Convection Heat Transfer 3qsy2012-13
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Transcript of Convection Heat Transfer 3qsy2012-13
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CONVECTIONHEAT TRANSFER
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CONVECTION
Heat transfer by CONVECTIONoccurs as a result of themovement of fluid on a macroscopic scale in the form ofeddies or circulating currents.
If currents arise from the heat transfer itself, NATURALCONVECTIONoccurs.
In FORCED CONVECTIONthe circulating currents are producedby an external agency (e.g. an agitator in a reaction vessel oras a result of turbulent flow in pipe).
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Newtons Law of Cooling:
Q = h A (Ts-T)
CONVECTION: heat transfer between a solid
and a fluid
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CONVECTION BOUNDARY
LAYERS
u
u
(x)
The Velocity Boundary Layer
- velocity boundary layer thickness
- the value of y for which u = 0.99u
y
x
free stream
velocity BL
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Velocity Boundary Layer
Develops whenever there is fluid flow over a
surface
Of fundamental importance to problems
involving convection transport
In fluid mechanics
For external flow, it provides the basis for
determining the local friction coefficient2
2
u
C sf
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T
t
T
t(x)
The Thermal Boundary Layer
t- thermal boundary layer thickness
- the value of y for which (TsT) = 0.99 (Ts- T)
y
xTs
free stream
thermal BL
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Thermal Boundary Layer
Must develop if the fluid free stream and surface
temperatures differ
At the surface, there is no fluid motion and energy
transfer occurs only by conduction
Conduction
Convection
TThA
Qs
s
0y
fs
y
TkA
Q
TT
y
Tk
hs
0y
f
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Significance of Boundary Layers
For the engineer, the principalmanifestation of the boundary layers areas follows:
SURFACE FRICTION
Key BL parameter: friction coefficient, Cf
CONVECTIVE HEAT TRANSFER Key BL parameter: convective heat transfer
coefficient, h
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Boundary Layer Parameters
Key BL parameters are evaluated from BL
equations BL approximations
Velocity BL
Thermal BL
x
u,
y
u,
x
u
y
u
uu
yyxx
yx
x
T
y
T
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Boundary Layer Parameters
BL similarity parameters
Parameter Definition Significance
Reynoldsnumber
Ratio of inertia and viscous forces
Prandtl
number
Ratio of momentum and thermal
diffusivities
Nusselt
number
Dimensionless temperature
gradient at the surface
k
C
Pr
p
k
hLNu
LuRe
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PRANDTL NUMBER (Pr):a measure of the relative
effectiveness of momentum and energy transport by
diffusion in the velocity and thermal boundary layers,respectively.
For laminar flow
n is a positive number
For gas: t (n =1) For liquid metal: t >> (n < 1)
For oil: t 1)
n
t
Pr
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Momentum and Heat TransferREYNOLDS ANALOGY
NuCf
2
Re
RePrNuuCh2CSt pf StantonNumber
for Pr = 1
Relates key parameters of thevelocity and thermal BL
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Momentum and Heat Transfer
CHILTON-COLBURN ANALOGY
If Pr 1 (0.60 < Pr < 60)
H
2/3f
jPrSt2
C
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FORCED CONVECTION
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Dimensional Analysis in Heat Transfer(Buckingham Method)
),,,,,( ukCLhh p
hukL
CukL
ukL
lkji
phgfe
dcba
3
2
1
For FORCED CONVECTION
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Final form of the correlation for convective heat
transfer coefficient (forced convection):
k
C,
Luf
k
hL p
PrRe,fNu
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FORCED COVECTION INSIDE PIPES
1. LAMINAR FLOW INSIDE A PIPE / TUBE (Re < 2100)
SIEDER-TATE EQUATION [(Re Pr D/L) > 100]
14.03/1
PrRe86.1
w
b
L
D
k
DhNu
Equation 4.5-4 Geankoplis 4ed
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2. TURBULENT FLOW INSIDE A PIPE / TUBE
2.1 FULLY-DEVELOPED (hydrodynamically and thermally)turbulent flow in a smooth circular tube
