Lecture 14

# Lecture 14 - Free Convection Cylinders Spheres and...

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

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Cylinders Cylinders The Long Horizontal Cylinder Boundary Layer Development and Variation of the Local Nusselt Number for a Heated Cylinder: The Average Nusselt Number: ( 29 2 1/ 6 12 8/ 27 9 /16 0.387 0.60 10 1 0.559/ Pr D D D Ra Nu Ra = + < + How do conditions change for a cooled cylinder?
Spheres Spheres Spheres The Average Nusselt Number: ( 29 1/ 4 4 / 9 9 /16 0.589 2 1 0.469/ Pr D D Ra Nu = + + In the limit as how may conditions be characterized? 0, D Ra R

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Enclosures Enclosures Enclosures Rectangular Cavities Characterized by opposing walls of different temperatures, with the remaining walls well insulated. ( 29 3 1 2 L g T T L Ra β αν - ( 29 1 2 q h T T R = - Horizontal Cavity 0, 180deg τ = Vertical Cavity 90 deg τ =
Enclosures (cont) Enclosures (cont) Horizontal Cavities Heating from Below ( 29 0 τ = , 1708: L L c Ra Ra < = Fluid layer is thermally stable . 1 L hL Nu k = = 4 L 1708 Ra 5 10 : < < Thermal instability yields a regular convection pattern in the form of roll cells . 5 9 3 10 7 10 : L Ra N < < Buoyancy driven flow is turbulent 1/ 3 0.074 0.069 Pr L L Nu Ra =

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Enclosures (cont) Enclosures (cont) Heating from Above ( 29 180 deg τ = Fluid layer is unconditionally stable . 1 L Nu = Vertical Cavities 3 10 : L Ra < 3 10 : L Ra A primary cellular flow is established, as the core becomes progressively more quiescent, and secondary (corner) cells develop with increasing .
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