Heat Exchangers - my.me.queensu.camy.me.queensu.ca/Courses/MECH4301/Heat Exchanger Notes for...
Transcript of Heat Exchangers - my.me.queensu.camy.me.queensu.ca/Courses/MECH4301/Heat Exchanger Notes for...
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Heat Exchangers
ME 430
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Heat Exchanger Performance
The performance of heat exchangers
operating under forced flow conditions is
defined by the amount of heat transferred
between the two fluid streams and is
characterized by the UA value or the
dimensionless factors: the effectiveness,e, or number of transfer units (NTU’s), and
the capacity ratio,Cr,
e
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Energy Balance
the rate of heat transfer between
the two fluid streams in the heat
exchanger, Q, is,
where is the heat
capacity rate of one of the fluid
streams.
c
ci
m
T
Q0Q 0Q
Q
s
so
m
T
c
co
m
T
s
si
m
T
( ) ( ) ( ) ( )p s so si p c ci coQ mc T T mc T T
pmc
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Simple Configurations
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Q = qx A
and
Q = UA (DT)
U = (1/h1 + Rwall +1/h2)-1
Heat transfer through a wall
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Simple Configurations
for Tube & Shell
Q = UA (DT)
Need to determine DT.
This is not straightforward
as for the parallel flow case.
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UA –Value & LMTD
The unit’s overall conductance or UA value is defined as
the product of the overall heat transfer coefficient and the
heat transfer area. For counter-flow applications, the heat
transfer rate is defined as the product of overall
conductance and the log-mean temperature difference,
LMTD, i.e.,Q UA LMTD
where the log-mean temperature difference is equal to,
ln
out in
out
in
T TLMTD
T
T
D D
D D
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Parallel Flow
Q UA LMTD
ln
out in
out
in
T TLMTD
T
T
D D
D D
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Counter Flow
Q UA LMTD
ln
out in
out
in
T TLMTD
T
T
D D
D D
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From “Heat Transfer”,
By Y. Cengel
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Types (cont.)
• Cross-flow Heat Exchangers
Finned-Both Fluids
Unmixed
Unfinned-One Fluid Mixed
the Other Unmixed
For cross-flow over the tubes, fluid motion, and hence mixing, in the transverse
direction (y) is prevented for the finned tubes, but occurs for the unfinned condition.
Heat exchanger performance is influenced by mixing.
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Types (cont.)
• Shell-and-Tube Heat Exchangers
One Shell Pass and One Tube Pass
Baffles are used to establish a cross-flow and to induce turbulent mixing of the
shell-side fluid, both of which enhance convection.
The number of tube and shell passes may be varied, e.g.:
One Shell Pass,
Two Tube Passes
Two Shell Passes,
Four Tube Passes
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Types (cont.)
• Compact Heat Exchangers
Widely used to achieve large heat rates per unit volume, particularly when
one or both fluids is a gas.
Characterized by large heat transfer surface areas per unit volume, small
flow passages, and laminar flow.
(a) Fin-tube (flat tubes, continuous plate fins)
(b) Fin-tube (circular tubes, continuous plate fins)
(c) Fin-tube (circular tubes, circular fins)
(d) Plate-fin (single pass)
(e) Plate-fin (multipass)
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Overall Coefficient
Overall Heat Transfer Coefficient
• An essential requirement for heat exchanger design or performance calculations.
• Contributing factors include convection and conduction associated with the
two fluids and the intermediate solid, as well as the potential use of fins on both
sides and the effects of time-dependent surface fouling.
• With subscripts c and h used to designate the hot and cold fluids, respectively,
the most general expression for the overall coefficient is:
, ,
1 1 1
1 1
c h
f c f h
w
o o o oc c h h
UA UA UA
R RR
hA A A hA
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Overall Coefficient
o,
Overall surface efficiency of fin array (Section 3.6.5)
1 1
o
f
c or h f
c or h
A
A
total surface area (fins and exposed base) surface area of fins only
t
f
A AA
Assuming an adiabatic tip, the fin efficiency is
,
tanhf c or h
c or h
mL
mL
2 /c or h p w c or hm U k t
, partial overall coe1
fficientp c or h
f c or h
hUhR
2 for a unit surfFouling fact ace area (m W)or K/fR
Table 11.1
conduction resistan Wall (K/Wce )wR
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Compact HX
Compact Heat Exchangers
• Analysis based on method NTUe
• Convection (and friction) coefficients have been determined for selected
HX cores by Kays and London . 5 Proprietary data have been obtained by
manufacturers of many other core configurations.
• Results for a circular tube-continuous fin HX core:
2 / 3
max
Pr
/
h
p
j St
St h Gc
G V
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EffectivenessThe heat exchanger effectiveness, e, is defined as the ratio
of the rate of heat transfer in the exchanger, Q, to the
maximum theoretical rate of heat transfer, , i.e.,maxQ
max
Q
Qe
The maximum theoretical rate of heat transfer
is limited by the fluid stream with the smallest
heat capacity rate, i.e.
min
( ) ( )
( ) ( )
p s so si
p ci si
mc T T
mc T Te
where the is the smaller of or .min( )pmc ( )p smc ( )p cmc
c
ci
m
T
Q0Q 0Q
Q
s
so
m
T
c
co
m
T
s
si
m
T
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NTUThe number of transfer units (NTU) is an indicator of the actual heat-transfer area or physical size of the heat exchanger. The larger the value of NTU, the closer the unit is to its thermodynamic limit. It is
defined as,
min( )p
UANTU
mc
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Capacity RatioThe capacity ratio, Cr, is representative of the operational condition of a given heat exchanger and will vary depending on the geometry and flow configuration (parallel flow, counterflow, cross flow, etc.) of the exchanger. This value is defined as the minimum heat capacity rate divided by the maximum capacity rate, i.e.,
min
max
( )
( )
p
r
p
mcC
mc
It is important to note that the capacity ratio will be directly
proportional to the ratio of the mass flow rates if the specific
heats of the flows are fairly constant.
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Effects of Capacity Ratio and NTU on Effectiveness
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Effectiveness Relations
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NTU Relations
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Special Conditions
Special Operating Conditions
Case (a): Ch>>Cc or h is a condensing vapor .hC
– Negligible or no change in , , .h h o h iT T T
Case (b): Cc>>Ch or c is an evaporating liquid .cC
– Negligible or no change in , , .c c o c iT T T
Case (c): Ch=Cc.
1 2 1mT T TD D D –
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Refrigeration
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Examples
Other Types
Heat Pipe
Rotary
ILC Enthalpy Wheel
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Heat Pipe
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Enthalpy WheelThe heart of the Energy Recovery Ventilator is
the desiccant coated energy recovery wheel,
which slowly rotates between its two sections.
In one section, the stale, conditioned air is
passed through the wheel, and exhausted in
the atmosphere. During this process, the
wheel absorbs sensible and latent energy
from the conditioned air, which is used to
condition (cool / heat) the incoming Fresh Air
in the other section, during the second half of
its rotation cycle.