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Page 1: Template and Instructions for Preparation of Full …Bandung, Bandung, Indonesia, ari@termo.pauir.itb.ac.id 2Indonesia National Nuclear Energy Agency, Bandung, Indonesia, efrizon_umar@yahoo.com
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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 1

Numerical Analysis of Natural Convection Air Cooling On

Containment of AP-1000 Reactor Model

Ari D. Pasek1, Efrison Umar2, Aryadi Suwono3, Dwitya Anggraini4

1Faculty of Mechanical and Aerospace Engineering, Institute Technology of

Bandung, Bandung, Indonesia, [email protected]

2Indonesia National Nuclear Energy Agency, Bandung, Indonesia,

[email protected]

3Faculty of Mechanical and Aerospace Engineering, Institute Technology of

Bandung, Bandung, Indonesia, [email protected]

4Faculty of Mechanical and Aerospace Engineering, Institute Technology of

Bandung, Bandung, Indonesia, [email protected]

ABSTRACT: To overcome the energy crisis in Indonesia, Nuclear Power Plant

(NPP) is proposed to be built. To increase the safety, a modern NPP has a feature

called PCS (Passive Containment Cooling System), where air with natural

circulation cool the containment surface when the containment overheated due to

an accident in the reactor. The objective of this research is to make a numerical

analysis of PCS air cooled characteristic at AP1000 model using CFD

(Computational Fluid Dynamics). This research started with developing a

numerical model which has similarity to the real containment. Based on the model

developed, a numerical simulation was done to get temperature, velocity

distribution and convection heat transfer coefficient in the air flow on the

containment surface. In this research, the influence of gap with between baffle

and containment, and the containment height to the heat transfer characteristic

were also investigated. Based on the numerical investigation, the presence of the

air baffle inside the containment increased the heat transfer and a better cooling

system was achieved. A critical heat flux was found in the simulation result. At

this critical heat flux, the heat transfer coefficient start to decrease as the heat flux

increases, indicating the failure of cooling with air natural convection. The critical

heat flux occurs at the mean temperature of wall containment of 395,672 K or

heat fluxes of 1118,256 W/m2. The heat transfer coefficient decreases as the air

baffle gap is too narrow or too wide. The heat transfer coefficient reached a

maximum value at 2 cm air baffle’s width or equivalent to 0.8 m at real

containment. Based on the analysis results, some correlation equations are also

proposed in this paper.

Keywords: PCS, natural convection, heat transfer coefficient, critical heat flux

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

NOMENCLATURE

g = gravitational acceleration, m/s2.

Gr* = Grashof Number

h = heat transfer coefficient, W/m2K

k = thermal conductivity, W/mK.

L = containment height, m.

Nu = Nusselt Number

qw” = wall heat flux, W/m2.

Ra* = Rayleigh Number

x = Distance, m

Greek

= volumetric expansion coefficient, 1/K.

= kinematic viscosity, m2/s.

1. INTRODUCTION

A modern nuclear power plants are equipped with a passive safety systems that do not rely

on equipment in addition to the active safety systems. One of the passive safety systems

available on nuclear power plant reactor such as the AP-1000 reactor is the Passive

Containment Cooling System (PCS), where overheated reactor containment is cooled by

natural air convection. As shown in Figure 1, heat arising as a result of the accident inside the

reactor will be transferred to the reactor containment wall so that its temperature increases. The

wall temperature difference with the surrounding air will generate free convection of air

circulation on the surface. The existence of the baffle on the outer side of the containment will

improve the air circulation. If the rate of heat on the containment walls are still rising, and

cooling air with natural convection heat transfer is no longer effective, the wall temperature

will increase further. In these conditions cooling the containment wall will be assisted by water

sprayed from the top of the containment.

Figure 1: Passive Containment Cooling System on AP-1000 reactor [1]

Given the importance of this passive cooling process for nuclear power plant safety, the

study of natural convection cooling process in the containment wall needs to be studied. In this

paper, the numerical analysis of natural convection heat transfer on the containment wall

surface is discussed. The aim of the analysis is to obtain the heat transfer characteristics such as

velocity distribution, temperature distribution and heat transfer coefficient along the

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 3

containment wall. The influence of baffle width, and containment height to the heat transfer

characteristic is also discussed. In addition, the occurrence of critical heat flux, i.e. the

condition where the natural convection no longer effective for surface cooling, is also

discussed. Correlation equations developed based on the analysis results are proposed in this

paper.

