experimental study on heat transfer augmentation …

JAERI-Tech--97-032

JAERI-Tech97-032 JP9709015

m

EXPERIMENTAL STUDY ON HEAT TRANSFER AUGMENTATIONFOR HIGH HEAT FLUX REMOVAL IN RIB-ROUGHENED

NARROW CHANNELS

July 1997

Md.Shafiqul ISLAM*, RyutaroHINO, Katsuhiro HAGAMasanori MONDE* and Yukio SUDO

Japan Atomic Energy Research Institute

VOL 2 8 m 2

- Mi,(T319-11

(T319-11

This report is issued irregularly.

Inquiries about availability of the reports should be addressed to Research Information

Division, Department of Intellectual Resources, Japan Atomic Energy Research Institute,

Tokai-mura, Naka-gun, Ibaraki-ken 319-11, Japan.

© Japan Atomic Energy Research Institute, 1997

m

JAERI-Tech 97-032

Experimental Study on Heat Transfer Augmentation

for High Heat Flux Removal in Rib-roughened Narrow Channels

Md. Shafiqul ISLAM*, Ryutaro HINO, Katsuhiro HAGA+

Masanori MONDE* and Yukio SUDO++

Center for Neutron Science

Tokai Research Establishment

Japan Atomic Energy Research Institute

Tokai-mura, Naka-gun, Ibaraki-ken

(Received June 11, 1997)

Frictional pressure drop and heat transfer performance in a very narrow rectangular

channel having one-sided constant heat flux and repeated-ribs for turbulent flow have been

investigated experimentally, and their experimental correlations were obtained using the

least square method. The rib pitch-to-height ratios(p/k) were 10 and 20 while holding the rib

hgight constant at 0.2mm, the Reynolds number(Re) from 2,414 to 98,458 under different

channel heights of 1.2mm, 2.97mm, and 3.24mm, the rib height-to-channel equivalent

diameter(k/De) of 0.03, 0.04, and 0.09 respectively. The results show that the rib-roughened

surface augments heat transfer 2-3 times higher than that of the smooth surface with the

expense of 2.8-4 times higher frictional pressure drop under Re=5000-105, p/k=10, and

H=1.2mm. Experimental results obtained by channel height, H=1.2mm shows a little bit

higher heat transfer and friction factor performance than the higher channel height,

H=3.24mm. The effect of fin and consequently higher turbulence intensity are responsible

for producing higher heat transfer rates. The obtained correlations could be used to design

the cooling passages between the target plates to remove high heat flux up to 12MW/m2

generated at target plates in a high-intensity proton accelerator system.

Keywords : Narrow Channel, Heat Transfer Augmentation, Rib-Roughened Surface,

Correlations, Turbulence Intensity, Cooling Passage, High Heat Flux,

Target Plate

+ Department of Advanced Nuclear Heat Technology, Oarai Research Establishment+ + Office of Planning* Saga University

JAERI-Tech 97-032

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Md. Shafiqul Islam*

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JAERI-Tech 97-032

Contents

1. Introduction 1

2. Literature Survey 2

3. Heat Transfer Augmentation 3

4. Experimental Program 4

4.1 Test Apparatus 4

4.2 Data Analysis 6

5. Results and Discussion 7

5.1 Frictional Pressure Drop Performance 7

5.2 Heat Transfer Performance 9

6. Concluding Remarks 12

Acknowledgements 13

References 14

Nomenclature 19

Appendix 42

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JAERI-Tech 97-032

1. Introduction

Surfaces roughened from one side with discrete small square ribs in very narrow

channels whose heights are so small as approximately 1 to 3 mm that are similar

to the gaps between the target plates could be introduced to remove high heat

flux up to 12 MW/m2 generated at target plates in a high-intensity proton

accelerator system. The high-intensity proton accelerator of 1.5 GeV and 1 mA

with a beam power of 1.5 MW is connected with a target and is now under

designing at Japan Atomic Energy Research Institute (JAERI) for contributing to

neutron science. The target consists of heavy metal plates such as, tungsten

and these are cooled by water. In designing, heat transfer augmentation is

very much important to keep the surface temperature of target plates below

200X from the view point of safety and extending its life.

Surface roughness with repeated-rib promoters is a well established method.

The ribs break the viscous sublayer and create local wall turbulence due to flow

separation and reattachment between the ribs, which greatly augment heat

transfer,usually with an increase in the flow friction and pressure drop.

Developing and fully developed turbulence heat transfer and friction in narrow

rectangular channels with rib turbulators on one-sided have been studied

experimentally. The effects of rib height, rib spacing and rib shape on heat

transfer coefficients and friction factors over a wide range of Reynolds numbers

have been well established for the very narrow rectangular channels.

Empirical friction and heat transfer correlations have been developed for heat

transfer designers. However, heat transfer designers are continually seeking

the high-performance enhanced surface. The concept of turbulence promoters

was examined for this current study. It is of interest how the surface with

rougheners can perform better than the surface without rougheners(smooth).

The objective of this study is to investigate the following topics on heat removal

phenomena of the solid targets.

1) the effect of flow conditions such as, inlet water temperature and velocity

2) the effect of gap size from 1 mm to 3 mm,

3) heat transfer and pressure loss coefficients for single-phase flow under

constant heat rate condition.

Such a very narrow channel with one-sided repeated-rib promoters with one-

sided constant heat flux condition can play a predominent role in achieving this

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goal. Twelve narrow rectangular channels were tested where four of them

were smooth and the remaining eight were rib-roughened from one side. Half

of the total test sections were tested under heating and remaining without

heating conditions at varying channels heights. The rib pitch-to-height ratios

(p/k) were 10 and 20 while holding the rib height constant at 0.2 mm, the

Reynolds number (Re) from 2,414 to 98,485 under different channel heights of

1.2 mm, 2.97 mm, and 3.24 mm, the rib height-to-channel equivalent diameter

(k/De) of 0.03, 0.04, and 0.09 respectively. The various investigations carried

out on internally augmented tubes including major information are listed in chap.