2/3
D
D2/3f Pr
PrRe
NuStPr
8
f
2
C
1/34/5
DD Pr0.023ReNu
COLBURN EQUATION
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n4/5DD Pr0.023ReNu
DITTUS-BOELTER EQUATION
n = 0.40 for heating (Ts> Tm)
n = 0.30 for cooling (Ts< Tm)
0.70 Pr 160
ReD10,000
L/D 10
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0.14
w
b1/34/5D
L
Pr0.027Re
k
DhNu
SIEDER-TATE EQUATION
0.70 Pr 16000
Re > 6,000
L/D 60
Equation 4.5-8 Geankoplis 4ed
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3. TRANSITION FLOW INSIDE A PIPE / TUBE
2100 < Re < 6000
Use Figure 4.5-2 Geankoplis 4ed
4. ENTRANCE-REGION EFFECT ON h
0.7
L L
D1
h
h
L
D61
h
h
L
2 < L/D < 20 4.5-12
20 < L/D < 60 4.5-13
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5. LIQUID-METALS HEAT-TRANSFER COEFFICIENT
0.40L 0.625Pek
DhNu
Fully developed turbulent flow in
tubes with uniform heat flux
L/D > 60
100 < Pe < 104
0.8L
0.025Pe5.0k
DhNu
Fully developed turbulent flow in
tubes with constant wall
temperaturesL/D > 60
Pe > 100
Eq. 4.5-14
Eq. 4.5-15
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Correlations from Perrys ChE handbook
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FORCED COVECTION OUTSIDE
VARIOUS GEOMETRIES
Heat-transfer coefficient on immersed
bodies is given by
1/3mPrcReNu
NOTE: FLUID PROPERTIES ARE EVALUATED AT THE
FILM TEMPERATURE:
bwf TT2
1T
Eq. 4.6-1
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FLOW PARALLEL TO FLAT PLATE
Re < 3 x 105(laminar)
Nu = 0.664 Re0.50Pr1/3 Eq. 4.6-2
Re < 3 x 105(turbulent)
Nu = 0.0366 Re0.80Pr1/3 Eq. 4.6-3
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CYLINDER WITH AXIS PERPENDICULAR TO FLOW
1/3m
PrcReNu Eq. 4.6-1
Re m c
1 - 4 0.330 0.989
4 - 40 0.385 0.911
40 to 4 x 103 0.466 0.683
4 x 103to
4 x 104
0.618 0.193
4 x 104 to
2.5 x 105
0.805 0.0266
TABLE 4.6-1
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FLOW PAST SINGLE SPHERE
1/30.50Pr0.60Re2.0Nu
1 < Re < 70,000 Eq. 4.6-4
0.60 < Pr < 400
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Correlations from Perrys ChE handbook
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FREE CONVECTION
or NATURAL CONVECTION
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Free or Natural Convection
Very common
Either external or internal flows
Main source of momentum: hydrostatic
force (buoyancy)
Tends to result in low Nusselt number
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No imposed flow = No Reynolds number
Since there is no free-stream velocity to quantify
the forces of momentum in free convection flows,
a new dimensionless group for inertial and
viscous forces is needed.
Since buoyancy is the source of movement:
TgL~vg gravitational acceleration
coefficient of thermal expansion
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Natural Convection from Vertical Planesand Cylinder
mm aRaGrPraNu
a and m are constants (see Table 4.7-1
Geankoplis)
Properties are evaluated at film temperatureTable 4.7-2 (Geankoplis) gives simplified
correlations for natural convection from
various surfaces
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Natural Convection from HorizontalCylinder
Same as the case of vertical planes and
cylinders
Replace L with D
mm
aRaGrPraNu
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Natural Convection from HorizontalPlates
Same as the case of vertical planes and
cylinder
L
Side of a square
Linear mean of 2 dimensions of a rectangle
0.90 times the diameter of circular disc
In general: L = area / perimeter
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Natural convection in enclosed surfaces
Refer to equations 4.7-5to 4.7-15
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TUBE BUNDLES /BANK OF TUBES
Typical industrial application as in heatexchangers
Bundles of tube improve heat transfer byincreasing the surface area
Bundles of tube are generally eitherarranged in ALIGNED or STAGGEREDconfiguration.
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In general, the STAGGERED configuration is best
for heat transfer.
Sn
Note: ST= SN(in lecture notes) SD= SP
SL = SP(in lecture notes)
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For more than 10 transverse rows and 2000 < Re