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One dimensional modeling of two phase heat transfer in a bi-porous structure
Alireza Rahimpour, Amir Mirza Gheitaghy, Hamid Saffari
*School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran.
* P.O.B. 16844, Tehran, Iran, [email protected]
A RTICLE I NFORMATION A BSTRACT
Original Research Paper Received 13 November 2015 Accepted 06 February 2016 Available Online 01 March 2016
Due to increasing the heat transfer surface area and providing high capillary pressure with high permeability, porous structures play a key role in improving the performance of two phase heat transfer devices such as heat pipes. New porous structures (bi-porous structures) have two distinct size distribution of pores, of which the small pores provide the capillary pressure required for delivering liquid to the surface and large pores help vapor escape from the surface through increasing its permeability. The main goal is to gain a deeper understanding of the evaporator section of heat pipes and compare the performances of sample biporous structures. Towards this goal, first the Kovalev modeling technique is applied to determine the possibility of each phase’s existence in pores of different sizes throughout the computational domain. One dimensional heat transfer in a bi-porous wick is investigated. Inside the domain the conservation equations are solved for each phase and the results such as heat flux versus wall superheat are presented. Thermo-physical properties of the fluid and the matrix like the fluid properties, phase saturation and permeability and the conduction heat transfer coefficient are calculated from the geometry of the matrix and experimental relationships.
Keywords:
Bi-porous
Two-phase heat transfer Heat pipe
Modeling
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( 100
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Fig.1 Schematic of biporous wick
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1 wick
2 Sintering
3 Bed of spheres
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125
Fig. 2 Biporous computational domain
2
-6
× 10 313 1 .
. 400
2257
77 1 .
-5
× 10 8 . - 1
129 0 . .
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= 2
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=
) ( 15
= = ( ) (1 ) (1 )
) ( 16 + ( ) (1 )
= 0
) ( 17 + (1 ( ) ) = 0
) ( 18 ( ) = 0
Fig.3 Schematic of Control Volume
3
z2R
Q
evapQ
evapQ
Cond( z ) Q
Cond( z+ z ) G ( z+ z )
G ( z )
Vapor Core (Upper Boundary)
Heater Wall (Lower Boundary)
Qw
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3 Probability Mass Function
4 Cumulative distribution function
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=
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127
Fig.4 SEM photograph of a biporous wick sintered copper powder consist 275 µm clusters
4 275
Fig.5 Probability mass function of pores and clusters for the bi-porous wick shown in Fig.4
5 4
100 5
0 . 100
. 400
1
. 400
1
( )
- 3 - 2 - 3
R CDF
.
] [ 18 R
. . R R
CDF
Fig.6 Cumulative distribution function of pores and clusters for the bi- porous wick shown in Fig.4
6 4
. 5
50 R
) 100
R
CDF5 0 . 50
50 . 100
R .
R
- 3 - 2 - 4 .
] [ 19 .
]
[ 19
15
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.
0.000 0.005 0.010 0.015 0.020 0.025 0.030
0 100 200 300 400 500 600 700
d m) 0
0.2 0.4 0.6 0.8 1
0 100 200 300 400 500 600 700
CDF
d m
)
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) ) ( 23 ( 24
) ( 23
= (0.04 × ( × 10 ) 0.83) × 10
) ( 24
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) ) 23 ( ( 23 4
4 ) )
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8 8
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] [ 19
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= (2987 × 10 )
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= 1
) ( 30
= 0
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) ( 32
= 1
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= ( ) + +
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= + 1 0 0 1
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= +
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- 4
- 4 - 1
. ]
[ 21 .
.
60 90
65 0 . . 7
69 275
] 8
[ 20 7
.
Fig.7 Probability mass function for one of Semenic’s biporous wicks [18]
] 7 [ 21
0 0.05 0.1 0.15 0.2
0 100 200 300 400 500 600 700
d m)
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129
- 4 - 2 .
:
.( )
5 . 900
9 . 500
900 80
. ( )
15 55 60 140 1
. 60
. 10
.
Fig.8 Comparison between Numerical results and Semenic [20] data for the wick with characteristics shown in Fig.6
8 ] [ 20 7
Fig.9 Thermal performance of the wick
9 .
11 .
R .
) ( 150
) ( 200
) 4 .( 4
) (
.
) .
( 1100
. )
1200
(
)
Fig.10 Liquid and vapor pressures through the computation domain
10
Fig.11 Kovalev critical radius vs. wall heat flux
11
0 10 20 30 40 50 60 70 80 90
0 100 200 300 400 500
Tw(K)
qw
(W/
cm2) Semenic (2007) Present Work
0 10 20 30 40 50 60 70 80 90
0 100 200 300 400 500
(K)
qw(W/cm2) 14500
14700 14900 15100 15300 15500 15700 15900
14500 14700 14900 15100 15300 15500 15700 15900
0 100 200 300 400 500 600 700 800 900 Pv(Pa) Pl(Pa)
z m)
P
lP
v050100150200250300
0 200 400 600 800 1000 1200
R(m)
qw(W/cm2)
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50 . 300 .
12
- 2 1
] [ 6 .
12
. 80
50
275 300
)
( 95
80
.
- 5
.
. ]
[ 16 .
.
Fig.12 Thermal performance of the wick with 50 and 300 micron characteristic pore sizes
12 50
300 - 6
m) d ( m) D ) ER ( m
ET (kgm
-2s
-1) G
) h kJkg
-1( ) k Wm
-1K
-1(
) P ( Pa ) q Wcm
-2( ) R ( m
Re ) T
( K ) v ms
-1(
Y
nm) z
) WKm
-3(
) ( K
(m
2)
) kgm
-1s
-1(
) kgm
-3( ) Nm
-1(
cond eff evap l n S v w
- 7
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