2.

2. Literature Survey

Improvements of heat transfer performance through passive and active

augmentation methods have been studied intensively for over three decades.

Heat exchangers with single-phase tube-side flow are one of the important

applications where passive surface-modification methods are popularly

employed. Typical examples of passive augmentation are surface roughness,

displaced promoters and vortex generators. Ribs, indentations, spiral flutes,

and coil inserts are some common surface modification techniques that are

effective for many applications, and can be used conveniently for retubing

existing heat exchangers. With the passage of time, the above types of surface

roughness are being utilized more and more for augmentation of heat transfer.

These methods are used to improve heat transfer coefficients inside tubes or out

side tubes or rods. Active augmentation, which has also been studied

extensively, requires the addition of external power to bring about the desired

flow modification. Examples include heat transfer surface vibration, fluid

vibration, and electrostatic field introduction, are costly and complex. Of

these, the most well-known method for augmentation heat transfer is to roughen

the surface using repeated-ribs, since these are relatively easy to manufacture,

and its simplicity in application. Many investigations have been carried out

both analytically and experimentally on tubes and annuli under air-flow

conditions where very few studies are on narrow rectangular channels. There

are almost no heat transfer data both analytically and experimentally on a very

narrow rectangular channel with one-sided repeated-ribs and one-sided

constant heat flux under water-flow conditions.

o

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A comprehensive list was prepared consisting of all the experimental

investigations from which heat transfer and friction factor data could be

extracted for different roughened surfaces for single-phase turbulent flow in

internally augmented tubes up to now. No restrictions were placed on the flow

parameters, namely, the Reynolds number and the Prandtl number, even though

much of the data were obtained in the turbulent regime with either air or water as

the test fluid. This file lists the authors of the investigation and the type of

enhanced tubes along with number of tubes tested in the experiments, which are

summarized in Tablei. The sources are listed in the reference section. In

addition, the type of experiment, whether the fluid is heated or cooled, and the

method of heat transfer are provided whenever possible for future reference.

The objective of this list is to make clear that our experiment will be the first step

to augment high heat transfer performance in a very narrow rectangular channel

with one-sided repeated square ribs, and one-sided constant heat flux under

water-flow conditions.

3. Heat Transfer Augmentation

Different techniques are available to augment the heat transfer performance.

The most well-known augmentative techniques are as follows :

a. Surface promoters

b. Displaced promoters

c. Vortex flow

Surface roughness is one of the promising techniques to be considered

seriously as a means of augmenting forced-convection with single-phase flow

heat transfer. Initially it was speculated that elevated heat transfer coefficients

might accompany the relatively high friction factors characteristic of rough

conduits. However, since the commercial roughness is not well defined,

artificial surface roughness - introduced through knurling or threading or formed

by repeated-rib promoters has been employed. Although the augmented

heat transfer with surface promoters is often due in part to the fin effect, it is

difficult to separate the fin contribution. For the experimental data discussed in

chap. 4, the augmented heat transfer coefficient is referenced to the envelope

diameter.

In certain cases it may be desirable to leave the heat transfer surface intact and

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achieve the augmentation by disturbing the flow near the heated surface.

Displaced promoters alter flow mechanics near the surface by disturbing the

core flow and can be done to place thin rings or discs in a tube. It is seen that

rings substantially improve heat transfer in the lower Reynolds number range

where discs are not particularly effective. Examples are baffles and mixing

elements. It has been established that swirling the flow will improve heat

transfer in duct flow. Generation of swirl flow has been accomplished by coiled

wires, spiral fins, stationary propellers, coiled tubes, inlet vortex generators, and

twisted tapes. Virtually all of these arrangements have been shown to improve

single-phase and boiling heat transfer at the expense of increased pumping

power. Heat transfer coefficients are relatively high for vortex flow due to

increased velocity, secondary flow produced by the radial body force when

favorable density gradients are present, and a fin effect with certain continuous

swirl generators.

Of the several methods discussed above, surface promoters with repeated-ribs

are the most popular as they are effective in enhancing the heat transfer,

relatively easy to manufacture, and are cost effective for many applications, and

was employed at the test section. The ribs break the viscous sublayer

thickness and create local wall turbulence due to flow separation and

reattachment between the ribs, which greatly augment the heat transfer. It is

concluded that the roughness height should exceed the sublayer thickness

before it becomes effective. This type of surface roughness is very much

effective for augmenting the heat transfer coefficients with the expense of

increased frictional pressure drop. The following chapter is concerned with the

experiments for the prediction of turbulent friction factors and heat transfer

performance in very narrow rectangular channels with repeated-ribs under one-

sided constant heat flux condition.

4. Experimental Program

4.1 Test apparatus

The layout of the experimental apparatus and measuring equipment is shown in

Fig. 1. It is seen that the closed-loop system incorporates the test section, flow

meters, a storage tank, a circulating pump, and a D.C power supplier. Water

from the pump was supplied to the test section through the flow meter, and then,

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it passed through a filter, a cooler, the storage tank and a preheater to the pump.

The filter was used to filter out solid particles more than 5 urn that may have

found their way into the system. A preheater was employed to control the

temperature of the working fluid in the test section. The storage tank served as

a container into which the working fluid from the test section was discharged,

conditioned, and recirculated. The flow rate was measured using two flow

meters in parallel and the flow rate through the test section was controlled by

adjusting as required a number of valves installed in the circuit. The test

section shown in Fig. 2 was 250 mm in length with a varying cross section.