Previous researches on reactor containment cooling by free convection have been

conducted by several researchers [2-6]. However the researches were done on the model of a

vertical cylinder, a cylindrical annulus without the dome and the flow conditions (Rayleigh

Number) are different from the conditions of the real reactor containment.

2. ANALYSIS METHODOLOGY

The analysis begins with determining the dimensions of the scaled down reactor model.

The dimension of the model was determined based on the consideration of the ease fabrication

the model for experimental purposes, so that later the results of numerical simulations can be

compared with experimental results. Assuming that the available heating power during the

experiment is no larger than 30 000 W, and by equating the number Grashof Number (Gr*) of

the model and the actual reactor containment, the model dimension is obtained as shown in

Table 1. Grashof number is defined as:

k

LqgGr

w

4

* (1)

Table 1: Comparison of model and actual reactor dimensions

No Component Real (m)

Model

1:40 (cm)

Adjusted (cm)

1 Width of baffle outer gap 1,6 4,0 3,0

2 Width of baffle inner gap (baffle-

containment gap) 0,28 0,7 1,0

3 Diameter of chimney 11,8 29,5 9,6

4 Diameter of containment 39,62 99,05 99,0

5 Thickness of baffle 0,04 0,1 0,20

6 Thickness of outer containment cylinder 1,0 2,5 0,30

7 Height of chimney 6,39 15,97 14,8

8 Height of containment cylinder 31,45 78,62 78,6

9 Height of ellipsoidal dome 11,47 28,67 28,7

Once the dimensions of the model were determined, then a numerical model was made

using GAMBIT (Geometry and Mesh Intelligent Building Toolkit) software. The numerical

model used is a two-dimensional axis-symmetric geometry. The geometry was done firstly by

drawing the endpoints of the plane. The dots were then connected into lines to form plane.

GAMBIT requires the procedure done this way in sequence, because the lines with coincide

edges that form a closed area will not be considered as a plane by GAMBIT before the lines

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 4

have not been given the command to connect. As a comparison, it was made also the

containment model with no baffle. Figures 2 and 3 shows the model without and with the

inside baffle created with GAMBIT. The dimensions are in millimeters.

The next step is generating mesh started firstly from line entity, then on the higher entities.

This was done in sequence so that a neat mesh formed at higher entities. Mesh element selected

in this research is map type rectangular or quad element. The use of this mesh will make the

calculation easier, thus speeding up the process of iteration in FLUENT later on. The result of

the mesh generation can be seen in Figures 4 and 5.

Determination of boundaries zone and their boundaries conditions are needed for the next

process which is the simulation process using FLUENT program. Boundary zones are shown

in Figure 4 and 5 as the lines with numbered, while their boundaries conditions are shown in

Table 2. The boundary zone for the containment walls were selected as constant heat flux or

constant temperature for two different simulations.

Figure 2: Containment without baffle model

Figure 3: Containment with baffle model

Figure 4: Mesh and boundaries zone for containment without baffle model

1

2

3 4

5

6 7 8

9

10

11

12

13

14

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 5

Figure 5: Mesh and boundaries zone for containment with baffle model

Table 2: Boundary Zones and their boundary conditions

No Boundary

Zone Boundary Conditions

1 wall applied constant heat flux or contant temperature

2 wall applied constant heat flux or contant temperature

3 wall applied constant heat flux or contant temperature

4 wall applied constant heat flux or contant temperature

5 wall no heat generation

6 wall no heat generation

7 wall no heat generation

8 pressure inlet imaginer wall, atmospheric pressure

9 wall no heat generation

10 wall no heat generation

11 wall no heat generation

12 pressure

outlet imaginer wall, atmospheric pressure

13 axisymetric axissymmetric – rotating axis

14 wall no heat generation

The next step is to define the continuum zone. For the reactor models, all the air area which

has been given mesh is defined as the continuum zone. The GAMBIT results were then

imported into FLUENT for simulation to obtain the velocity and temperature distribution.

