Uncertainty Analysis

An uncertainty analysis is carried out here to estimate the uncertainty levels in the experiment. Kline and McClintock [34] proposed a formula for evaluating the uncertainty in the result F as a function of independent variables, X₁, X_2, X₃∙∙∙∙∙∙∙∙∙∙∙∙Xn,

F=F (X1 ,X2, X3∙∙∙∙∙∙∙∙∙∙∙∙Xn) (3.6) The absolute uncertainty of F is expressed as

2

and the relative uncertainty of F is

2

level associated with the variableX . The values of the uncertainty intervals_i X_i are

24

obtained by a root-mean-square combination of the precision uncertainty of the instruments and the unsteadiness uncertainty, as recommended by Moffat [35]. The choice of the variableX to be included in the calculation of the total uncertainty _i level of the result F depends on the purpose of the analysis.

The uncertainties of the parameters in the present study are calculated as follows:

(1) Uncertainty of temperature difference, Tw=Tw-Tsat

 

(2) Uncertainty of total power input, Q_t

V

25 (4) Uncertainty of space-average heat transfer coefficient, h

sat

26

Table 3.1 Summary of the results from the uncertainty analysis.

Parameter Uncertainty

Geometry Length & thickness (%)

Area (%) Particle diameter (%)

Particle density(%)

0.167%

0.334%

10%

13.4%

Parameter measurement Temperature, T (C)

Temperature difference, ∆𝑇_𝑠𝑎𝑡 (C) System pressure, P (kPa)

0.2

0.36

0.5 Boiling heat transfer on the copper flat plate Total power input, Q_t (%)

Imposed net heat flux, qn (%) Heat transfer coefficient, h(%)

5.9%

8.3%

8.5%

27

Fig. 3.1 Schematic diagram of six main directions of the heat loss.

2

3

4 5

6

1

Copper block

28

Fig. 3.2 Schematic diagram of T'5 and T'6

Film heater

Copper block

T′₅ T′₆

T₆

29

CHAPTER 4

POSSIBLE POOL BOILING HEAT TRANSFER ENHANCEMENT OF FC-72 OVER HEATED COPPER SURFACE

The experimental results to illustrate possible enhancement of saturated pool boiling heat transfer of FC-72 by placing movable particles on the heating surface obtained in the present study are examined in this chapter. The present experiments are carried out for the copper and stainless steel particles with the diameter of the particles d_𝑝 fixed at 1.0 and 1.5 mm, and the total number of particles 𝑁_𝑝 varied from 100 to 1800 for the particles with the diameter 1.0 mm or from 100 to 800 for the particles with the diameter 1.5 mm. The FC-72 liquid in the test chamber is maintained at saturated liquid state corresponding to the atmospheric pressure. Note that the maximum number of particles forming a single closely packed particle layer over the boiling surface 𝑁_𝑝𝑓 is 900 and 400 respectively for the particles with the diameter of 1.0 mm and 1.5 mm when each particle contact directly with neighboring particles. In the experiment tests are also conducted for the particle number well exceeds 𝑁_𝑝𝑓 and many particles are on top of the other particles. The measured data are presented in terms of the boiling curves and boiling heat transfer coefficients for various diameters and numbers of the copper and stainless steel particles and for a bare heating surface. Effects of the experimental parameters on the possible boiling heat transfer enhancement will be examined in detail. Selected data are presented in the following to illustrate the possible pool boiling heat transfer enhancement by the boiling flow driven metallic particles.