Heated length was 200 mm, an entry and exit sections of 25 mm long, were

provided a smooth flow out of the test section. The test section consists of a

heating surface made of copper plate with an electric heater, glass windows etc.

A nichrome plate (0.905 /2/m) was used as a heater and received electricity from

the D.C power supply. Heating of the copper test section was effected by the

passage of a high current(0-300A) at voltage(0-60V) through the test specimen.

The total heat input to the heating surface was calculated from a knowledge of

the current which was measured by a precision ammeter together with the

voltage across the heating surface, which was measured with a voltmeter. The

ribs were square-type where cross sectional dimension was 0.2 mm x 0.2 mm

and pitches were 2 or 4 mm.

Figure 3 shows the cross section of flow channel and schematic of flow channel

with rib-roughened surface. The cross sectional dimensions can be varied

according to channel heights. The width of the test section was 20 mm and

channel heights can be varied from 1.2 mm to 3.24 mm. The channel heights

found variation from the inlet to the outlet sections and assumed linear variation.

The heights were measured by a digital microscope and rechecked by a

ultrasonic method. The measuring heights are listed in Figs. (4-6). The major

parameters along with *N.H /E.H. conditions of the test section are presented in

Table 2. Surface temperature was measured using 26 copper-constantan

thermocouples distributed across the span of the copper plates, 2 mm far from

the tip of the heating surface, and was recorded by the acquisition system

consisting of a data logger and a personal computer. The difference between

the two consecutive thermocouples was 8 mm. Three thermocouples of each

inlet and outlet of the test section were provided to measure the inlet and outlet

*N. H =Non heating E. H = electrical heating

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bulk temperatures of water. Eleven differential pressure taps were installed at

opposite side of the heating surface to measure the static pressure drop across

the test section. The difference between the two consecutive pressure taps

was 20 mm. The range and accuracy of the measuring instruments are given

in Table 3 and Table 4, respectively. The data, which were obtained under the

following experimental conditions are listed in Table 5 .

4.2 Data analysis

The friction factor in a rib-roughened narrow rectangular channel can be

determined by measuring the pressure drop across the test section and the flow

rate of the water. The friction factor can then be calculated from :

f=AP/(2x /0Um2/g).(De/AL) (1)

The friction factor.f is based on isothermal condition (test section without

heating). The present friction factor was compared with the friction factor for

fully developed turbulent flow in smooth rectangular channels by means of the

Blasius correlation :

f/fo = f/[0.079Re"°25] (2)

An average outlet temperature of the water was used in the following equation

(3) to obtain the net heat transfer rate. The average outlet temperature of the

water was obtained by averaging three thermocouples located cross section of

the test section at the outlet. The net heat transfer rate can be calculated from :

Q=CpPvAx(T0U, -Tin) (3)

The local heat transfer coefficient was calculated from the net heat transfer rate

per unit surface area to the heating water, the corrected surface temperature

(Twc) on each measured section, and local bulk mean water temperature as :

h = Q/As(Twc-Tb) (4)

where the local temperature (Tw) was read from each cross-sectional

thermocouple output. The corrected local surface temperature (Twc) for

equation (4) was calculated by one dimensional steady state heat conduction

equation as:

Twc = T w - ( Q x 5 ) / ( A s A ) (5)

where the axial and span wise heat conductions were not considered in this

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study. The surface area, As was based on the smooth surface area, not

including an increase of the area due to ribs. Equation (4) was used for the

rib-roughened surface and the smooth surface heat transfer coefficient

calculations. The maximum heat loss was taken place at the entry and exit of

the test section. The local inner wall temperature (Tw) was at maximum 2 3 ^ in

the fully developed region at low Reynolds number and smaller channel heights

of the test channel. The local inlet bulk water temperature was at best 15°C

depending on the test conditions. The local bulk water temperature,Tb was

calculated assuming a linear water temperature rise along the flow channel and

is defined as:

Tb = Tin + (T0 U t-T i n)x/L (6)

The local Nusselt number of the present study was compared with the Nusselt

number for fully developed turbulent flow in smooth surfaces correlated by the

Dittus-Boelter as:

N U / N U D . 8 = [Q' .De /{A(Twc-Tb)}]/(0.023Re08Pr04) (7)

NUD-B =0.023 Re 0 8 Pr 0 4 (8)

where Q* was surface heat flux supplied by the electrical input.

5. Results and Discussion

5.1 Frictional pressure drop performance

Most of the experimental f data using water, air etc. as a working fluid show

negligible effects on the Reynolds number for tubes or channels with surface

roughness. Citings of such type of experiments are Webb et al. (1971), Liou et

al.(1992), Han et al.(1984) etc. For the rib-roughened surface, rib pitch / height

plays predominent role to increase the friction factor for turbulent flows. Figure

7 shows the friction factor predictions from the experimental data with the data of

Webb et al. for the k/De=0.09, k/De=0.04,w/k=1.0 channel geometry and then the

k/D=0.02, w/k=0.52 tube geometry with varying p/k ratios. The results show

that the friction factor is the highest at p/k=10 both the narrow channel and tube;

then it decreases with increasing or decreasing pitch (p). Frictional pressure

drop of the narrow channel causes lower pressure drop than that of the tube.