Once imported into FLUENT, the mesh must be checked and repaired if necessary, so there is

no error message or the value of a negative volume. Then, the solver type used in the

simulation was selected. It was selected as single precision, segregate solver, axis-symmetric,

and steady. While the other parameters used were the default values. The basic equations used

are the equation of mass conservation, momentum conservation, energy conservation and the

k- equation for turbulence model. In the simulation all wall material properties were assumed

1

2

3 4

5

6 7 8

9

10

11

12

13

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 6

N

i

iA

Nh

1

1

)(ln

ln

12132

21

pqr

p

constant except the air properties which are considered to change with temperature. The

pressure parameter was selected as weighted body force. This is because the heat transfer that

occurs in the model is free convection. Containment wall and the baffle materials were

assumed as stainless steel 304.

Verification is needed to ensure that the FLUENT calculation will give good results. In this

study the verification is done by counting discrete deviations and iteration deviation. Iteration

deviation verification was done by looking at the resulting residual value, which is the

difference between the results obtained from iteration with the results from the previous

iteration. Discrete verification was conducted by using ASME V & V 20 year 2008 [7] and

INL/EXT-06-11789 [8] procedures. Discrete error is caused by discrete mesh and discrete

continuity equation. The steps being undertaken to determine the discrete error is:

1. Calculate the parameters of the grid (lattice) h as a parameter of cell size mesh. For 2-

dimensional model:

(2)

with ΔAi is cell i area, and N is the total number of cells used in the

simulation.

2. Select three types of mesh grid with a different number of meshes. Then calculate the ratio

of cell size as r = hcoarse/ hfine, the value of r should be larger than 1.3 to obtain results that

are significantly different. In this work, it was made three types of grids where h1 < h2 < h3,

and R21 = h2/h1, r32 = h3/h2, with the index 1 indicates the most refined grid.

3. Calculate of the multipliers order between grid cells:

(3)

with

sr

srpq

p

p

32

21ln (4)

2132

1 signs (5)

where ε32 = ϕ3 – ϕ2 and ε21 = ϕ2 – ϕ1. The value of q(p) = 0 for constan r.

4. Calculate the extrapolation value ϕ

1/212121

21

pp

extrr

(6)

In similar way, ϕ32 can be calculated.

5. Calculate relative deviation error and GCI (Grid Convergence Index)

2

3232

ae

(7)

1

2121

ae

(8)

extrapolation error can be calculate from

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 7

12

1

12

21

ext

ext

exte

(9)

GCI can be calculated from:

25,1,

121

21

21

sp

as

fineF

r

eFCGI (10)

6. Calculate discrete error as:

21212132,,, GCIeeemean

extaadis (11)

3. RESULTS AND DISCUSSION

3.1 Temperature and velocity distribution

The simulation results on the containment wall are shown in Figure 6 to 9. Figure 6 and 7

show the temperature and air velocity distributions on the surface of the containment wall

without baffle at heating power 3000 W. The temperatures are presented with the heat index

level in color scale on the left side of the picture. From this picture it can be seen the wall area

that cools well and which ones are bad. On models without baffle, the area that cools well is in

the top part of the containment, while the temperature at the bottom is still very high. The

velocity distribution shows that air enter into the containment wall surface through the chimney

at the top of the lid and out of the cavity that should be a place for the air inlet. In the area near

the containment wall surface the air flow upward while in areas near the outside wall the air

flow downward. This phenomenon occurs because to the gap is too wide and air circulation is

not running as intended.

Figure 6: Temperature distribution on the containment model without baffle

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 8

Figure 7: Velocity distribution on the containment model without baffle

Meanwhile, on the model with baffle (Figure 8 and 9) the air cools more effectively

because the baffle directs the air flow. Air enters from the cavity and flows downward through

the outer gap, and moving upward and cooling the containment in the inner gap and finally

goes out through the chimney. Areas at the lower part of the containment get a good cooling so

the temperature becomes lower than the top.