30

4.1 Single-phase Natural Convection Heat Transfer

Before conducting the pool boiling experiment, we first measure steady natural convection heat transfer of FC-72 liquid over the heated copper surface without the presence of any particles which prevails at low imposed heat flux, intending to verify the present experimental setup. The measured data for the natural convection heat transfer coefficient are compared with the empirical correlation of Radziemska and Lewandowski [39] in Fig. 4.1. Their correlation is

NuL=(2.1e^-48W+1.2)RaL0.2

(4.1) where w is the width of the heating plate (m). The correlation given in Eq.(4.1) is based on the data for a small horizontal plate heated from below for 10⁵<RaL<10⁸. Note that the characteristic length L used in defining the dimensionless groups in the above equation is chosen to be the ratio of the heated surface area and its perimeter, and the Nusselt and Rayleigh numbers are respectively defined as

(4.2) and

(4.3) The results in Fig. 4.1 indicate that our natural convection data are in good agreement with that calculated from Eq. (4.1). Thus the experimental system established here is considered to be suitable for the present study.

4.2 Saturated Pool Boiling on Bare Copper Surface

To further verify the suitability of the present experimental system, the measured boiling curve for saturated pool boiling of liquid FC-72 on the bare heated copper plate is obtained next. These data are compared with that from Rainey and You [22] in Fig. 4.2 for pool boiling of FC-72 on a square copper plate of 5 × 5 cm² in

k

Nu_L  hL



 ³

L

)L Ra g (T^sat



31

surface area. Note that the present data are in good agreement with theirs.

4.3 Effect of Surface Aging on Boiling over Bare Copper Plate

It is well known that the change of the boiling surface properties with time, the so called “aging effect”, can be significant in affecting the boiling heat transfer from a surface after the surface has been used over certain period of time. Obviously, the measured boiling heat transfer data for the cases with and without the presence of the particles on the surface can be meaningfully compared only when the surface aging effect is small. Thus tests are carried out here to investigate the aging effect of FC-72 liquid boiling on the present heated surface. The results show that the boiling curves and heat transfer coefficients measured over a time interval of 6 hours do not differ to a noticeable degree, as seen from Fig. 4.3. But a significant aging effect is found for an interval of 24 hours. Thus in the present experiment the boiling heat transfer data for the corresponding cases with and without the presence of particles on the surface are obtained within 6 hours.

4.4 Effects of Moving Copper Particles on Boiling Heat Transfer

Possible boiling heat transfer enhancement by particles moving on the heated surface is then examined. Results are presented first for the FC-72 nucleate boiling heat transfer affected by the moving copper particles freely placed on the heated surface by showing the heat transfer data for the bare surface and for the surface with copper particles on it for various d_𝑝 and 𝑁_𝑝 in Figs. 4.4-4.28. The results in Figs.

4.4-4.6 for d_𝑝=1.0 mm and 𝑁_𝑝=100 to 300 indicate that at a small particle number the boiling heat transfer can be slightly enhanced by the copper particles only at low wall superheat near the onset of nucleate boiling. The enhancement gets smaller at

32

increasing wall superheat. Besides, the moving copper particles does not affect the boiling heat transfer to a significant degree in the single-phase flow at very low wall superheat and in the fully developed nucleate boiling region at high wall superheat.

Moreover, a slight reduction in the boiling heat transfer by the copper particles is noted at an even higher wall superheat.

As the total number of the copper particles is increased to 400, 500 and 600, noticeable augmentation in the boiling heat transfer by the copper particles appears at low wall superheat (Figs. 4.7-4.9). Correspondingly, the degradation in the boiling heat transfer at high wall superheat is also noticeable. Note that the degradation is larger at a higher wall superheat. For a further increase in the number of the copper particles to 700-900, the particles on the copper plate are rather crowded. However, enhancement in the boiling heat transfer by the copper particles is even more significant at low ∆𝑇_𝑠𝑎𝑡 (Figs. 4.10-4.12), implying strong interactions between the particles and boiling flow at this large 𝑁_𝑝. Apparently, substantial retardation in the boiling heat transfer by the copper particles exists at high ∆𝑇_𝑤. It is of interest to find from the data given in Figs. 4.13-4.18 that even when the total number of the copper particles well exceeds 𝑁_𝑝𝑓 for 𝑁_𝑝 ≥ 1,000 the boiling heat transfer enhancement by the copper particles is still significant at low ∆𝑇_𝑤. This suggests that the presence of a large number of metallic particles on top of the other particles dose not lower the boiling heat transfer performance at low wall superheat.

