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

TTBk

h

y

T

x

T

The heat transfer coefficient is given as

… (2)

The boundary conditions are :

3

1

(Pr)(Re)n

air

Ck

hd

0,0,

0,0,

0,0,

0,0,

,,0

y

Txry

x

Txry

y

Tyrx

x

Tyrx

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

r

xn

r

prp

r

py

pn

r

yn

r

pxp

r

px

pnTT

TT

r xr

xr

ab

r xr

xr

a

dxdyTTh

dxdyTTh

0

)(

)(

0

)(

)(5.022

5.022

5.022

5.022

)(2

)(2

222

4

)12(m

np

Approximated temperature profile

…(6)

…(7)

Where …(8)

h = heat transfer coefficient

r = radius of semicircular fin

kf= thermal conductivity of fin

B = thickness of fin

42

222

2

22232

0347.00044.01

6

1

2231

mm

yxm

r

mxm

r

xm

TT

TT

b

a

Bk

hrm

f

22 2

Comparing the efficiency of a semicircular fin with a circular fin

Constraint – Same volume of material

Relations between radii of the fins -

…(9)

…(10)

R2 = Radius of circular fin

R1 = 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

Radiu

s o

f fi

n (

mm

)

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)

Radiu

s o

f fi

n (

mm

)

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

Effic

ienc

y (%

)

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 (%

)

SF

CF

Air velocity

1.5 2 2.5 370

75

80

85

90

95

100

Air velocity (m/s)

Effi

cien

cy(%

)

SF

CF

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 (%

)

SF

CF

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 (%

)

SF

CF

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

Acm

TAcmATT

pair

apairba 5.0

)5.0( 12

)1(2)2( 12

21 NBRfNrhmmA

Predicted exit air temperatures

Exit 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)

Exit A

ir T

em

pera

ture

(oC

)

SF

CF

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)

Exit A

ir T

em

pera

ture

(oC

)

SF

CF

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 A

ir T

empe

ratu

re (

oC)

SFCF

Effect of air velocity

1.5 2 2.5 3

30

40

50

60

70

80

90

100

Air velocity (m/s)

Exit a

ir t

em

pera

ture

(oC

)

SF

CF

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.

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Chakraborty R. and Sirkar A. (2011) Efficiency comparison between circular and semicircular fins circumscribing circular pipes, Journal of Heat Transfer, 133 / 044501-1.

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