Figure 10 shows the temperature distribution along the containment wall for all tested heat

load. At this figure the points of 0.292 to 0.579 indicates the points in the ellipsoidal section

while the point of 0,579 m to 1.365 m indicates the points in the cylindrical section. Point

0.292 is at top and point 1.365 m is at the bottom of the containment. From the picture, it can

be seen that up to 4000W heat load, the containment wall get a good cooling from the natural

circulated air. This is shown by a gradual increase in temperature from the bottom to top of the

containment wall. But if the heat load increase above 4000W, the temperature of the cylindrical

sector will be higher than temperature of the ellipsoidal sector. This shows that if the heat load

is larger than 4000W the free convection is no longer effective in cooling.

Figure 8: Temperature distributions on the containment model with baffle

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ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia

9-11 December 2010

006- 9

Figure 9: Velocity distributions on the containment model with baffle

Figure 10: Containment wall temperatures at various heat load

3.2 Verification of Iteration and grid/mesh errors

The iteration errors can be ignored because the residual values resulting in the FLUENT

calculation are in the order of 10-3 (0.1%). Residual value is the difference between the results

obtained from iteration with the results from the previous iteration. Residual values obtained

are as follows: Continuity = 1x10

-3

Velocity x axis direction = 1x10-3

Velocity y axis direction = 1x10-3

Energy = 1x10-6

k = 1x10-3

epsilon = 1x10-3

Then, the discrete errors were calculated in accordance with the procedure describe before.

The results of the calculation for the models without and with the baffle in are shown in Table

1.

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Table 1: Minimum and maximum discrete errors for model without and with baffle.

error () minimum error () maximum

model without baffle

normal grid 0,0194 0,0940

very fine grid 0,0189 0,0450

model with baffle

normal grid 0,0010 0,0543

very fine grid 0,0036 0,1454

Discrete errors for both models are quite small when using the normal grid, but to determine

the best grid resolution, it is also need to be taken into account the other factor which is mass

flux balance; good calculation should result small differences in the inlet and outlet mass flux.

The mass flux balance for models with baffle is shown Table 2.

Table 2: Mass flux balance for model with baffle at heat load 3000 W.

grid inlet mass flux (kg/s) outlet mass flux (kg/s) difference(kg/s)

coarse 0,022346029 -0,02234504 9,88E-07

medium 0,021539388 -0,02153998 -5,86E-07

fine (normal) 0,021611705 -0,02161194 -2,32E-07

very fine 0,021745352 -0,0217457 -3,45E-07

Very fine grid gives smaller errors (deviations), but finer grid causes a longer computation

process. Therefore, the normal grid is good enough to be used in the simulation process. In the

model with baffle, error in very fine grid became larger, due to larger mass flux difference.

3.3 Heat Transfer Coefficient

The local convection heat transfer coefficient is defined as:

TT

qh

w

w

x (12)

and, the average heat transfer coefficient is defined as the integral of the local heat transfer

coefficient:

L

xdxh

Lh

0

1 (13)

The results of average heat transfer coefficient calculation for model with baffle at various heat

fluxes for ellipsoidal and cylindrical sectors can be seen in Figures 11 and 12 respectively.

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Figure 11: Variation of the average heat transfer coefficient with heat fluxes for ellipsoidal sector of model with

baffle

Figure 12: Variation of the average heat transfer coefficient with heat fluxes for cylindrical sector of model with

baffle

Based on these figures, it can be seen that the heat transfer coefficient tends to increase

with heat flux applied on the containment wall. However, the wall heat transfer coefficient

starts to decrease at 1118.2 W/m2 heat flux. On this critical heat flux the average temperature

of the containment wall is 395.6 K. The occurrence of the critical heat fluxes have also been

reported by Guo [9] and Umar [10].

3.4 Containment wall with constant temperature

The comparison of heat transfer coefficient calculation results with constant wall

temperature and at constant heat flux condition are shown in Figure 13 and 14 for ellipsoidal

and cylindrical sector respectively.