Figures 8 and 9 compare the friction factor with the smooth surface along with

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prediction and experimental results at different channel heights. The smooth

surface friction data agrees well enough with the Blasius correlation. The

experimental friction data are underpredicted by about 8 times lower than the

prediction at p/k=1O, Re=104 and, H=1.2 mm where experimental results predict

2.4 times higher than the smooth surface. It is seen that the friction factor

strongly depends on Re and decreases with increasing Re and p/k ratios. It is

obvious that the roughness increases the friction factor with the expense of

pressure drop along the flow direction. For the case of a very narrow

rectangular channel with one-sided square ribs, the friction factor is expected to

be high. The experimental results show very low friction data for the narrow

channels which claim further investigation. Since there are almost no data to

predict the frictional pressure drop in a very narrow rectangular channel having

one-sided repeated-ribs, it is necessary to develop correlations to agree well

with the experimental data. Following experimental correlations will be

applicable for those narrow channels whose roughness will be one-sided

repetitive nature. These correlations are related with the parameter of Re and

expressed by the following equations :

f = 0.27 Re"03 ;

f = 0.14 Re"025 ;

f= 0.054 Re"012 ;

f= 0.040 Re"01 ;

p/k=10 ,

p/k=20 ,

p/k= 10 ,

p/k=20 ,

H=1.2mm

H=1.2mm

H=3.2 mm

H= 3.2 mm

(9)(10)

(11)

(12)

The solid lines passing through the data points are the least-square fits and the

average deviations from the measured data are±1.2, ±1.3, ± 3 and±2%

respectively. The correlation [50] which is used to predict the evaluation

results is expressed by the following equation :

(2 / f ) H = 2.5 In (D/2k) - 3.75 + 0.95 (p/k)053 (13)

The friction factor affects very small on higher channel heights. It is expected

that the friction factor approaches an approximately constant value as the

Reynolds number increases which is consistent with the Moody diagram. It can

be mentioned that the frictional pressure drop data were taken in the fully

developed turbulent flow regime where the location falls under the following

categories: x/De=41~66 (TP05) at p/k=10 to x/De=45~74 (TP05) at p/k=20

while H=1.2mm, x/De=17~28 (TP05) at p/k=10 to x/De=18~29 (TP05) at

p/k=20 while H=3.2mm for the case of the rib-roughened surface, but for the

JAERI-Tech 97-032

smooth surface, x/De=41~67 (TP05), H=1.2mm and x/De=18~30 (TP05),

H=2.97mm. These are shown in Figs. (7-9).

5.2 Heat transfer performanceFigures (10-15) show the surface temperature distribution along the length of

the test section for the smooth and rib-roughened surfaces at different channel

heights over a wide range of the Reynolds number. The results show that

surface temperature first increases, then it becomes axially unchanging in the

fully developed regime and then it decreases. The increasing and decreasing

occurs due to not only entrance and exit effects but also heat losses. Surface

temperature is higher at lower Reynolds numbers for the smooth cases but

opposite for the roughened surfaces. More scattering data are found at higher

Reynolds numbers. Figures (16-27) present the surface and bulk temperature

distributions along the length of the test section for different channel heights at

lower and higher Reynolds numbers. It is seen that at higher Re, the surface

temperature is low and the difference between the surface and bulk

temperatures is small, because more heat is taken away by the fluid which

assists convection mechanism. These figures also reveal that there is a

portion of the test section where the surface and bulk temperature distributions

are parallel, yielding a uniform value of (Tw -Tb) as expected for constant heat

flux. At the inlet and exit of the test section, surface temperature changes

remarkably due to entrance and exit effects. The variation of local Nusselt

number along the length of the test section for different Re numbers are shown

in Figs. (28-33). The Nusselt number is large in the entrance and exit regions.

It decreases with increasing axial distance approaching the fully developed

values. It is also seen that at higher Re, the curve of the local Nu along the

length of the test section is higher whereas at lower Re more uniform Nu data

are found.

Figure 34 shows the Nusselt number predictions from the experimental data with

the data of Webb et al. for the k/De=0.09, k/De=0.04, w/k=1.0 channel geometry

and then the k/D=0.02, w/k=0.52 tube geometry with varying p/k ratios. The

results show that Nu is the highest at p/k=10 both the narrow channel and tube

and then it decreases with increasing or decreasing p/k ratios. The solid line

passing through the data points of Fig. 34 is the least-square fits which is

expressed by the following equation :

NU/NU[>B = 5.12 (p/k)-0252 (14)

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The maximum scatter of the data points relative to the least-square line is ±

6.5%. This correlation is much simpler than the Webb et al.'s correlation, fits

much closer to the experimental data and basically shows the rib pitch/height

effect on heat transfer only. The smooth surface Nu was calculated from the

Dittus-Boelter equation. It is also seen from this figure that this correlation will

not be applicable to the narrow channel because large variation of heat transfer

performance occurs between the tube and narrow channel.

The results would be explained as follows : Since repeated-rib surface is

considered as a roughness geometry, it may be also viewed as a problem in

boundary layer separation and reattachment. Separation occurs at the rib,

forming a widening free shear layer where reattachment occurs down stream

from the separation point. A reverse flow boundary layer is originated at the

reattachment point. The wall shear stress is zero at the reattachment point and

increases from zero in the reverse flow and reattachment regions ; however, the

direction of the shear stress is opposite in these regions. As reattachment

length is a strong function of rib width(w), rib height(k), and channel height(H), it

does not occur for p/k less than about eight. So, the maximum heat transfer

coefficient occurs in the vicinity of the reattachment point even though heat

transfer coefficients in the separated flow region are larger than those of an

undisturbed boundary layer.