To be more quantitative on the boiling heat transfer affected by the small copper particles presented above for d_𝑝=1.0 mm, the ratios of the boiling heat transfer coefficients for the cases with the presence of the particles to the bare surface ℎ_𝑝⁄ ℎ are shown in Fig. 4.19 for various ∆𝑇_𝑤 and 𝑁_𝑝. Note that the enhancement in the boiling heat transfer can exceed 200% for 𝑁_𝑝 ≥800. The best enhancement for these

33

cases is 430% for 𝑁_𝑝=1600 at ∆𝑇_𝑤 ≈13K. Note that the best enhancement usually occurs at very low ∆T_𝑤 near the onset of nucleate boiling. Beyond this low ∆T_𝑤 the boiling heat transfer enhancements are nearly the same for 𝑁_𝑝= 1400 ~ 1800. On the contrary the reduction in the boiling heat transfer at high ∆𝑇_𝑤 can be as high as 25%. Besides, in the single-phase natural convection flow the change in the heat transfer coefficient by the particles is within ±20% of that for the bare surface.

Aside from the boiling heat transfer, the above results also show that the presence of the copper particles can substantially lower the wall superheat needed for the onset of nucleate boiling for most cases (Table 4.1). This is also beneficial in electronics cooling by employing moving metallic particles on the boiling surface.

Next, the measured heat transfer data for the larger copper particles with d_𝑝=1.5 mm are given in Figs. 4.20-4.27 for 𝑁_𝑝 ranging from 100 to 800. By and large, these results are similar to those for the smaller copper particles presented above. However, some noted differences do exist. Specifically, the larger particles exhibit more pronounced effects on enhancing and retarding boiling heat transfer.

Besides, the onset of nucleate boiling is much earlier for the large particles. For instance, at 𝑁_𝑝=600 a 55% reduction in the incipient boiling wall superheat can be obtained by the moving particles. Checking with the data for ℎ_𝑝⁄ given in Fig. 4.28 ℎ for 𝑑_𝑝=1.5 mm indicates that boiling heat transfer coefficient can be increased up to more than 440% by placing the larger copper particles on the boiling surface for 𝑁_𝑝=800 at ∆T_𝑤 ≈12.5 K. At higher ∆T_𝑤 the best boiling heat transfer augmentation can be procured at 𝑁_𝑝 = 700.

34

4.5 Effects of Moving Stainless Steel Particles on Boiling Heat Transfer

Attention is then turned to examining the data for the stainless steel particles, which have a slightly lower density than copper. The measured heat transfer data for the stainless steel particles with d_𝑝=1.0 mm shown in Figs. 4.29-4.37 qualitatively resemble that for the copper particles given in Figs. 4.4-4.18. But for the lighter stainless steel particles, the boiling heat transfer augments more drastically with a large number of the particles present in the liquid FC-72 on the heated plate.

Relatively substantial boiling heat transfer augmentation has been achieved already at 𝑁_𝑝=400 for the lighter particles. Besides, the boiling heat transfer enhancement extends to a slightly higher wall superheat. The data in Fig. 4.38 show that the best boiling heat transfer enhancement can be up to 530% for the small stainless steel particles at ∆𝑇_𝑤 ≈ 12.7 𝐾. Moreover, the enhancement reduces faster with the wall superheat. Furthermore, the lighter particles cause even earlier onset of nucleate boiling. It is of interest to note from the data for the large stainless steel particles given in Figs. 4.39-4.43 that the resulting boiling heat transfer exhibits opposite trends when compared with the large copper particles shown in Figs. 4.20-4.27. Specifically, the large stainless particles produce worse boiling heat transfer enhancement than the large copper particles. This can be seen by comparing the data for ℎ_𝑝⁄ given in ℎ Figs. 4.38 and 4.44 for the stainless steel particles with Figs. 4.19 and 4.28 for the copper particles.

