Lecture 21 Forced Convection 2

# Lecture 21 Forced - 1 MECE 4364 Heat Transfer Prof Dong Liu Department of Mechanical Engineering University of Houston Lecture 21 Lecture 21 2

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MECE 4364 Heat Transfer Prof. Dong Liu Department of Mechanical Engineering University of Houston 1 Lecture 21 – Oct 28, 2010 Lecture 21 Forced Convection 2

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Lecture 21 Internal Convection: Overview ± Laminar flow in circular tube ± velocity boundary layer thickens on surface of tube with increasing x ± inviscid region of uniform velocity shrinks as boundary layer grows ± subsequent to boundary layer merger at the centerline, the velocity profile becomes parabolic and invariant with x hydrodynamically fully developed u x = 0 u x 0 3 Lecture 21 Pressure Gradient and Friction Factor ± Define the Moody (or Darcy) friction factor ± Fanning friction factor ± Note that ± For fully-developed laminar flow in circular tube ( ) 2 2 h m dp dx D f u ρ 4 0 22 rr s f mm du dr C uu μ τ ρρ = ⎜⎟ ≡= 4 f f C = 64 Re D f = (why?) ( ) () 2 , 2 , o c c r A m co o urxdA r x r d r Ar ==
Lecture 21 Moody Diagram ± Fully-developed turbulent flow in a smooth circular tube 5 ( ) 2 6 0.790 1n Re 1.64 3000 Re 5 10 DD f =− × 1/4 4 1/5 4 0.316Re Re 2 10 0.184Re Re 2 10 D D f f =≤ × =≥ × or Lecture 21 Pressure Drop and Pumping Power ± The pressure drop can be determined from the friction factor f ± For fully developed flow from the axial position x 1 to x 2 ± The pump power required to overcome the resistance to flow from this pressure drop is Δ p = p 1 p 2 dp p 1 p 2 = f ρ u m 2 2 D h dx x 1 x 2 = f u m 2 2 D h x 2 x 1 () ( )( ) ( ) ( ) Pp p m =Δ ∀=Δ ± ± 6 (apply for both laminar and turbulent flows)

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Lecture 21 Thermal Considerations ± Internal Flows: Thermal Effects ± assume laminar flow with uniform inlet temperature T i ± two common boundary conditions ² uniform heat flux ² uniform surface temperature ± simplest internal flow:
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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 21 Forced - 1 MECE 4364 Heat Transfer Prof Dong Liu Department of Mechanical Engineering University of Houston Lecture 21 Lecture 21 2

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