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21CONVECTIVE
HEAT-TRANSFER COEFFICIENT
Introduction
In most transport processes heat transfer in fluids is accompanied by some form of fluid motionso that the heat transfer does not occur by conduction alone.
Forced convection: fluid motion arises principally froma pressure gradient caused by a pump or blower
Natural convection: fluid motion arises only fromdensity differences associated with the temperature field
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Introduction
Whether the heat-transfer mechanism is natural or forced convection, the fluid motion can be described by the equations of fluid mechanics.
@ low velocities → the flow is laminar throughout the system@ high velocities → laminar near the heating surface
+ turbulent some distance away
Although fluid velocities in natural convection are usually lower than in forced convection, it is incorrect to think of natural convection as causing only laminar flow; turbulence dose occur when critical Reynolds number for the system is exceeded.
Supercritical Fluid Process Lab
Heat transfer between a fluid and a flat platewhen the fluid is flowing parallel to the plate.
(Fig. 21-1)
All problems of convective heat transfer can be expressed in terms of the differential mass, energy, and momentum balances. However, the mathematical difficulties connected with integration of these simultaneous nonlinear partial differential equations are such that analytical solutions exist only for simplified cases.
One of the problems simplest to deal with analytically is that of
Supercritical Fluid Process Lab
Analytical Solution
Heat transfer between a fluid and a flat platewhen the fluid is flowing parallel to the plate.
(Fig. 21-1)
Supercritical Fluid Process Lab
x0 x1 x2 x3tS tS tS tS
t0
t0
t0t0
x
y
flat plate
Edge of thermalboundary layer
Fig. 21-1Development of a thermal boundary layer for flow over a flat plate
Direction of flow
t0
t0 t0>ts
Leading edge of the plate
Supercritical Fluid Process Lab
Temperature profiles in a developing thermal boundary layer on a flat plate
y, distance normal to flat plate
t, flu
id te
mpe
ratu
re
t0
ts
x1 x2 x3
x0
x0 x1 x2 x3tS tS tS tS
t0
t0
t0t0
x
y
flat plate
Edge of thermalboundary layer
Supercritical Fluid Process LabSupercritical Fluid Process Lab
Heat transfer systemHeat is transferred between a fluid and the wall of a pipe
Supercritical Fluid Process Lab
Thermal-entrance length
Direction of flow
Edge of thermalboundary layer
t0
t0t0
t0
t0
t0
tS tS tS tS tS tS tS
tS tS tS tS tS tS tS
Temperature profile become flatter.
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Temperature profiles near the entrance of a pipe
ri rir=0
ts
t0 x0x1x2x3
Figure 21-4
Supercritical Fluid Process Lab
Temperature profiles vs Velocity profiles
The temperature profile at a point in a flow system is influenced by the velocity profile.
The velocity profile is influenced by the temperature profile. (The velocity profile of an isothermal system may differ substantially from the velocity of a system in which heat is being transferred.)
Supercritical Fluid Process Lab
(8-11)
Differential energy balance
Navier-Stokes equation
Supercritical Fluid Process Lab
Simplification
The non-isothermal velocity profile can be used in solving the differential momentum and energy balances for a non-isothermal system.
This simplification may introduce a serious error when the viscosity of the fluid is strongly dependent on temperature.
Frequently the temperature gradient is greatest near the wall, and it is in this region that the velocity gradient is also greatest. The effect of temperature on the viscosity of the fluid at the wall may therefore have a pronounced effect on both the velocity and temperature profiles of the system.
ts
t0
t0
Supercritical Fluid Process Lab
m
Supercritical Fluid Process Lab
Individual heat transfer coefficient, h
h is a function of
the properties of the fluid,the geometry and roughness of the surface, andthe flow pattern of the fluid.