35

4.6 Proposed Correlations

The data for ℎ_𝑝⁄ presented in Figs. 4.19, 4.28, 4.38 and 4.44 can be ℎ correlated empirically as

^ℎ𝑝

ℎ

= {𝑎 + 𝑏 ln (

^𝑁𝑝

𝑁_𝑝𝑓

)} ∙ [

^{𝐶𝑝𝑙(∆𝑇𝑤−∆𝑇𝑂𝑁𝐵,𝑏+1)}

𝑖_𝑙𝑣

]

^[𝑐+𝑑(

𝑁𝑝 𝑁𝑝𝑓)

1.5 ]

(4.4)

𝑎 = [−0.69 + 0.14 (𝜌𝑝

𝜌_𝑙)] + [12.1 − 2.33 (𝜌𝑝

𝜌_𝑙)] (d_p⁄√σ g∆ρ⁄ )

𝑏 = [1.683 − 0.325 (𝜌𝑝

𝜌_𝑙)] + [−30.77 + 5.8 (𝜌𝑝

𝜌_𝑙)] (d_p⁄√σ g∆ρ⁄ )

𝑐 = [−10.61 + 1.8 (𝜌𝑝

𝜌_𝑙)] + [164.08 − 30.28 (𝜌𝑝

𝜌_𝑙)] (d_p⁄√σ g∆ρ⁄ )

𝑑 = [2.88 − 0.55 (𝜌𝑝

𝜌_𝑙)] + [−50.89 + 9 (𝜌𝑝

𝜌_𝑙)] (d_p⁄√σ g∆ρ⁄ )

The present data for the boiling heat transfer coefficient for the bare surface can be expressed empirically as

h = 436.55 + 748.581 ∙ (∆𝑇𝑤− ∆𝑇𝑂𝑁𝐵) for 0 < [∆𝑇_𝑤− ∆𝑇𝑂𝑁𝐵] < 1𝐾

h = 61.58 + 1135.51 ∙ (∆𝑇𝑤− ∆𝑇𝑂𝑁𝐵) for 1𝐾 < [∆𝑇𝑤− ∆𝑇𝑂𝑁𝐵] < 4𝐾 (4.5)

The mean absolute error (MAE) for the above correlation for ℎ_𝑝⁄ when compared ℎ with the present data is 17.3%. For the correlation given in Eq. (4.5) for h the mean absolute error is 14.2%.

Finally, we illustrate the ranges of the experimental parameters in which the boiling heat transfer can be enhanced by placing the metallic particles on the heated surface in Fig. 4.45. The results manifest that the lower bounds of the imposed heat flux for enhancing boiling heat transfer do not significantly vary with the ratio of the

36

particle number placed on the plate to the maximum particle number forming a single particle layer on the plate 𝑁_𝑝⁄𝑁_𝑝𝑓 and with the particle size and material. But the lower bounds for the wall superheat decrease noticeably with 𝑁_𝑝⁄𝑁_𝑝𝑓 (Fig. 4.45 (b)).

The upper bounds of q and ∆𝑇_𝑤 for enhancing boiling heat transfer, however, show nonmonotonic variations with 𝑁_𝑝⁄𝑁_𝑝𝑓, particle size and material. Specifically, at small and large 𝑁_𝑝⁄𝑁_𝑝𝑓 the upper bound of q is higher for the small stainless steel particles. While for 𝑁_𝑝⁄𝑁_𝑝𝑓 > 1.0 placing the large stainless steel particles results in a lowest upper bound.

