Heat Transfer/Heat Exchanger
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How is the heat transfer?
Mechanism of Convection
Applications .
Mean fluid Velocity and Boundary and their effect on the rate of heat
transfer.
Fundamental equation of heat transfer
Logarithmic-mean temperature difference.
Heat transfer Coefficients.
Heat flux and Nusselt correlation
Simulation program for Heat Exchanger
How is the heat transfer?
• Heat can transfer between the surface of a solid conductor
and the surrounding medium whenever temperature
gradient exists.
Conduction
Convection
Natural convection
Forced Convection
Natural and forced Convection
Natural convection occurs whenever heat flows
between a solid and fluid, or between fluid
layers.
As a result of heat exchange
Change in density of effective fluid layers taken
place, which causes upward flow of heated
fluid.
If this motion is associated with heat transfer mechanism
only, then it is called Natural Convection
Forced Convection
 If this motion is associated by mechanical means such as
pumps, gravity or fans, the movement of the fluid is
enforced.
 And in this case, we then speak of Forced convection.
Heat Exchangers
• A device whose primary purpose is the transfer of energy
between two fluids is named a Heat Exchanger.
Applications of Heat Exchangers
Heat Exchangers
prevent car engine
overheating and
increase efficiency
Heat exchangers are
used in Industry for
heat transfer
Heat
exchangers are
used in AC and
furnaces
• The closed-type exchanger is the most popular one.
• One example of this type is the Double pipe exchanger.
• In this type, the hot and cold fluid streams do not come
into direct contact with each other. They are separated by
a tube wall or flat plate.
Principle of Heat Exchanger
•
First Law of Thermodynamic: “Energy is conserved.”
0
0
0
0
dE


ˆ
ˆ
 .hin   m
 .hout   q
w
s  e
generated
 m
dt
out
 in

Qh  A.m h .C ph .Th
Qc  A.m c .C pc .Tc
•Control Volume
 m .hˆ   m .hˆ
in
out
COLD
HOT
Cross Section Area
Thermal Boundary Layer
THERMAL
Region III: Solid –
Cold Liquid
Convection
BOUNDARY LAYER
Energy moves from hot fluid
to a surface by convection,
through the wall by
conduction, and then by
convection from the surface to
the cold fluid.
NEWTON’S LAW OF
CCOLING
dqx  hc .Tow  Tc .dA
Th
Ti,wall

To,wall
Tc
Region I : Hot LiquidSolid Convection
Q hot
Q cold
NEWTON’S LAW OF
CCOLING
dqx  hh .Th  Tiw .dA
Region II : Conduction
Across Copper Wall
FOURIER’S LAW
dT
dqx  k.
dr
• Velocity distribution and boundary layer
When fluid flow through a circular tube of uniform crosssuction and fully developed,
The velocity distribution depend on the type of the flow.
In laminar flow the volumetric flowrate is a function of the
radius.
r  D/2
V
 u2rdr
r 0
V = volumetric flowrate
u = average mean velocity
 In turbulent flow, there is no such distribution.
• The molecule of the flowing fluid which adjacent to the
surface have zero velocity because of mass-attractive
forces. Other fluid particles in the vicinity of this layer,
when attempting to slid over it, are slow down by viscous
forces.
Boundary
layer
r
• Accordingly the temperature gradient is larger at the wall
and through the viscous sub-layer, and small in the
turbulent core.
Tube wall
qx  hAT
qx  hA(Tw  T)
heating
Warm fluid
Metal
wall

h
Twh
cold fluid
Twc
qx 
cooling
Tc
k

A(Tw  T)
• The reason for this is
1) Heat must transfer through the boundary layer by
conduction.
 conductivity (k)
2) Most of the fluid have a low thermal
3) While in the turbulent core there are a rapid moving
eddies, which they are equalizing the temperature.
U = The Overall Heat Transfer Coefficient [W/m.K]
qx
qx  hhot .Th  Tiw .A
Th  Tiw 
hh .Ai
Region I : Hot Liquid –
Solid Convection
Region II : Conduction

Across Copper Wall
Region III : Solid –
Cold Liquid Convection

Th  Tc 
qx 
qx
R1  R2  R3
1
A.R

qx  hc To,wall  Tc Ao

qx  U.A.Th  Tc 
U
kcopper .2L
r
ln o
ri


ro 
qx .ln 
ri 
To,wall  Ti,wall 
kcopper .2L
qx
To,wall  Tc 
hc .Ao


ro 
ln  


r
1
1
 i 

Th  Tc  qx 


hh .Ai k copper .2L hc .Ao 






 ro 
ro . ln  


r
r
1

 i 

U  o 
 hhot .ri
kcopper .ri
hcold 




1
r
r
i
o
+
Calculating U using Log Mean Temperature
Hot Stream :
 h .C ph .dTh
dqh  m
Cold Stream:
 c .C .dTc
dqc  m
d (T )  dTh  dTc
T  Th  Tc
c
p
dq  dqhot  dqcold
 dq  U .T .dA
 1
1 

d (T )  U .T .dA.

 m .C h m .C c 
c
p 
 h p

T2
T1

T2
T1
 dqh
dqc 

d (T ) 

 m .C h m .C c 
c
p 
 h p
 Th Tc  A2
d (T )
. dA
 U .

