double pipe heat exchangers with finned inner tube p m v subbarao professor mechanical engineering...
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Double Pipe HEAT EXCHANGERS with Finned Inner Tube
P M V SubbaraoProfessor
Mechanical Engineering Department
I I T Delhi
Ideas for Creation of Compact HX!!!
NTU Curves: Counter flow
NTU
How to decide the height of fin for a Double Pipe HX ?
nth order Longitudinal Fins
2/1
212
2
2
0
b
nnn
k
hm
bmdx
dnx
dx
dx
b
L
x=a=0b
x=b
bx
qb
L
b
qb
b
x=b x=a=0
xb
Effect of geometrical Order on Fin Effectiveness
Cost – Benefit Analysis of Fins
• The benefit of a fin is defined as effectiveness of a fin.• An ideal fin will have highest value of effectiveness.• An ideal fin is the one whose temperature is equal to temperature of
the surface.• This is possible only if the thermal conductivity of fin material is
infinitely high.• The effectiveness of an actual fin material is always lower than an
ideal fin.• The relative performance of a given fin is defined as efficiency of a
fin.• Provision of fins on a surface requires more material and hence more
capital cost.• A judicial decision is necessary to select correct factors of fin design.• Best fin design should have higher benefits with a lower amount of
material.
Performance of Least Material Strip Fin
Optimum shape for a given qb & b
mbk
hAhkq b
pb tanh
27918.02
3/122/1
And solve for Ap with [ tanh (1.4192) = 0.8894 ]
3
2
5043.0
b
bp
q
khA
627.0
Comparison of Longitudinal Strip Fin
profile area varies as the cube ofqb b/
To double the heat flow, you use two fins or make one fin eight times as large.
There is a virtue in using short stubby fins.
3
2
5043.0
b
bp
q
khA
Longitudinal Fin Of Triangular Profile
The differential equation for temperature excess :
b
L
x=a=0b
x=b
bx
qb
0)(
TThPdx
dxdT
kAd c
b
cs
bLxxLxLxA
tan2)(
Longitudinal Fin Of Triangular Profile
The differential equation for temperature excess is a form of Bessel’s equation:
xd
dx
d
dxm b
2
22 0
; m
h
k b
21 2
/
b
L
x=a=0b
x=b
bx
qb
Triangular Fin : Adiabatic Tip
The particular solution for ( )x is:
( )x
I m bx
I mbb 0
0
2
2
The fin heat dissipation is:
mbI
mbI
m
Lhq bb 2
22
0
1
The fin efficiency is:
I mb
mb I mb1
0
2
2
Optimum Shape (Minimum Material) for Triangular Fin
b
p
p
p
b
p
A h kA
h
k
bA A k
h
4 2
2 618813263
2
210560
2
1 2 2 3
2
1 3
1 3
/
..
.
/ / /
/
Comparison of Longitudinal Fins
Ah k
q
Ah k
q
pb
b
pb
b
05043
0 3471
2
3
2
3
.
.
Rectangular Profile:
Triangular Profile:
For the same material, surrounding conditions and qb b/which is basically the user’s design requirement.
Triangular profile requires only about 68.8% as much metal as rectangular profile.
Comparison of Longitudinal Fin
In both fins, profile area varies as the cube of qb b/
To double the heat flow, you use two fins or make one fin eight times as large.
There is a virtue in using short stubby fins.
Longitudinal Fin Of Concave Parabolic Profile
The differential equation for temperature excess is an Euler equation:
xd
dxx
d
dxm b
mh
k b
22
22 2
1 2
2 0
2
/
L
b
qb
b
x=b x=a=0
x
b
The heat dissipated is:
qk
bbb b
3
2
And the efficiency is:
2
3 or = 0.667
Optimum Shapes (Least Material) of Parabolic Profile
Double Pipe HX with finned inner Tube
Equivalent diameter of annulus heat transfer, De:
perimeter ledheated/coo
area freenet 4eD
244
Area Free2
12
rs WWHWN
DD
NWNHDDs 2Perimeter Cooled 1
NWNHDD
WWHWNH
DD
Ds
rs
e
2
2444
1
21
2
Longitudinally Welded fins
HSk
Ph
HSk
hP
Q
Q
fin
fin
f
ffin
tanh
max,
h, should be resulting heat transfer coefficient on annulus side.
Fins with surface area, Afin, communicate as much as heat as an area of tube surface equal to finAfin .
Therefore, the total annulus side effective area is Atube + finAfin.
The ratio of total surface area to effective surface area is called as overall finned tube efficiency factor.
Accounting of Heat Transfer due to strip Fins
total
fin
total
finfin
basefin
basefinfinfinnedtube A
A
A
A
AA
AA1
Effective annulus side overall heat transfer coefficient:
hh finnedtube
Overall Heat Transfer coefficient of finned Double tube HX:
insidetube
total
tubepipe
total
A
A
uLk
ADD
hU ,
1
1
2
ln11
More Ideas for Compact Double Pipe HXs
• The configuration should be similar to a straight double-pipe heat exchanger.
• But both the tubes are concentrically curved to take advantage of the space saving characteristics and through enhanced heat transfer coefficients.
• One such idea is double pipe Hx with the helical geometry.
• There are some distinct advantages from this type of design over hair pin DPHX.
• Firstly, the whole surface area of the coil will be exposed to moving fluid, eliminating the dead-zones that could be found in the outer tube of hair pin hx.
• Secondly, the flow in the outside tube will also experience secondary flows.
Helical Double-tube HX