Based on the above data, the ranges of the imposed heat flux and wall superheat in which the boiling heat transfer can be enhanced by the movable particles are correlated as

3 ∙ 10⁻⁵+ 0.04 ∙ 10⁻⁶[ln (_𝑁^𝑁𝑝

𝑝𝑓)]² < ^𝑞

𝜌_𝑙𝛼_𝑙𝑖_𝑙𝑣⁄√_𝑔∆𝜌^𝜎 < 3.4 ∙ 10⁻⁴− 4.93 ∙ 10⁻⁵[ln (_𝑁^𝑁𝑝

𝑝𝑓)]²- (4.6)

0.15 − 0.03 (_𝑁^𝑁𝑝

𝑝𝑓) <^𝐶𝑝𝑙_𝑖^∙∆T𝑤

𝑙𝑣 < 0.21 − 9.38 ∙ 10⁻³/ (_𝑁^𝑁𝑝

𝑝𝑓) (4.7)

The mean absolute errors (MAE) between the above correlations and the present data for q and ∆T_𝑤 are 11.5% and 5.8%, respectively.

4.7 Interactions between Particles and Boiling Flow

To delineate the complicate effects of the moving metallic particles on the boiling heat transfer, motions of the particles and bubbles in the boiling flow are visualized. The results from this visualization for selected cases are presented in Figs.

4.46-4.51. More specifically, photos taken from the top view of the boiling flow in a

37

small region around the geometric center of the heated surface are shown in Fig. 4.46 for the small copper particles with 𝑁_𝑝=600 at low imposed heat flux of 0.85 𝑤 𝑚⁄ ². In these figures, the symbol“t=0” denotes an arbitrary time instant in the statistical state. At high heat flux and large particle number the vigorous motions of the particles and bubbles and their strong interactions are prone to overshadow each other, causing the top view photos to be rather ambiguous. Instead the side view photos of the flow are given in Figs. 4.47-4.51 under this situation for various imposed heat fluxes.

Our flow visualization reveals that when a given heat flux is imposed to the boiling surface the fast growth of bubbles after their incipience on the heated surface can push the surrounding particles to move away from these original sites horizontally over a certain distance. As the particles move on the heated surface, they in turn can push the bubbles along their path to depart from the surface, resulting in earlier bubble departure. Besides, the moving particles can collide with other particles. At higher imposed heat flux more bubbles nucleate from the heated plate and the force resulting from the growth of bubbles can be very strong. Consequently, the particles can be lifted directly up by the growing bubbles too. Later, the heavy metallic particles may drop back to the plate due to gravity and the surrounding bubbles and liquid can be pushed away. Besides, collision between the particles is frequent. These mutual particle-bubble interactions in the boiling flow schematically shown in Fig.

4.52 get more intense at increasing heat flux, causing the three-phase liquid-vapor-particle flow over the heated surface to become highly turbulent and tending to enhance boiling heat transfer from the plate.

At an even higher heat flux a very large number of bubbles nucleate at the heated surface and the metallic particles can impede the bubbles of certain size to grow further and depart from the heated surface. The bubbles are then trapped beneath

38

the particles, as schematically illustrated in Fig. 4.53. Meanwhile, the particles can reduce the inrush of the bulk liquid to the heated surface especially at large particle number. Therefore the boiling heat transfer is retarded by the particles. These heat transfer retarding effects are more severe at higher heat flux when more particles are placed on the heated plate.

39

Table 4.1 Wall superheats at onset of nucleate boiling for copper particles Particle diameter

d_𝑝(mm)

𝑁_𝑝 (Tw) _ONB (^OC)

(Tw) ONB (^OC) For bare surface

1.0

100 10.7 12.5

200 10.8 11.6

300 10.8 10.7

400 9.8 11.7

500 9.12 12.4

600 9.9 10.5

700 9.06 12.1

800 9.3 11.7

900 9.7 12.4

1000 8.01 13.1

1100 8.5 9.6

1200 6.2 11.8

1400 6.89 12.84

1600 6.29 13.14

1800 6.12 12.89

1.5

100 10.3 11.7

200 9.5 11.9

300 9.3 12.8

400 5.6 12.9

500 8.5 12.4

600 6 13.2

700 6.61 13.32

800 5.97 12.78

40

Table 4.2 Wall superheats at onset of nucleate boiling for stainless steel particles

