heat exchanger with cooling fins
DESCRIPTION
Heat Exchanger with cooling fins. Hyun Jae Kim EGEE 520, Mathematical Modeling. Contents. 1. Introduction of Heat Exchanger with Fins. 2.1. Governing Equation. 2.2. Formulation. 2.3. Solution. 3. Validation of Model using 1-D calculation. 4. Parametric Study of Radiation and Convection. - PowerPoint PPT PresentationTRANSCRIPT
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Heat Exchanger with cooling finsHyun Jae Kim
EGEE 520, Mathematical Modeling
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Contents
3. Validation of Model using 1-D calculation
2.3. Solution
2.2. Formulation
2.1. Governing Equation
1. Introduction of Heat Exchanger with Fins
4. Parametric Study of Radiation and Convection
5. Conclusion
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1. Introduction
Heat Exchangers ?Heat Exchangers ?
Commonly used in many fields of industry, which are composed of finned surfaces for dissipation of heat by convection and conduction.
Fin ?Fin ?
Used to increase the cooling area of system available for heat transfer between metal walls and condu-cting fluid such as gases and liquids.
In this Study..In this Study..
To calculate the conduction of cooling fins in heat exchanging cataly- tic reactor system with FEM and direct calculation of LDE and compare eachother
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2. 1. Governing Equation
( ) 0k T
0 ,2( ) ( )fn k T q h T T
The heat transfer within the fin is governed by the stationary heat equation.
On the external boundaries of the fin, heat convection term is added.
On the external boundaries of the wall is also governed by above equation.
1m
0.25m
20
mm
AIR
Reactant
8m0.4m
Reactant Product
Catalysts
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2.2. Formulation
4 40 inf( ) ( ) ( )ambn k T q h T T const T T
①②
③
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2.3. Solution
Fin
300
400
500
600
700
800
900
1000
0.00 0.13 0.25 0.38 0.50 0.63 0.75 0.88 1.01 1.13
Fin length
Tem
per
atu
re(K
)
2.6
2.7
2.8
Forced Convection with radiation
200
300
400
500
600
700
800
900
1000
0.00 0.13 0.25 0.38 0.50 0.63 0.75 0.88 1.01 1.13
Fin Length
Tem
per
atu
re(K
)
1.2
2
2.8
3.6
4.4
5.2
6
6.8
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3. Validation
0.0 0.2 0.4 0.6 0.8 1.0 1.2
400
500
600
700
800
900
1000
Tem
pera
ture
(K)
Length
Forced Convection-FEMLAB Natural Convection-FEMLAB Forced Convection-Validation Natural Convection-Validation
,
, inf
infw
T T
T T
x
L
2hLN
kB
cosh[ (1 )]
cosh( )
N
N
2
inf2( )
d T hT T
dx kB
T Tw 0x 0dT
dx x L
Boundary Condition
(2)(1)
22
2
dN
d
1 0 0d
d
1 (2)(1)
Boundary Condition
By defining dimensionless
variables,
4 40 inf( ) ( ) ( )ambn k T q h T T const T T
1) T is a function of x(fin length) alone2) No heat lost from the end or from the edge3) Heat flux at surface is inf( )q h T T , where h=constant, T=T(x)4) Radiation is not concerned in validation.
Assumption
0.25m
1.0mL
2B=0.4m
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4. Parametric Study
Natural convection with radiation
Forced convection
with radiation
Natural convection without radiation
Forced convection without radiation
Convection
300
400
500
600
700
800
900
1000
0.00 0.13 0.25 0.38 0.50 0.63 0.75 0.88 1.01 1.13
Fin Length
Tem
per
atu
re(K
)
0
50
100
150
Convection and Radiation
200
300
400
500
600
700
800
900
1000
0.00 0.13 0.25 0.38 0.50 0.63 0.75 0.88 1.01 1.13
Fin Length
Tem
per
atu
re(K
)
Natural Conv & rad
Natural Conv
Forced Conv & Rad
Forced Conv
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5. Conclusion
1
Heat exchange with fins was examined and we can find convection term is important factor in calculation of surface temperature.
2
Comparison between solution from FEMLAB and direct calculation of ODE indicates that the former might get the more exact estimated value than the latter which needs more assumptions
3
Even though consideration of radiation is important in the natural convection system, it can be easily ignored when convection becomes significant term.
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