From another point of view, the reason can be explained that the reattachment

length behind the rib alters slightly with the rib shape as p/k>10 and for larger

rib spacing, the redeveloping flow beginning at the reattachment point has a

larger distance to develop into a thicker boundary layer before the succeeding

rib is encountered, hence reduced heat transfer. Figure 35 shows the heat

transfer performance for the k/De=0.09, w/k=1.0, H=1.2 mm geometry and

varying p/k ratios along with prediction. The prediction of heat transfer

performance is calculated by the Webb et al.[50] correlation and is expressed by

the following equation:

St = (f/2 ) / [1 +(f/2)</4 [4.5 (k+)°28 Pr°57 - 0.95 (p/k)°53 ] (15)

From this figure, it is seen that the experimental results predict slightly lower

heat transfer performance than the prediction and it augments heat transfer

about 2-3 times higher than the smooth surface by means of 2.8-4 times

frictional pressure drop with p/k=10 and Re=5000 -105. As shown in Fig. 35,

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the solid lines passing through the data points are the least-square fits and can

be expressed by the following equations :

Nu = 0.416 Re057 Pr04 ; p/k= 10 , H =1.2 mm (16)

Nu = 0.434 Re 0 5 5Pr 0 4 ; p/k=20 , H =1.2 mm (17)

The maximum scatters of the data points relative to the least-square lines are

±15 and ±22 % respectively. Figure 36 shows the heat transfer performance

for the k/D«=0.04 , w/k=1.0 and H= 3.2 mm geometry with varying p/k ratios

along with prediction and experimental results. The experimental correlations

are expressed by the following equations:

Nu = 0.384 Re 0 6 Pr 0 4 ; p/k = 10 , H= 3.2 mm (18)

Nu = 0.365 Re 0 6Pr0 4 ; p/k = 20 , H=3.2 mm (19)

It is seen from this figure that higher channel heights do not play any significant

role from the view point of heat transfer augmentation. The solid lines passing

through the data points are the least-square fits and the maximum deviations are

±10 and ±13% respectively. The heat transfer data were taken in the fully

developed region where the location falls under the following categories:

x/De=29~71 at p/k=10 to x/De=25~76 at p/k=20 while H=1.2mm and x/De=17

~26 at p/k=10 to x/De=11~29 at p/k=20 while H=3.2mm for the case of the

rib-roughened surface, but for the smooth surface, the position belongs to

x'De=42~6? while H=1.2mm to x/De=18~27, H=3.2mm respectively. They

are shown in Figs.(34-36).

Such a high heat transfer augmentation performance in a very narrow channel

with repeated-ribs would be responsible for creation of turbulence eddies,

recirculation and overall increase of surface area. Due to the presence of

these, the velocity profiles are relatively flat for the rib-roughened surface

compared to the smooth surface. The flatter profiles enhance the transfer of

momentum and energy, and hence increase surface friction as well as

convection heat transfer rates. The causes for the disagreement of

experimental results with the prediction seem to be that the prediction

correlations are obtained for those experiments whose parameters are large,

experimental conditions are different compared to this experiment. The

present experiment is not only non uniform heating but also non symmetric

rib-roughened surface from one side. In addition, the heat transfer

performance reveals the similar tendency. This discrepancy suggests for

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further investigation.

6. Concluding Remarks

The thermal and hydraulic characteristics of the narrow rectangular channels

with and without repeated-rib promoters in a single-phase turbulent flow for the

target system have been studied experimentally. The friction factor distribution

is not consistent with that of the existing works [50]. For the smooth channel

flow, both the measured Nusselt number and friction factor agree well with

available theoretical correlations. The main findings are :

1. Semi-empirical correlations for friction and heat transfer that are

applicable to a very narrow rectangular channel with internally one-sided

repeated-rib promoters are presented. These correlations could be useful

in the design of the cooling passages between the target plates to remove

high heat flux in a high-intensity proton accelerator system.

2. Relative to a smooth surface, the presence of periodic ribs at one-sided

walls augments heat transfer 2-3 times higher by means of 2.8-4 times

frictional pressure drop for the ranges of Reynolds number, Re=5000 -10s,

dimensionless rib/pitch, p/k=10 and channel height,H=1.2 mm investigated

in this current study.

3. The highest heat transfer augmentation which causes the highest frictional

pressure drop occurs at p/k=1O compared to other larger or smaller p/k

ratios.

4. Friction factor is a strong function of the Reynolds number from the

transition to the fully developed regime and is expected to be a asymptotic

value at higher Re.

5. Reattachment length is expected to be a strong function of rib width (w), rib

height (k), and channel height (H) and be independent of the Reynolds

number.

6. Higher channel heights do not play any significant role from the view point of

heat transfer augmentation.

Based on the results in this study, it is recommended for further study including

the following:

1. Symmetric condition of ribs in the channel with uniform heating and ribs of

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various shapes,

2. Non transverse ribs (helix angles other than 90° ), which induce a spiral

component to the flow,

3. Closer rib spacings corresponding to the separation and recirculation

mechanism,

4. Various rib heights to see the effects of its, and

5. Various channel heights to make clear the effectiveness of channel heights.

Acknowledgements

In this study, the authors wish to express their sincere gratitude to Mr. Hideki

Aita, Mr. Kenji Sekita, and Mr. Fujisaki for their assistance to carry out the

experiments. Without their contributions, the work would not have been

possible. Finally with deep sincerity, the authors acknowledge profound

indebtness to Dr. M. Z. Hasan, Assoc. professor, Mechanical Engineering

Department, Saga University for his guidance, constant encouragement,

valuable comments and suggestions.