T
qc  A1
 qh
 1
d (T )
1
 U .

 m .C h m .C c
T
c
p
 h p
 A2
. dA
 A1

 T 
U . A.
Th  Tc    U .A Thin  Thout  Tcin  Tcout
ln  2   
q
q
 T1 

 
q  U .A
Log Mean Temperature

T2  T1
 T2 
ln 
 T 

1 

Log Mean Temperature evaluation
m h .C ph .T3  T6  m c .C pc .T7  T10 
T2  T1
TLn 
U

 T2 
A.TLn
A.TLn

ln 
 T1 
COUNTER CURRENT FLOW
1 CON CURRENT FLOW
2
1
2
T3
T4
T6
T1
∆ T1
∆ T2
T6
Wall
T7
T2
T8
T9
T10
∆A
A
A
T10
T1
T4
T5
T2
T10
T1
T6
T3
T4
T2
T5
T3
T6
T9
T8
T7
Parallel Flow
T1  T  T
in
h
in
c
 T3  T7
T2  Thout  Tcout  T6  T10
T8
T7
T9
Counter - Current Flow
T1  T  Tcout  T3  T7
in
h
T2  Thout  Tcin  T6  T10
q  hh Ai Tlm
(T  T )  (T6  T2 )
Tlm  3 1
(T  T )
ln 3 1
(T6  T2 )
1
2
T3
T4
T1
T6
T6
Wall
T2
T7
T8
T9
T10
q  hc Ao Tlm
(T1  T7 )  (T2  T10 )
Tlm 
(T1  T7 )
ln
(T2  T10 )
A
DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER
Nu  f (Re, Pr, L / D, b / o )
h.D
k
v.D.
C p .

k
•Further Simplification:
Nu  a.Re b .Pr c
Nu 
Can Be Obtained from 2 set of experiments
One set, run for constant Pr

And second set, run for constant Re
q
k

h
A(Tw  T )
D

•Empirical Correlation
•For laminar flow
Nu = 1.62 (Re*Pr*L/D)
•For turbulent flow
Nu Ln  0.026. Re
0.8
. Pr
1/ 3
 b 
. 
 o 
•Good To Predict within 20%
•Conditions:
L/D > 10
0.6 < Pr < 16,700
Re > 20,000
0.14
Experimental
Apparatus
Switch for concurrent
and countercurrent
flow
Temperature
Indicator
Hot Flow
Rotameters
Cold Flow
rotameter
Heat
Temperature
Controller Controller
• Two copper concentric pipes
•Inner pipe (ID = 7.9 mm, OD = 9.5 mm, L = 1.05 m)
•Outer pipe (ID = 11.1 mm, OD = 12.7 mm)
•Thermocouples placed at 10 locations along exchanger, T1 through T10
Theoretical trend
y = 0.8002x – 3.0841
Examples of Exp. Results
Theoretical trend
y = 0.026x
6
Experimental trend
y = 0.0175x – 4.049
ln (Nu)
5.5
5
4 .5
4
3 .5
Experimental trend
y = 0.7966x – 3.5415
3
2 .5
2
9 .8
10
10 .2
10 .4
10 .6
10 .8
250
11
200
Nus
ln (Re)
150
100
Theoretical trend
y = 0.3317x + 4.2533
50
0
150
ln (Nu)
4.8
2150
4150
6150
8150
10150
12150
Pr^X Re^Y
4.6
4.4
Experimental Nu = 0.0175Re0.7966Pr0.4622
4.2
Theoretical
4
0.6
0.8
1
ln (Pr)
1.2
1.4
Experimental trend
y = 0.4622x – 3.8097
Nu = 0.026Re0.8Pr0.33
Effect of core tube velocity on the local and
over all Heat Transfer coefficients
Heat Transfer Coefficient Wm-2K-
35000
30000
25000
hi (W/m2K)
ho (W/m2K)
U (W/m2K)
20000
15000
10000
5000
0
0
1
2
3
Velocity in the core tube (ms
4
-1
)