Lecture 14 - Free Convection Free Convection Cylinders...

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Unformatted text preview: 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 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 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 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 = 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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This note was uploaded on 03/30/2008 for the course ME 3304 taught by Professor Stern during the Spring '08 term at Virginia Tech.

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Lecture 14 - Free Convection Free Convection Cylinders...

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