Supercritical Fluid Process Lab
Evaluation of individual heat transfer coefficient, h
Several methods are available for evaluating hLaminar flow systems→ Analytical methods
Turbulent systems → Integral methods→ Mixing-length theory→ Dimensional analysis
Supercritical Fluid Process Lab
Evaluation of individual heat transfer coefficient, h
dAtthdydtkdAdq s
y
)( 00
−=⎟⎟⎠
⎞⎜⎜⎝
⎛=
=
[ ]0
0
00
)/()(
== ⎭⎬⎫
⎩⎨⎧ −−
=⎟⎟⎠
⎞⎜⎜⎝
⎛−
=y
ss
ys dyttttdk
dydt
ttkh
Velocity of flow past the heated surface ↑Temperature gradient at the wall ↑Heat transfer coefficient, h ↑
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Individual film coefficient, h
exkhΔ
=
Fully developedTurbulent flow
Bufferzone
Laminarsublayer
t
r
If the resistance to heat flow is through of as existing only in a laminar film, h is k/Δxe where Δxe is the equivalent thickness of a stationary film just thick enough to offer the resistance corresponding to observed value of h. Since there is often an appreciable resistance in the turbulent core and since the stationary film has not even an approximate physical counterpart in laminar flow, boiling and radiation, we shall refer h as an individual heat transfer coefficient.
exΔFictitious film
∫=A
xav
b tdAuAu
t 1
Supercritical Fluid Process Lab
Definition of h
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Example 21-1
The analysis of unsteady-state heating or cooling of solid objects can
be often be simplified by assuming that the resistance to heat
conduction inside the solid is negligible compared to the convective
heat-transfer resistance in the surrounding fluid.
The circumstances necessary to justify this assumption are a high
thermal conductivity for the solid and a low convective heat transfer
coefficient in the adjacent fluid. A metallic object being heated or
cooled in air often constitute such a system.
Supercritical Fluid Process Lab
Example 21-1
To illustrate, we shall calculate the time required for a mercury
thermometer initially at 70oF, placed in an oven at 400oF, to reach
279oF. The thermometer bulb has a diameter of 0.24 in and will be
assumed to be adequately represented as an infinitely long cylinder
with negligible resistance to heat transfer either in the glass which is
very thin or in the mercury, which has an adequately high thermal
conductivity [k=5.6 Btu/(h)(ft)(oF) at 140oF]. The mean convective
heat-transfer coefficient between the outside of the thermometer and
the air in the oven will be taken as h=2 Btu/(h)(ft2)(oF).
Supercritical Fluid Process Lab
Supercritical Fluid Process LabFor an infinite cylinder, A/V=(πDL)/(πD2/4)= 4/D
= 4.24 min
Supercritical Fluid Process Lab
For an infinite cylinder, L=V/A=D/4
FoBieY ⋅−=
τθ
−= eY
min24.4=τ
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θ
Supercritical Fluid Process Lab
τ
θ
Temperature response, t =time constant
50 20 10 5 1 0.5
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50=τ20
10510.5
min,θ
t
Temperature response, t, with time
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BiotBiot Number (Bi)Number (Bi)
skhLBi =
resistance mallayer therboundary the solid a of resistance thermalinternal the
=Bi
Supercritical Fluid Process Lab
Fourier Number (Fourier Number (FoFo))
2LFo αθ
=
solid ain storageenergy thermalrate theconductionheat of rate the
=OF
Supercritical Fluid Process Lab
Reynolds Number (Re)Reynolds Number (Re)
ν= ∞LuRe
forces viscoustheforces inertia theRe =
Supercritical Fluid Process Lab
Prandtl Number (Pr)Prandtl Number (Pr)
αν
=μ
=k
C pPr
ydiffusivit thermalthemomentummolecular thePr =
Supercritical Fluid Process Lab
overalltUAq Δ=
individualthAq Δ=
Individual heat transfer coefficient, hOverall heat transfer coefficient, U