• 1 3 -

JAERI-Tech 97-032

References

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[7] Webb, R.L., Turbulent Heat Transfer in Tubes Having Two-Dimensional

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[8] Nakayama, M., Takahashi, K., and Daikoku, T., Spiral Ribbing to

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JAERI-Tech 97-032

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[12] Gee, D.L., and Webb, R.L., Forced Convection Heat Transfer in

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JAERI-Tech 97-032

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JAERI-Tech 97-032

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Institute, JAERI-Tech, 97-008. 1997- 1 8 -

JAERI-Tech 97-032

Nomenclature

a,, a2, a3 empirical constants

b i , b2, b3 empirical constants

Ax f low cross sectional area, m2

As surface area , m2

Cp specific heat, J / k g ^

D, equivalent diameter, De = 4WH / 2( W + H ) , m

f roughened friction factor

g acceleration due to gravity , m/s2

h forced convection heat transfer coeff icient, W / m2oC

H channel he ight , m

k rib he ight , m

K geometry constant

k+ roughness Reynolds number, k* = (k/De) Re (f/2)*

L channel length , m

Nu Nusselt number, Nu = hD e / A

p rib spacing , m

A P pressure difference , N / m2 [ refer to eq.(1) ]

Pr Prandtl number, Pr = Cp fi IA

q ' heat flux , W / m2

Re Reynolds number, Re = De um / v

St Stanton number, St = Nu / Pr Re

Tb bulk mean temperature, °C

Tw, wall temperature , °C

um average fluid velocity , m/s

w rib width , m

W width of the channe l , m

x local distance along the axial direction , m

Greek symbolH dynamic viscosity , kg/m.s

v kinematic viscosity , m2/s

p densi ty , kg/m3

S copper material thickness, m

X thermal conductivity, WmV

A increment

- 1 9 -

Subscripts

bm0

weD-B

JAERI-Tech 97-032

bulk

mean

smooth surface

corrected wall

Dittus-Boelter

- 2 0 -

(T) Thermocouple

® Pressure gauge

Diff. pressuregauge

Filter

DC powersupply

CO

IWater

•1.5MPa

Pre-heater ®©—

Cooler

Water pump

Watertank

Fig.1 Schematic diagram of test apparatus

Glass window

Rib-roughenedsurface

Heater element

Thermocouple

\Thermalinsulation

290

>tnS2T

i?

Rib-roughened surface

(unit: mm)

Fig.2 Schematic drawing of test section

Outlet

H=1, 3mm

to(S3

Cross section of flow channel Flow channel with rib-roughened surface

Fig.3 Schematic drawing of cross section of flow channel with

rib-roughened surface

Inlet

pT~| 11.24 mm

1.24 mm

|i.19mm |

[1.20 mm |

|i.20mm I

11.24 mm I

|1.12 mm

plT| |i.10 mm

I2.68 mm I

12.81 mm

|2.90mm

|2.91 mm I

|2.95 mm |

13.01 mm I

[1.23 mm | |3.02 mm [ jw

|8 | |i.22mm| [3.03 mm |

[9 | [1.12 mm [ |3.04 mm

|3.06 mm

|3.08 mm

I

Fig. 4 Local channel height for two different channels(Smooth)

Outlet

ICO

toI

|i.26mm|

li.26mm|

|i,25mm |

[4~| [1.25 mm)

[5~] [1.24 mm

| 6 | 11.22 mm |

11,20 mm]

18 I |i.17mm|

|9 I |i.19mm

1.20 mm

3.33 mm

3.31 mm

[3.28 mm |

|3.26mm|

13.24 mm |

3.23 mm

3.22 mm

13.20 mm |

|3.19mm

3.19 mm

TT[ |i.23mm | |3.19mm

Inlet

Fig. 5 Local channel height for two different channels(Roughened surface, p= 2 mm)

-itOutlet

>

|TP01 |

160mm

>

|TP02 |

100mm

>

|TP05|

60mm

InletJt

|i.17mm[ |3.15mm

1.16 mm 3.15 mm

1.18 mm 3.13 mm

I mm | |3.06mm|

| l 15mm | [3.02 mm |

[I.18mm|

|i.20mm|

|8 | | l19mm|

|9 | [1.20 mm

[To~l |i.28mm

TT] 11.28 mm

|3.0 mm ]

|3.12mm1

|3,13mm]

|3.13 mm~|

|3.13mm

3.28 mm

"7"

i

Fig. 6 Local channel height for two different channels( Roughened surface, p= 4 mm)

20

15

10

ICO

0 Webb et al. (Tube): D=36.83 mmp/k=10 ; Re=6903~ 123852

=20;Re=6512-142501=40 ; Re=6512~140845

Present work (Narrow Channel)H=1.2mm:

# p/k=10 ; Re= 6887- 23494 x/De=41 - 6 6=20 ;Re= 10791-27679 x/De=45~74

• H=3.2mm:p/k=10 ; Re= 4546 - 77508 x/De=17~28

=20 ; Re= 3790- 83886 x/De=18~29oo

Ioo8o

ooooooo

5ScoIIII

10 20 30 40

Rib pitch / height(p/k) ratio

50

10°86

10"1

8

e 2

10"21

86

4

210-3

Webb et al.'s correlationO Expt. data p/k =10 x/De=41— 66• Expt. data p/k =20 x/De=45~74D Expt. data (no rib) x/De=41~67

p/k=10 - ^

30

Present correlationp/k=10

20

H=1.2mmk=0.2 mmw=0.2 mm

2

i

10J 6 8 104 2

Reynolds number

4 6 8 1Q5

Fig. 7 Friction factor predictions from the experimental datawith the data of Webb et al. for the k/De=0.09, k/De=0.04, w/k=1.0 channel geomerty and for the k/D=0.02,w/k=0.52 tube geomerty with varying p/k ratios.

Fig. 8 Comparison of friction correlations with Webb et al.

an

10-1

8

6

10"

Webb et al.'s correlationp/k=10

20

30p/k=10 20

10J

H=3.2 mmk=0.2 mmw=0.2 mm

O Expt. data• Expt. dataD Expt. data

Blasius

p/k=10 x/De=17~28p/k=20 x/De=18~29(no rib) x/De=18~30

4 6 8 104 2

Reynolds number

4 6 8 -in5

Fig. 9 Comparison of friction correlations withWebb et al.

~ 20

Q.

(D

3 10

• Re

A Re

o Re

A Re

•

• •"* S A 9! * a

•

:4271

:7660

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° A *

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A A

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height

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0 0

A AA

:H=1.2: Water

wall

m

A A

0 o

A A

mm

* •

A A

o oA A

•

A

O

A '

@

II

50 100 150

Axial distance [mm]

200

Fig. 10 Local surface temperature distributions alongthe flow direction of the test section.

