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Assessment of thermal performance of semicircular
fins under forced air convection : Application to air preheater
Rajarshi Sengupta Under the supervision of Dr. Rajat Chakraborty
Chemical Engineering DepartmentJadavpur University
ICAER 2013
Motivation Improved performance of air preheaters increase boiler
efficiency.
Boiler efficiency increases by 1% for every 22oC rise in combustion air temperature.
Better design of heat exchangers lead to increased thermal efficiency and reduced costs.
Key to the improved design of existing thermal systems is enhancing the heat transfer between hot and cold streams.
Enhancement can be done by improvisations of the extended surfaces.
Brief Overview
Mathematical modeling
Efficiency comparison
Application to air preheaters
MATHEMATICAL MODELING
Assumptions of the model Two directional heat conduction.
Insulated tip.
Thermal conductivity of fin is constant.
Negligible thermal contact resistance between pipe wall and fin.
Heat is lost only by convection. No loss by radiation.
Curvature of fin base can be neglected.
Heat transfer coefficient is a function of Reynolds number and Prandtl number.
Front and side view
Chakraborty et al. (2011)Side view Front view
Control volume and the Differential equation The control volume is shown below
The partial differential equation the describes heat conduction is
. . . (1) 0)(2
2
2
2
2
af
TTBkh
yT
xT
The heat transfer coefficient is given as
… (2)
The boundary conditions are :
31
(Pr)(Re)n
air
Ckhd
0,0,
0,0,
0,0,
0,0,
,,0
yTxry
xTxry
yTyrx
xTyrx
TTryrx b
Solution Using separation of variables, the temperature
profile obtained is
…(3)
…(4)The efficiency is calculated as
…(5)
0
0
2)12(sinsinhtanhcosh
cosh)12(4
2)12(sinsinhtanhcosh
cosh)12(4
n
nab
a
rxn
rprp
rpy
pn
ryn
rpxp
rpx
pnTTTT
r xr
xrab
r xr
xra
dxdyTTh
dxdyTTh
0
)(
)(
0
)(
)(5.022
5.022
5.022
5.022
)(2
)(2
222
4)12( mnp
Approximated temperature profile
…(6)
…(7)
Where …(8)
h = heat transfer coefficientr = radius of semicircular finkf= thermal conductivity of fin
B = thickness of fin
42
222
2
22232
0347.00044.01
61
2231
mm
yxmr
mxmrxm
TTTT
b
a
Bkhrmf
22 2
Comparing the efficiency of a semicircular fin with a circular finConstraint –
Same volume of materialRelations between radii of the fins -
…(9)
…(10)
R2 = Radius of circular finR1 = Radius of tube
2
180sin
22
122
1
frRR
fRr
Variation of fin radii with no. of semicircular fins
4 6 8 100
5
10
15
20
25
30
35
Radius of semicircular finRadius of circular fin
No. of semicircular fins
Radi
us o
f fin
(m
m)
Nominal diameter of pipe = 40mm
Variation of fin radii with pipe size
No. of semicircular fins
= 6
25 32 40 50 65 80 900
10
20
30
40
50
60
70
80
Radius of semicircular fin
Radius of circular fin
Nominal Diameter (mm)
Radi
us o
f fin
(m
m)
EFFICIENCY COMPARISON AND INFLUENCE OF VARIOUS FACTORS ON EFFICIENCY
No. of semicircular fins
4 5 6 7 8 9 1075
80
85
90
95
100
No. of semi-circular fins
Effi
cien
cy (%
)
SFCF
Pipe size
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.0970
75
80
85
90
95
Nominal diameter (m)
Effi
cien
cy (%
)
SFCF
Air velocity
1.5 2 2.5 370
75
80
85
90
95
100
Air velocity (m/s)
Effi
cien
cy(%
)
SFCF
Base temperature
420 430 440 450 460 470 48080
82
84
86
88
90
92
94
96
98
100
Base Temperature (K)
Effi
cien
cy (%
)
SFCF
Thermal conductivity of the fin
100 105 110 115 120 125 13080
82
84
86
88
90
92
94
96
98
100
Thermal conductivity of fin material (W/mK)
Effi
cien
cy (%
)
SFCF
APPLICATION TO AIR PREHEATERS
The systemInline arrangement of finned tubes
with 8 rows and 4 columns.