Supercritical Fluid Process Lab
hi
h0
Supercritical Fluid Process Lab
0054
,43
,32
21
1
1
Ahqtt
Akrqtt
Akrqtt
Ahqtt
lmcc
c
lmbb
b
ii
=−
Δ=−
Δ=−
=−
Individual temperature drops
Supercritical Fluid Process Lab
Overall temperature drops
⎟⎟⎠
⎞⎜⎜⎝
⎛+
Δ+
Δ+=
+Δ
+Δ
+=−
−=Δ
00,,
00,,51
51
11
11
AhAkr
Akr
Ahq
Ahq
Akrq
Akrq
Ahqtt
ttt
lmcc
c
lmbb
b
ii
lmcc
c
lmbb
b
ii
overall
⎟⎟⎠
⎞⎜⎜⎝
⎛+
Δ+
Δ+
−=
00,,
51
11AhAk
rAkr
Ah
ttq
lmcc
c
lmbb
b
ii
Rtq overall
ΣΔ
=
Supercritical Fluid Process Lab
⎟⎟⎠
⎞⎜⎜⎝
⎛+
Δ+
Δ+
Δ=
0,
0
,
00
0
1hAk
rAAk
rAAh
AtAq
lmcc
c
lmbb
b
ii
overall
Overall coefficients of heat transferbased on the outside area U0
0,
0
,
00
0
11hAk
rAAk
rAAh
AU lmcc
c
lmbb
b
ii
+Δ
+Δ
+=
overalltAUq Δ= 00
Supercritical Fluid Process Lab
⎟⎟⎠
⎞⎜⎜⎝
⎛+
Δ+
Δ+
Δ=
00,,
1Ah
AAk
rAAk
rAh
tAqi
lmcc
ci
lmbb
bi
i
overalli
Overall coefficients of heat transferbased on the inside area U0
i
i
lmcc
ci
lmbb
bi
ii AhA
AkrA
AkrA
hU 0,,
11+
Δ+
Δ+=
overallii tAUq Δ=
Supercritical Fluid Process Lab
Overall coefficients of heat transfer
overallii
overall
tAUqtAUq
Δ=Δ= 00
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Rtq overall
ΣΔ
=
Overall coefficients of heat transfer
ii AUAUR 11
00
==Σ
ii AUAU =00
Supercritical Fluid Process Lab
Approximation of overall coefficients of heat transferbased on the inside area Ui
i
i
lmcc
ci
lmbb
bi
ii AhA
AkrA
AkrA
hU 0,,
11+
Δ+
Δ+=
0
111hk
rkr
hU c
c
b
b
ii
+Δ
+Δ
+=
Approximation0
1,,1hk
rkr
h c
c
b
b
i
ΔΔ>>
Supercritical Fluid Process Lab
Overall coefficients of heat transferof the flat parallel walls
00
1111hk
xkx
hUU c
c
b
b
ii
+Δ
+Δ
+==
Supercritical Fluid Process Lab
Overall coefficients of heat transfer
U, Btu/(h)(ft2)(oF)
Stabilizer reflux condenser 94Oil pre-heater 108Reboiler (condensing steam to re-boiling water) 300-800Air heater (molten salt to air) 6Steam-jacketed vessel evaporating milk 500
Table 21-2
Fouling in heat exchanger
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Fouling in heat exchanger
Supercritical Fluid Process Lab
Supercritical Fluid Process Lab
Fouling Coefficients
Fouling: deposits on heat transfer surface
- porous deposits (mud, soot, vegetable)
- hard scale (boiler or evaporator)
- coke (oil heater in a refinery)
Heat thermal conductivityTransfer =Coefficient thickness of scale
Sandblasting, pneumatic cleaningtools, chemical cleaning
Thermal conductivity itself may be highBut effective thermal conductivity may bealmost as low as that of the fluid.
Steam (air, hot water) blowing
Supercritical Fluid Process Lab
Fouling Coefficients
olmc
o
c
c
lmb
o
b
b
idi
o
ii
oo
scaled
hAA
kr
AA
kr
AhA
AhAU
tAhq
11
,,
+Δ
+Δ
++=
Δ=
Outsidefluid Outside
fluid
Insidefluid
Outsidefluid
kc kb
Insidefluid
fouling
ho
Outsidefluid
hi
hdi
Supercritical Fluid Process Lab
Fouling Coefficients
odolmc
o
c
c
lmb
o
b
b
idi
o
ii
oo
scaled
hhAA
kr
AA
kr
AhA
AhAU
tAhq
111
,,
++Δ
+Δ
++=
Δ=
Outsidefluid Outside
fluid
Insidefluid
Outsidefluid
kc kb
Insidefluid
Insidefouling
ho
Outsidefluid
hi
hdi
outsidefouling
hdo
Supercritical Fluid Process Lab
Fouling coefficients
hd, Btu/(h)(ft2)(oF)
Overhead vapors from crude-oil distillation 1000Dry crude oil (300-100oF):
Velocity under 2 ft/sec 250Velocity 2-4 ft/sec 330Velocity over 4 ft/sec 500
Air 500Steam (non-oil-bearing) 200Water, Great Lakes, over 125oF 500
Table 21-3
Tubular Exchanger Manufacturers Association, New York, 1949
Supercritical Fluid Process Lab
Example 21-2
A reflux condenser contains ¾ in. 16-gauge copper tubes in which cooling water circulates. Hydrocarbon vapors condense on the exterior surfaces of the tubes. Find the overall heat-transfer coefficient Uo. The inside convective coefficient can be taken as 4500 W/m2·K, and the outside coefficient as 1500 W/m2·K.
