Lecture 19 External Flow

# Lecture 19 External Flow - 1 MECE 4364 Heat Transfer Prof....

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1 MECE 4364 Heat Transfer MECE 4364 Heat Transfer Prof. Dong Liu Prof. Dong Liu Department of Mechanical Engineering Department of Mechanical Engineering University of Houston University of Houston 1 Lecture 19 Oct 21, 2010 External Flow: External Flow: Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) (Cylinders, Spheres, Packed Beds) Chapter 7 Chapter 7 Sections 7.4 through 7.8 Sections 7.4 through 7.8

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2 Cylinder in Cross Flow The Cylinder in Cross Flow • Conditions depend on special features of boundary layer development, including onset at a stagnation point and separation , as well as transition to turbulence. Stagnation point : Location of zero velocity and maximum pressure . ( ) 0 u = Followed by boundary layer development under a favorable pressure gradient and hence acceleration of the free stream flow . ( ) /0 dp dx < ( ) du dx > As the rear of the cylinder is approached, the pressure must begin to increase. Hence, there is a minimum in the pressure distribution, p(x), after which boundary layer development occurs under the influence of an adverse pressure gradient ( ) ,/0 . dp dx du dx >< Cylinder in Cross Flow (cont.) Separation occurs when the velocity gradient reduces to zero 0 / y du dy = and is accompanied by flow reversal and a downstream wake . Location of separation depends on boundary layer transition . Re D VD VD ρ μ ν ≡=
3 Cylinder in Cross Flow (cont.) • Force imposed by the flow is due to the combination of friction and form drag. The dimensionless form of the drag force is () 2 Figure 7.8 /2 D D f F C AV ρ =→

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4 Cylinder in Cross Flow (cont.) Heat Transfer Considerations The Local Nusselt Number : How does the local Nusselt number vary with for ? θ 5 Re 2 10 D < x What conditions are associated with maxima and minima in the variation? How does the local Nusselt number vary with 5 for Re 2 10 ? D What conditions are associated with maxima and minima in the variation? Cylinder in Cross Flow (cont.) Heat Transfer Considerations The Average Nusselt Number ( ) /: D N uh D k Churchill and Bernstein Correlation: () 4/5 5/8 1/2 1/3 1/4 2/3 0.62Re Pr Re 0.3 1 282,000 10 . 4 / P r DD D Nu ⎛⎞ =+ + ⎜⎟ ⎝⎠ ⎡⎤ + ⎣⎦ Cylinders of Noncircular Cross Section: Re Pr m D D Nu C = ,T a b l e 7 . 3 Cm
5 Tube Banks Flow Across Tube Banks • A common geometry for two-fluid heat exchangers . max S T VV SD T = Aligned and Staggered Arrays : Aligned: Staggered: () if 2 max S T S D S D DT T =− if 2 max 2 S T S D S D D or, Tube Banks (cont.) Flow Conditions : How do convection coefficients vary from row-to-row in an array?

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## This note was uploaded on 01/27/2011 for the course MECE 4364 taught by Professor Lipinglui during the Winter '10 term at University of Houston.

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Lecture 19 External Flow - 1 MECE 4364 Heat Transfer Prof....

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