25

20

£I5 15Q.

I

110

•

•

#i

•

A

A

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2.97 mm: water

wall

30

50 100 150Axial distance [mm]

200

20

2Ia>a.

B

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Channel height : H=1.2 mmRib pitch : p=2 mmRib height : k=0.2 mmFluid : water

* * * •

A 9 z 0 " o v " 6

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A Re :9762

a Re :11777

oRe : 13789

A Re :16218

• Re : 18599

• Re .21100

A Re :23313

• Re :26964

° ° t0

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Axial distance [mm]

s

II

sCO

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• Re :

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AI m •

B B A <

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11615

13841

16586

18996

22221

26411

32209

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50 100Axial distance [ mm]

150 200

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. • Re

. A Re

. o Re

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•

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: H-3.2mm: k=0.2 mmp=4mm

: water

t2

25

20

15

IE 10

Re:4271

• Tiwo Tw

• o

Local inner walltemperature

Local surfacetemperature

50 100 150

Axial distance [mm]

200

Fluid local bulkmean temperature

Channel height : H=1.2 mmFluid : WaterSmooth heated wall

50 100 150

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200 5

Fig. 15 Local surface temperature distributions alongthe flow direction of the test section. Fig. 16 Local surface and bulk temperature distributions

along the flow direction of the test section.

20

16

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• Tiwo Tw

— T b

Local inner wall R e . 2-| 73-1temperature

o• o

O o

o oLocal surface

temperaturef ~



O o

50 100 150

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200

25

20

10Q.

15

10

0

• Tiwo Tw

— T b

Re: 47158 8



Fluid local bulk meantemperature

Channel height : H= 2.97 mmFluid : waterSmooth heated wall

TO

50 100 150

Axial distance [mm]

200

Fig. 17 Local surface and bulk temperature distributionsalong the flow direction of the test section.


o

24

20

,-, 16

"5 12

t 8

• Tiw

o Tw

— T b

Re:72647



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Channel height : H= 2.97 mmFluid : waterSmooth heated wall

1I

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200

25

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; Re: 7460 Channel height : H=1Rib pitch : p=2

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' Local surface • , • * • ,. temperature • o * o ° ^ ° <

o °\ m*o Local inner wall

• 0 temperature. • 0 0

00

Fluid local bulktemperatutre

3 0 # *° O •

o

• —

I50 100Axial distance [mm]

150 200

Fig. 19 Local surface and bulk temperature distributions Fig. 20along the flow direction of the test section.

Local surface and bulk temperature distributionsalong the flow direction of the test section.

I00

25

20

_ 15

kL

^ 10<aa.

Re : 26961Local inner walltemperature


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50 100 150

Axial distance [mm]

200


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P 15

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5

0

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; Rib pitch : p=2mmFluid : water


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•o—

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150 200

500

400

.2Ic

"05

300

200

100

•A

A

• •

• Re: 4271 ; Q": 111kW/m2

• Re : 7660 ; Q": 130.2kW/m2

A Re : 13086; Q": 154.4kW/m2

• Re : 21732; Q": 120kW/m2


•

A • _ • *A

A * A A

. . A ' A A : ' A A . -• _ • •

• • ' • • • • • •* • • • • • • • • • * *

so

3

50 100 150 200

Axial distance [mm]


Fig. 28 Local Nusselt number distributions along the flowdirection of the test section.

2000

1500

E

±s 1000CD<O

co2

500COen

ChannelFluid

• Smooth

•

' A

• Re :

• Re:

A Re:

o Re :

A Re :

• Re :

A

A

0 A

A A A O O

' • • H A A. A• * • • • • _• • • : : :

height

heated

4715;

8590;

14327;

23890;

40932;

72647;

•

A *

o ° c

• • I

: H= 2.97 mm: water

wall

Q": 75 kW7m2

Q": 82.5 kW/m2

Q": 87.5 kW/m2

Q": 93.7 kW/m2

Q"; 129kW/m2

Q": 158.2 kW/m2

•

• •• • A

• A A

0 ° A ° o o ° 0

! • • • • • • • • •, • • • • • • • • • •

2000

S 1000CDCOto

Channel heightRib pitchRib heightFluid

oo

Aao•

H=1.2mmp=2mmk=0.2 mmwater

• Re :7460o Re :9762

Q": 330kW/m2Q": 355 kW/m2

a Re :11777 ; Q": 355 kW/m2ARe:137B9; Q": 364 kW/m2o Re .16218 ; Q": 364 kW/m2oRe:18599; Q": 364 kW/m2ARe:21100; Q": 364 kW/m2• Re:23313; Q": 364 kW/m2• Re :26964 ; Q": 364 kW/m2

50 100 150

Axial distance [mm]

200 50 100 150

Axial distance [mm]

1I

200

Fig. 29 Local Nusselt number distributions along the flow Fig. 30direction of the test section.

Local Nusselt number distributions along the flowdirection of the test section.

3000

.2 2000E

(/)(A

z 1000

i l l ?