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Figure 13: Comparison of average heat transfer coefficients on ellipsoidal sector of model with baffle

Figure 14: Comparison of average heat transfer coefficients on cylindrical sector of model with baffle

Based on the above figures, it can be seen that the average heat transfer coefficients of the

wall with constant heat flux are higher than when the walls were subjected to conditions of

constant temperature. Figure 14 shows that critical heat flux occur earlier on the condition of

constant heat flux in compare to the constant temperature condition. The real heating condition

in the containment wall is not exactly a constant heat flux or constant temperature, but it is on

the condition combination of these two ideal cases. Thus, the average heat transfer coefficient

obtained from the experimental results will be in the values between the two ideal conditions

mentioned above.

3.5 Correlation equations

Based on the results obtained from the numerical simulations, correlation equations are

proposed to predict heat transfer coefficient. Correlation equations obtained in the form of

Nusselt number (Nu) as the function of Rayleigh number (Ra). The characteristic length used is

the height of the containment (L). Seeing the different phenomena occurs in the ellipsoidal and

cylindrical sectors, the correlation equations are then proposed for each sector. The proposed

correlation equations are:

621,0*

00017.0LL

RauN (14)

for ellipsoidal sector

065,0*

043.0LL

RauN (15)

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for cylindrical sector, where

f

Lk

hLuN (16)

Pr**

GrRaL (17)

Comparison of correlation equations proposed with other correlation equations can be seen

in Figure 15 and 16, for ellipsoidal and cylindrical sectors respectively. From the figure it can

be seen that the proposed correlation equation has an agreement with other correlation

equations. Deviation occurred is caused by differences in model geometry and range of

Rayleigh number.

Figure 15 Comparison of proposed correlation equation with other for ellipsoidal sector; Lienhard[11], Yuge[12], Merk&Perlin[13], Amato&Tien[14], and Laksmono[15].

Figure 16 Comparison of proposed correlation equation with other for cylindrical sector; Umar[10], Mc. Adam[16],

Landis[17], MacGregor[18], Churchill[19]dan Laksmono[15].

3.6 Effect of Gap Width and Height Fume

Figure 17 shows the temperature distribution along the containment wall at different baffle

gap width. Heat load applied for all conditions is 3000 W. The figure shows that if the gap is

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too wide or too narrow then it will lead to malfunction of the baffle. Temperature distribution

in a narrow gap of 0.5 cm or larger than 3 cm, has similar trend with temperature distribution

on the containment without baffle. The narrow gap cause less amount of air that can flow to

cool the containment wall, while the wide gap causes undirected flow similar to that of

containment without baffle. The heat transfer coefficient variation with the gap width can be

seen in Figure 18. From the picture it can be seen that the optimal gap width is around 2 cm or

0.8 m on the real reactor. From this picture it also can be seen that the gap variation does not

significantly affect the heat transfer coefficient on ellipsoidal sector, unless the width of the

gap is so large that the air flow is similar to the containment without the baffle.

Figure 19 shows the heat transfer coefficient changes with the variation of the containment

height. In the simulation, the containment height variation simulation used the same constant

heat flux that is equal to 838.692 W/m2. From the picture it also can be seen that the higher the

containment the worse heat transfer occurs as indicated by the decreasing in heat transfer

coefficient.

Figure 17 Temperature distributions along the containment wall at various baffle gap width.

Figure 18 Variation of average heat transfer coefficient with baffle gap width.

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Figure 19 Variation of average heat transfer coefficient with containment height.

4. CONCLUSION

The simulation results discussed above can be concluded as:

1. The inner baffle provides a better air cooling of the containment wall.

2. The effectiveness of natural air circulation is limited up to a certain value of heat flux. This

upper limit of heat flux is called a Critical Heat Flux. The simulation found that for

containment with baffle the Critical Heat Flux is 1118,2 W/m2.

3. The average heat transfer coefficient on the containment wall can be predicted using the

proposed correlation equations stated in Equation (14) and (15).

4. The narrow and too wide baffle gap will decrease the average heat transfer coefficients.

The narrow gap will impede the circulation, and too wide gap will make a free flow similar

to the containment without baffle. The optimum gap width is 2 cm for the model or 0.8 m

for the real containment.

