1
Heat Exchangers
ME 430
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,ε, or number of transfer units (NTU’s), and the capacity ratio,Cr,
ε
2
Heat Exchangers
Plate Style
3
Solar Water Heating
4
Okotoks Solar Seasonal Storage and District Loop Simplified Schematic
Two StorySingle Family
Homes
Underground ThermalStorage Located Beneath
MRDistrict Heating
Loop (Below Grade) Connects to Homes in Community
Detached Garages withSolar Collector roofsGlycol / Water
Heat Exchanger
District Heating LoopCentral Plant OutlineLocated on MR
5
Okotoks – Energy Delivery
Bore Hole Storage
6
10 20 30 40 50 60
-80
-70
-60
-50
-40
-30
-20
-10
0
5
10
15
20
25
30
35
40
45
50
55
60
Energy Balancethe 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&
7
Simple Configurations
Q = qx A
and
Q = UA (∆T)
U = (1/h1 + Rwall +1/h2)-1
Heat transfer through a wall
8
Simple Configurationsfor Tube & Shell
Q = UA (∆T)Need to determine ∆T.This is not straightforward as for the parallel flow case.
UA –Value & LMTDThe 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 TLMTDTT
∆ − ∆=
⎛ ⎞∆⎜ ⎟∆⎝ ⎠
9
Parallel Flow
Q UA LMTD= ⋅
ln
out in
out
in
T TLMTDTT
∆ − ∆=
⎛ ⎞∆⎜ ⎟∆⎝ ⎠
Counter Flow
Q UA LMTD= ⋅
ln
out in
out
in
T TLMTDTT
∆ − ∆=
⎛ ⎞∆⎜ ⎟∆⎝ ⎠
10
From “Heat Transfer”,By Y. Cengel
11
EffectivenessThe heat exchanger effectiveness, ε, 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
ε =
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 Tmc T T
ε−
=−
&
&
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
&
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
UANTUmc
=&
12
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
( )( )
pr
p
mcC
mc=
&
&
It is important to note that the capacity ratio will be directlyproportional to the ratio of the mass flow rates if the specificheats of the flows are fairly constant.
Effects of Capacity Ratio and NTU on Effectiveness
13
Effectiveness Relations
14
NTU Relations
15
16
Refrigeration
Examples
Other TypesHeat Pipe
RotaryILC Enthalpy Wheel
17
Heat Pipe
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.
