclosures

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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

- 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

- The Average Nusselt Number:

- Horizontal Cavity

- Vertical Cavity

Enclosures

- Rectangular Cavities

- Characterized by opposing walls of different temperatures, with the
remaining walls well insulated.

- Heating from Below

- 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

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).

- Inclined Cavities

- Relevant to flat plate solar collectors.

Annular Cavities

- Concentric Cylinders

- Critical Rayleigh Number:

- Concentric Spheres

- Critical Rayleigh Number:

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