Approximately fouling coefficients from Table 21-3 are
hd0 = 5700 W/m2·Khdi = 2840 W/m2·K
Overhead vapors from crude-oil distillation 1000
Water, Great Lakes, over 125oF 500
Btu/(h)(ft2)(oF)
Supercritical Fluid Process Lab
Outsidefluid Outside
fluid
Coolingwater
Outsidefluid
k
Insidefluid
insidefouling
ho=1500
Condensingvapor
hi =4500
hdi =2840outsidefouling
hdo =5700
Example 21-2 Find Uo
¾” 16-gauge copper tuberi=0.0157ro=0.0191
unit: W/m2·K
Supercritical Fluid Process Lab
Fouling Coefficients
odolmc
o
c
c
lmb
o
b
b
idi
o
ii
oo
hhAA
kr
AA
kr
AhA
AhAU 11
1
,,
++Δ
+Δ
++=
Outsidefluid Outside
fluid
Insidefluid
Outsidefluid
kc kb
Insidefluid
Insidefouling
ho
Outsidefluid
hi
hdi
outsidefouling
hdo
Supercritical Fluid Process Lab
Example 21-2
00067.01500
11,00018.05700
11
0000047.0)0175.0)(380(
)0191.0)(00165.0(
00043.0)0157.0)(2840(
0191.0
00027.0)0157.0)(4500(
0191.0
0175.0
0157.00191.0ln
0157.00191.0
ln
0191.0,0157.0,/380
/2840678.5500
/5700678.51000
/1500,/4500
0
0
0
0
0
0
0
2
2
20
2
0
0
====
==⋅Δ
==
==
=−
=−
=
==⋅=
⋅=×=
⋅=×=
⋅=⋅=
hh
rkrr
rhrrh
r
m
rrrrr
mrmrKmWk
KmWh
KmWh
KmWhKmWh
d
lmb
idi
ii
i
il
i
d
d
i
m
i
0
0000 11
1
0hhrk
rrrh
rrh
rU
dlmbidii i
++⋅Δ
++=
hi
hdihdo
k
ho
Supercritical Fluid Process Lab
Example 21-2
KmWU
AUAU
KmW
hhrkrr
rhr
rhrU
i
ooii
dlmbidii i
⋅==
=
⋅==
++++=
++⋅Δ
++=
2
2
0
0000
/785)0157.0/(()0191.0)(645(
/64500155.0
1
00067.000018.00000047.000043.000027.01
111
0
hi
hdihdo
k
ho
Resistance of metal wall is negligible
Fouling Resistance is significant~39%
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Shell–and–Tube Heat Exchangers
Supercritical Fluid Process Lab
Shell–and–Tube Heat Exchangers
Supercritical Fluid Process Lab
Heat Exchangers
Supercritical Fluid Process Lab
Crossflow heat exchangers
(a) Finned with both fluid unmixed(b) Unfinned with one fluid mixed and the other unmixed
(a) (b)
Supercritical Fluid Process Lab
Compact heat exchangers
Supercritical Fluid Process Lab
Double-pipe heat exchanger
Supercritical Fluid Process Lab
Double-pipe heat exchanger
HotFluid
InWh lb/hr
HotFluidOut
Wh lb/h
Cold Fluid inWc lb/hr
Cold Fluid outWc lb/hr
Differential section
“1” “2”
tc
tc th
The choice of path for each fluid depends on considerations such as
corrosion, plugging, fluid pressure, and permissible
pressure drop.