5. The short containment have a better air circulation compared to the tall one. This is

indicated by the decreasing average heat transfer coefficient with the decreasing height.

ACKNOWLEDMENT

The authors would like to gratitude the Ministry of Research and Technology, for the

research grant provided for this work, under Hibah Riset Insentif Program year 2009 to 2011.

REFFERENCE

1. Cummins, WE. Corletti, M.M, Schulz, T.L., 2003, Westinghouse AP1000 Advanced

Passive Plant, Proceedings of ICAPP, Cordoba, Spain.

2. Warner, Y, Arpaci, V.S, 1968, An Experimental Investigations of Turbulent Natural

Convection in Air at Low Pressure along a Vertical Heated Flat Plate, International Journal

of Heat Mass Transfer, Vol. 11, p.397.

3. Vliet, G.C, Lin, C.K, 1969, Natural Convection Local Heat Transfer on Constant Heat Flux,

Journal of Heat Transfer, 91, 511-515.

4. Vliet, G.C, Lin, C.K, 1969, An Experimental Study of Turbulent Natural Convection

Boundary Layers, Journal of Heat Transfer, 91, 517-521.

5. Al-Arabi, M., 1980, Laminar Natural Convection Heat Transfer from the Outer Surface of

a Vertical Circular Cylinder , Journal of Heat and Mass Transfer, 23.

6. Davis, V., 1969, Natural Convection Between Concentric Vertical Cylinder, High Speed

Computing in Fluid Dynamics, pp 198-207.

7. Celik B.I., Ghia, U., Roache P.J., Frietas C.J., Coleman H., Raad P.E, 2008, Procedure for

Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,

Journal of Fluid Engineering, ASME, Vol 130.

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8. Johnson, R.W., Schultz, R.R., Roache, P.J., Celik, I.B., Pointer, W.D., Hassan, Y.A.,

Process and Procedures for Application of CFD to Nuclear Reactor Safety Analysis,

INL/EXT-06-11789, Idaho National Laboratory.

9. Guo, Z.Y., 1993, Thermal Drag and Critical Heat Flux to Natural Convection of Air in

Vertical Parallel Plates, Journal of Heat Transfer, Vol. 115:124-129.

10. Umar,E., 1993, Studi Karakteristik Sistem Pendinginan pada Model Sungkup APWR, Tesis

Program Magister Ilmu dan Rekayasa Nuklir, ITB.

11. Lienhard, J.H., 1973, Laminar Free Convective Heat Transfer From The Outer Surface of

Vertical Slender Circular Cylinder, Fifth International Heat Transfer Conf., Tokyo, NC

1.4:15-19.

12. Yuge, T., 1960, Experiments on Heat Transfer from Spheres Including Combined Natural

and Forced Convection, J. Heat Transfer, 82: 214–220.

13. Merk, H. J., Prins, J.A., 1953-1954, Thermal Convection in Laminar Boundary Layers I, II,

and III, Appl. Sci. Res., A4:11–24, 195–206, 207–221.

14. Amato,W. S., Tien, C., 1972, Free Convection Heat Transfer from Isothermal Spheres in

Water, Int. J. Heat Mass Transfer, 15:327–339.

15. Laksmono, W., 2009, Kaji Numerik Karakteristik Sistem Pendinginan Pasif dengan Udara

Secara Konveksi Alamiah pada Penyungkup Model AP1000, Tesis Program Magister Ilmu

dan Rekayasa Nuklir, ITB.

16. Mc.Adams, W. H., 1954, Heat Transmission, 3rd ed., McGraw-Hill, New York.

17. Landis, A., 1966, Transient Natural Convection Narrow Vertical Cell, Proc. International

Heat Transfer Conf., Chicago.

18. Macgregor, R.K., Emery, A.P., 1969, Free Convection Through Vertical Plate

Layers:Moderate and High Prandtl Number, Journal of Heat Transfer, Vol 91:391.

19. Churchill, S.W., 1983, Free Convection Around Immersed Bodies, E.U. Schlunder Heat

Exchanger Design Handbook, Chapter 2.5.7, Hemisphere Publishing, New York.

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