Particle diameter d_𝑝(mm)

𝑁_𝑝 ^(Tw) _ONB (^OC)

(Tw) ONB (^OC) For bare surface

1.0

200 8.3 10

400 7.9 12.2

600 7.8 12.8

800 7.9 11.7

1000 7.77 12.2

1200 7.5 12.77

1400 7.13 12.76

1600 7.06 12.57

1800 6.73 12.84

1.5

200 10.7 11.6

400 8 11.5

600 7 11

700 7.1 12.67

800 6.07 12.24

41

8.0x10⁶ 1.0x10⁷ 1.2x10⁷ 1.4x10⁷ 1.6x10⁷

Ra_L 20

40 60 80 100

NuL

Single-phase liquid Natural Convection Heat Transfer at T_w=56^C

Radzimeska and Lewandowski (2005) : Nu_L=(2.1e^-48W+1.2)Ra_L^0.2



Present data at 1 atm

Fig. 4.1 Comparison of the present single-phase natural convection data with the empirical correlation of Radziemska and Lewandowski (2005).

42

0 10 20 30

Tw (K)

0 2 4 6

q (W/cm2)

 Rainy and You (2000)(5x5-cm²) for polished plate

 Present data for bare surface

Fig. 4.2 Comparison of the present nucleate boiling heat transfer data for bare surface with Rainy and You (2000).

43

Fig. 4.3 Effects of surface aging on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) for bare surface.

0 10 20 30

Tw (K) 0

1000 2000 3000 4000

h (W/m2

K

)

(b)

 bare surface-1(measured at time t)

 bare surface-2(measured at time t+6 hours)

0 10 20 30

Tw (K) 0

2 4 6

q (W/cm2)

(a)

 bare surface-1(measured at time t)

 bare surface-2(measured at time t+6 hours)

44

Fig. 4.4 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 100 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K

)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=100

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=100

ONB ONB

ONB ONB

45

Fig. 4.5 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 200 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=200

ONB ONB

ONB ONB

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=200

46

Fig. 4.6 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 300 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=300

0 5 10 15 20 25

Tw (K)

0 1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=300

ONB

ONB

ONB ONB

47

Fig. 4.7 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 400 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=400

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=400

ONB

ONB ONB

ONB

48

Fig. 4.8 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 500 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K

)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=500

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=500

ONB

ONB ONB

ONB

49

Fig. 4.9 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 600 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K

)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=600

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=600

ONB

ONB ONB

ONB

50

Fig. 4.10 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 700 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=700

ONB ONB ONB

ONB

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=700

51

Fig. 4.11 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 800 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=800

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=800

ONB ONB

ONB ONB

52

Fig. 4.12 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 900 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=900

0 5 10 15 20 25

Tw (K) 0

1 2 3 4 5 6 7 8

q (W/cm2)

(a) Boiling Curves

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=900

ONB ONB

ONB ONB

53

Fig. 4.13 Effects of copper particle diameter and number on saturated pool boiling curves (a) and boiling heat transfer coefficients (b) at d_𝑝=1.0 mm and 𝑁_𝑝 = 1000 .

0 5 10 15 20 25

Tw (K) 0

1000 2000 3000 4000 5000 6000

h (W/m2

K)

(b) Heat Transfer Coefficients

 bare surface

 with copper particles on plate for d_p=1.0 mm and N_p=1000

 with copper particles on plate for d_p=1.0 mm and N_p=1000

在文檔中 放置可移動擾動粒子在一水平加熱銅板上對FC-72池沸騰熱傳增強研究 (頁 42-0)