Supercritical Fluid Process Lab
Double-pipe heat exchanger
t
Δt1
t Δt
Δt2
Δt= Δt1= Δt2= constant
Supercritical Fluid Process Lab
Double-pipe heat exchanger
t t
Supercritical Fluid Process Lab
Double-pipe heat exchanger
HotFluid InWh lb/hr
HotFluid OutWh lb/h
Cold Fluid inWc lb/hr
Cold Fluid outWc lb/hr
Differential section
“1” “2”
tc
tc th
∫ ∫=Δ
q A
overalldA
tUdq
0 00
0
0
(21-23)
The determination of the required heat transfer area is one of the principal objective in the design of heat exchangers. For a differential segment of the exchanger for which the outside tube area is dA0,
ii
overall
overall
tdAUtUdAtUdq
GenerallytAUq
Δ=Δ←Δ=
Δ=
varingare&,
000
00
Supercritical Fluid Process Lab
Double-pipe heat exchanger
∫ ∫=Δ
q A
overalldA
tUdq
0 00
0
0
The overall coefficient of heat transfer U0
Outside heat transfer area, A0
The difference between the mixing-cup temperatures of the hot and cold fluids, Δt
Under steady conditions, the mixing-cup temperature of the hot and cold fluids in a heat exchanger are assumed to be fixed at any cross section normal to the flow. The overall temperature difference is Δt = th - tc.
Supercritical Fluid Process Lab
Countercurrent vs. Concurrent
HotFluid InWh lb/hr
HotFluid OutWh lb/h
Cold Fluid inWc lb/hr
Cold Fluid outWc lb/hr
“1” “2”
HotFluid InWh lb/hr
HotFluid OutWh lb/h
Cold Fluid inWc lb/hr
Cold Fluid outWc lb/hr
“1” “2”
Countercurrent
Concurrent(Parallel-flow)
Supercritical Fluid Process Lab
Mix
ing-
cup
tem
pera
ture
Hot fluid, th
Cold fluid, tc
1tΔ
2t
“1” “2”Length
Δ
Mix
ing-
cup
tem
pera
ture
ch ttt −=Δ
Hot fluid, th
Cold fluid, tc
1t
“1” “2”q
Δ2tΔ
Double-pipe heat exchangerCountercurrent
ch ttt −=Δ
dqtd )(Δ
If Cp=constant
Supercritical Fluid Process Lab
Heat balance for the differential section
HotFluid
InWh lb/hr
HotFluidOut
Wh lb/h
Cold Fluid inWc lb/hr
Cold Fluid outWc lb/hr
Differential section
“1” “2”
tc
tc th
00 )( dAttUdtCwdtCwdq chhphhcpcc −===
dA0
dq
Supercritical Fluid Process Lab
Double-pipe heat exchangerM
ixin
g-cu
p te
mpe
ratu
re
ch ttt −=Δ
Hot fluid, th
Cold fluid, tc
“1” “2”q
1tΔ2tΔ
dqtd )(Δ
If Cp=constant
qtt
dqtd 12)( Δ−Δ=
Δ
The difference between the mixing cup temperatures, Δt, is also linear w.r.t. q.
Supercritical Fluid Process Lab
Heat Balance in the differential section of the exchanger
qtt
dqtd
tdAUdAttUdtCwdtCwdq chhphhcpcc
12
0000
)(
)(
Δ−Δ=
Δ
Δ=−=== (21-25)
(21-26)
Supercritical Fluid Process Lab
Heat Balance in the differential section of the exchanger
( )⎥⎦⎤
⎢⎣
⎡ΔΔΔ−Δ
=
Δ−Δ=
ΔΔ
Δ−Δ=
ΔΔ
=Δ
∫∫Δ
Δ
12
12
012
12
/ln
)(
)()(
2
1
ttttAUq
dAq
tttUtd
qtt
tdAUtd
dqtd
oo
A
o
t
to
oo
o
If Uo=constant
(21-27)
(21-28)
(21-29)LMTDLogarithmicMeanTemperatureDifference
00 tdAUdq Δ=
Supercritical Fluid Process Lab
Heat Exchange in double pipe heat exchanger
( ) hphhcpccoo tCwtCwtt
ttAUq Δ=Δ=⎥⎦
⎤⎢⎣
⎡ΔΔΔ−Δ
=12
12
/ln
Supercritical Fluid Process Lab
Example 21-3
Crude oilWc=2000 lb/hr90oF
Kerosene450oF
If the temperature of approach (minimum temperature difference between fluids) is 20oF, determine the Ao, wh for (a) concurrent flow and (b) countercurrent flow.
