ME150_Lect11-2_External Convection
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Transcript of ME150_Lect11-2_External Convection
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
1
Forced Convection: External Flow
Chap. 13: Emperical Correlations – External Flow
Development of turbulence over a certain length:
crit crit crit x
transition
Flate Plate:
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
2
Chap. 13: Emperical Correlations – External Flow
124.92 Rexx
δ −= ⋅
21
Re664.0 −⋅= xfxc
31
Pr=Tδδ
21
Re328.1 −⋅= xfxc
Heat transfer
6.0Pr >
100PrRePex >⋅= x ( ) 41
32
31
21
Pr0468.01
PrRe3387.0Nu
⎥⎦
⎤⎢⎣
⎡ +
⋅⋅= x
x
Laminar Flow: Exact solution
Boundary layer thickness:
Friction coefficient:
6.0Pr < 21
Pr)(Re565.0Nu ⋅⋅=⋅
= xx kxh
31
21PrRe332.0Nu ⋅⋅=
⋅= xx k
xh
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
3
Chap. 13: Emperical Correlations – External Flow
Turbulent Flow: Semi-empirical solution
λα xxU
c
x
x
xxf x
⋅=
⋅=
⋅⋅=
≤⋅=
∞
−
x
31
54
x
751
NuRe
PrRe0296.0Nu
10ReRe0592.0
ν k h
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
4
Circular Cylinder in Cross-Flow
D
Cross-Flow with U∞ und T∞ Wall temperature TW = constant
For temperature-dependent values ρ(T), µ(T):
Use mean film temperature:
Tfilm = (TW + T∞)/2
Chap. 13.1: Emperical Correlations – Cylinders
31
PrReNu ⋅⋅=⋅
= mDD C
kDh
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
5
Chap. 13.1: Emperical Correlations – Cylinders
Non-Circular Cylinder in Cross-Flow
U
U
U
U
U
D
D
D
D
D
Square
Square
Hexagon
Hexagon
Vertical plate
Re C m
5.103 – 105
5.103 – 105
5.103 – 1.95.104
1.95.104 - 105
5.103 – 105
4.103 – 1.5.104
0.246
0.102
0.160
0.0385
0.153
0.228
0.588
0.675
0.638
0.731
0.638
0.782
D
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
6
41
4.032
21
Pr)Re06.0Re4.0(2Nu ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅+⋅+=
wDDD
µµ
Flow around Spheres
Example for an important application: evaporating small droplets in sprays
.2 constNu ≈≈
2.30.1
106.7Re5.3
380Pr71.04
<<
⋅<<
<<
W
D
µµ
Valid for:
Chap. 13.2: Emperical Correlations – Spheres
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
7
Chap. 13.3: Emperical Correlations – Multi-Structures
Bank of tubes
41
36.0max, Pr
PrPrReNu ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅⋅=
W
mDD C
ReD,max C m
10 - 102 0.80 0.40 103 - 2.105 0.27 0.63 2.105 - 2.106 0.021 0.84
ReD,max C m
10 - 102 0.90 0.40 103 - 2.105 0.40 0.60 2.105 - 2.106 0.022 0.84
Aligned
Staggered
A
A1
A2
ReD,max: based on maximum velocity (i.e. minimum cross section A). All properties evaluated for mean temperature (inlet/outlet).
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
8
Packed Bed of Spheres
Chap. 13.3: Emperical Correlations – Multi-Structures
31
PrRe06.2Nu 425.0 ⋅⋅= DDε
ReD,max: based on undisturbed inlet velocity and particle diameter
ε: Porosity or void fraction
Pr: valid for gases
7.0Pr4000Re90
≈
≤≤ D
U
Prof. Nico Hotz
ME 150 – Heat and Mass Transfer
9
Chap. 13.4: Emperical Correlations – Methodology
(1) Identify the flow geometry (configuration, wetted area, etc.)
(2) Specify the appropriate reference temperature and determine the flow properties (density, viscosity, etc) at that temperature. Appropriate reference temperature: often the free-stream temperature. Some correlations use other reference temperatures!
(3) Calculate the Reynolds number using the appropriate reference dimension (length for plates / wings, diameter for spheres, cylinders, etc.)
(4) Decide whether you want an average heat transfer coefficient (often the case) or a local heat transfer.
(5) Select the appropriate correlation (often: Nusselt correlations)
Methodology