Tube side fluid – condensing steam.
Shell side fluid – ambient air.
Ambient air inlet temperature – 25 o
C
Schematic of the preheater
Air Flow
Heat Transfer (Holman J. P.)
Heat transfer inside the preheaterHeat is transferred both from the finned and
unfinned surface.
Over unit length, the amount of heat transferred is
…(11)Assuming no loss of heat, the exit air temperature is
…(12)where
…(13)
)()1(2)2( 12
21 ab TTNBRNfrhmm
AcmTAcmAT
Tpair
apairba 5.0
)5.0( 12
)1(2)2( 12
21 NBRfNrhmmA
Predicted exit air temperaturesExit air temperature depends on a
couple of physical and geometrical parameters.
The effect of these have been studied.
Exit air temperature for the circular and semicircular fins have been compared.
Effect of fin spacing
4 5 6 7 8 9 10
30
40
50
60
70
80
90
Fin spacing (mm)
Exi
t Air
Tem
pera
ture
(oC
)
SFCF
Effect of tube pitch
0.2 0.25 0.3 0.35 0.4 0.45
30
40
50
60
70
80
90
100
Tube pitch (m)
Exi
t Air
Tem
pera
ture
(oC
)
SFCF
Effect of pipe size
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
30
40
50
60
70
80
90
100
110
120
130
Nominal Diameter (m)
Exi
t Air
Tem
pera
ture
(oC
)
SFCF
Effect of air velocity
1.5 2 2.5 3
30
40
50
60
70
80
90
100
Air velocity (m/s)
Exi
t air
tem
pera
ture
(oC
)
SFCF
Concluding remarksSemicircular fins show a greater thermal
efficiency as compared to a circular fin of same volume.
A larger amount of preheat can be achieved owing to the larger surface area.
Great energy savings can be accomplished by incorporating this design.
This has the potential for high energy efficiency and sustainable development.
References Razelos, P. (2003) A critical review of extended surface heat
transfer, Heat Transfer Eng., 24(6), pp. 11–28.
Chakraborty R. and Sirkar A. (2011) Efficiency comparison between circular and semicircular fins circumscribing circular pipes, Journal of Heat Transfer, 133 / 044501-1.
Khaled A.-R.A. (2007) Heat transfer enhancement in hairy fin systems, Applied Thermal Engineering, 27, pp. 250-257.
Kundu B. and Das P.K. (2007) Performance analysis and optimization of elliptic fins circumscribing a circular tube, International Journal of Heat and Mass Transfer, 50, pp. 173-180.
Chen Han-Taw and Hsu Wei-Lun (2008) Estimation of heat transfer characteristics on a vertical annular circular fin of finned tube heat exchangers in forced convection, International Journal of Heat and Mass Transfer, 51, pp. 1920-1932.
Sapkal P.N., Baviskar P.R., Sable M.J. and Makasare P.A. (2011) Optimization of air preheater design for the enhancement of heat transfer coefficient, International Journal of Applied Research in Mechanical Engineering, Volume-1, Issue-2.
Yodrak L., Rittidech S., Poomsa-ad N. and Meena P. (2010) Waste heat recovery by heat pipe air-preheater to energy thrift from the furnace in a hot forging process, American Journal of Applied Sciences, 7(5), pp. 675-681.
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Holman J.P., (1986) Heat Transfer, 6th ed., McGraw-Hill Book Co., Singapore.
Incropera F.P. and Dewitt D.P. (1996) Fundamentals of Heat and Mass Transfer, 4th ed., Wiley, New York.
Zukuskas A.A., Makarevicius V. and Schlanciauskas A. (1968) Heat transfer in banks of tubes in crossflow of fluid, Mintis, Vilnius, Lithuania.