wh
countercurrent flow
“1” “2”
Overall coefficient Uo=80 Btu/(h)(ft2)(oF)Specific heat of crude oil = 0.56 Btu/(ib)(oF)Specific heat of kerosene = 0.60 Btu/(ib)(oF)
200oF
Supercritical Fluid Process Lab
Example 21-3 (a) Concurrent flow
The temperature distribution
450
90
200220
The approach=20oF
2
12
12
1.13
)20/360ln(2036080
000,123)/ln(
/891)220450)(60.0(
000,123
/000,123)90200)(56.0)(2000(
ft
ttttU
qA
hlbtC
qw
hBtutCwq
o
o
hphh
cpcc
=
⎥⎦
⎤⎢⎣
⎡ −=
⎥⎦
⎤⎢⎣
⎡ΔΔΔ−Δ
=
=−
=Δ
=
=−=Δ=Total heat load:
3601 =Δt
202 =Δt
Crude oil
kerosene
Supercritical Fluid Process Lab
Example 21-3 (b) Countercurrent flow
2
12
12
9.16
)20/250ln(2025080
000,123)/ln(
/603)110450)(60.0(
000,123
/000,123)90200)(56.0)(2000(
ft
ttttU
qA
hlbtC
qw
hBtutCwq
o
o
hphh
cpcc
=
⎥⎦
⎤⎢⎣
⎡ −=
⎥⎦
⎤⎢⎣
⎡ΔΔΔ−Δ
=
=−
=Δ
=
=−=Δ=
The temperature distribution
Total heat load:
11090
200
450
The approach=20oF
201 =Δt 2502 =Δtkerosene
Crude oil
Supercritical Fluid Process Lab
If Uo is a function of temperaturetbaU o Δ+=
12
21
1
1
2
2
120
12
ln1
ln1
ln1
)ln(1ln1
)(//1)()(
)()()(
2
1
2
1
2
1
2
1
2
1
2
1
tUtU
a
ttba
tbat
a
tbat
a
tbaa
ta
tdtba
abta
ttbatd
Aq
ttttba
tddAq
tttUtd
o
o
t
t
t
t
t
t
t
t
o
t
t
A
o
t
to
o
ΔΔ
=
⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ+
⎟⎟⎠
⎞⎜⎜⎝
⎛Δ+
Δ=
⎥⎦⎤
⎢⎣⎡
Δ+Δ
=
⎥⎦⎤
⎢⎣⎡ Δ+−Δ=
Δ⎟⎠⎞
⎜⎝⎛
Δ+−
+Δ
=ΔΔ+
Δ
Δ−Δ=
ΔΔ+Δ
→Δ−Δ
=ΔΔ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
∫∫
∫∫∫(21-30)
(21-31)
Supercritical Fluid Process Lab
12
1221
12
12
1212
11
22
)(
tttUtUa
ttUUb
ttbUU
tbaUtbaU
oo
oo
oo
o
o
Δ−ΔΔ−Δ
=
Δ−Δ−
=
Δ−Δ=−
Δ+=Δ+=
If Uo is a function of temperaturetbaU o Δ+=
(21-32)
Supercritical Fluid Process Lab
If Uo is a function of temperaturetbaUo Δ+=
12
2112 ln1tUtU
aA
qtt
o
oo Δ
Δ=
Δ−Δ
12
1221
tttUtUa oo
Δ−ΔΔ−Δ
=
o
o
o
oo A
tUtU
tUtUq
12
21
1221
lnΔΔ
Δ−Δ=
(21-34)
Supercritical Fluid Process Lab
o
o
o
oo A
tUtU
tUtUq
12
21
1221
lnΔΔ
Δ−Δ=
(21-34)
⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔΔ−Δ
=
1
2
12
lntt
ttAUq oo(21-29)
Heat transfer rate in double pipe heat exchanger
tbaU o Δ+=
constU o =
Supercritical Fluid Process Lab
Homework
PROBLEMS21-121-621-1021-1521-17
Due on November 2