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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

Free Convection:Cylinders, Spheres, and Enclosures

Chapter 9

Section 9.6.3 through 9.8


Cylinders

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?


Spheres

Spheres

Spheres

  • The Average Nusselt Number:


Enclosures

  • Vertical Cavity

Enclosures

Enclosures

  • Rectangular Cavities

  • Characterized by opposing walls of different temperatures, with the

    remaining walls well insulated.


Enclosures cont

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


Enclosures cont1

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


Enclosures cont2

  • 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.


Enclosures cont3

Annular Cavities critical angle ,

Enclosures (cont)

  • Concentric Cylinders

  • Critical Rayleigh Number:


Enclosures cont4
Enclosures (cont) critical angle ,

  • Concentric Spheres

  • Critical Rayleigh Number:


Problem batch reactor
Problem: Batch Reactor critical angle ,

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






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