11615; Q":304kw/m2

13841 ; Q": 304 kW/m2

16586; Q": 304 kW/m2

18996; Q":304kW/m2

22221; Q":389kW/m2

26412; Q":389kW/m2

32209 ; Q": 429.2 kW/m2

Channel height: H=1.2mmRib height : k=0.2 mmRib pitchFluid

p=4mm: water

29

50 100 150

Axial distance [mm]

SZ3C±1D

200

DUUU

5000

4000

3000

2000

1000

I

! Channel height: H=3.24mm; Rib height : k=0.2 mm

Rib pitch : p=2mm• Fluid : water

*A

• Re : 4673 ; Q"; 113.2 kw/m2• Re: 8827; Q": 150.2 kW/m2A Re : 15177 ; Q": 202.5 kW/m2o Re: 26578; Q": 249 kW/m2A Re : 49695 ; Q": 300.2 kW/m2• Re: 83084; Q": 377.4 kW/m2

' 4 ° O A O O A • • m ^ • A A * AA °

"::?;::hf iiiiiiiiiiH:50 100 150

Axial distance [mm]

S2

i200



3000

| 2000

EC

CD

1000

0

Channel heightRib heightRib pitchFluid

: H=3.2mm: k=0.2 mmp=4mm

: water

•

o

A

•

Re:6453;

Re:7977;

Re:13323;

Re :23616;

Re : 43625;

Q":

Q":

Q"

Q"

Q"

167.5 kW/m2

199kW/m2

: 199kW/m2

: 325.5 kW/m2

: 472.5 kW/m2

A • •

O _ r, * _A A

3

I4

50 100 150

Axial distance [ mm]

200

• Webb et al.( p/k=10 ;

=20;=40;

Present work (n H=1.2mm:

p/k=10,Re

(Tube): D= 36.83 mmRe = 8131 to 56597Re = 7580 to 101533Re = 7943 to 59306 )

Narrow Channel)

= 7475 to 27041, x/De=29~71Q =20, Re=11508 to 31992, x/De=25~76

H=3.2 mm:p/k=10, Re

=20, Re0

= 4673 to 82984, x/De=17~26= 6383 to 43546, x/De=11 - 2 9

Nurib / NuD.B = 5.12 (p/k)"0252

10 20 30 40 50 60

Rib pitch / height(p/k) ratio


Fig. 34 Nusselt number predictions from the experimental datawith the data of Webb et al. for the k/De=0.09,k/De=0.04, w/k=1.0 channel geometry and for thek/D=0.02, w/k=0.52 tube geomerty with varyingp/k ratios.

00

0)

V)

Z

10"86

864

2

10

WebtO Expt.• Expt.• Expt.

Presentcorrelation

p / k = 1 0 = ^20

c

) et al.datadatadata

correlatorp/k =10;p/k =20;(no rib) ;

p/k=10

y

I

X/De =X/De =X/De =

20

29-7125-7642-62

a / Dittus- Boelter

H=1mmk=0.w=0

.2

2 mm.2

10J 4 6 8 104 2

Reynolds number

4 6 8 105

Fig. 35 Comparison of heat transfer correlations withWebb et al.

Ec

(D(A

>

10"86

10"86

1010J

Webb et al.'s correlationO Expt. data p/k=10 x/De=17~26• Expt. data p/k=20 x/De=11~29• Expt. data (no rib) x/De=18—27

Present correlation

Dittus-Boelter

H= 3.2 mmk= 0.2 mmw= 0.2 mm

4 6 8 104 2

Reynolds number

6 8 105

Fig. 36 Comparison of heat transfer correlations withWebb et al.

to

I

Table 1 Investigations

Study1. Lietal. [6]2. Webb [7]3. Nakayama et al. [8]4. Yoshitomi et al. [9]5. Withers I [10]6 Withers II [11]7. Gee and Webb [12]8. Berger and Whitehead [13]9. Migai and Bystrov [14 ]10. Kalinin etal. [15]11. Bolla et al. [16]

12. Ganeshan and Rao [17]13. Gupta and Rao [18]14. Nunner[19]15. Sams [20]16. Kumar and Judd [21]17. Novozhilov and Migai [22]18. Snyder [23]19. Sethumadhavan and Rao [24]20. Chiou [3]21Molloy[25]22. Ravigururajan [26]23. Mehta and Rao [ 27 ]24. Ravigururajan and Bergles [5]25. Zhang et al. [4]26. Cunningham and Milne [28]27. Mendes and Mauricio [29]28. Yampolsky et al. [30]29. Scaggs et al. [31]30. Scaggs et al. [31]31. Newson and Hodgson [32]32. Sutherland and Miller [33]33. Smith and Gowen [34]34. Takahashi et al. [35]35. Obot and Esen [36]

Tubestested

20561813133310101

7541314101181515843233433

24123

24

Type

indribindindindindribrib

ind / flindribindindribcoilcoilcoilcoilcoilcoilcoilcoilindindcoilindrib

flute3d3d

fluterib3d3dall

cited in

Fluid

WA,WWWWWAirAirAirAir

He, N2

WWAirAirWAirWWOilAirAirWWAirWWWWWW

StmA.W.Gly

WAir

this study

Expt.condition

E.H.E.H.E.H.E.H.

T=ConstT=Const

E.H.E.H.

T=ConstW.cooledW.heated

W.heatedW.heatedW.heated

E.H.E.H.E.H.E.H.

W.heatedW.cooled

E.H.W.cooledW.heated

E.H.W.cooledW.heated

SublimationW.heated

ISOISO

W.heatedE.H.E.H.E.H.E.H.

a

f

20561813133310101

7541301011801584

323003600024

N-ISO-f

05000030

0

00

0

0

0

0

14

0

0

8

15

0

0

0

4003100

24120

24

HT

20561813133310101

754

13

14

10

11

8

15

1584

32

0

3

1

0

0

24122

24

Table 2 Major parameters and conditions of the expt.

TypeSmoothSmooth

SmoothSmooth

Square ribsSquare ribs




H1,21.2

2.972.97

3.243.24

1.21.2

3.243.24

1.21.2

p /k

—

1010

1010

2020

2020

k/De

0.090.09

0.040.04

0.030.03

0.090.09

0.030.03

0.090.09

Expt.condition

N. HN. H, E.H.

N. HN. H, E.H.

N. HN. H, E.H.

N. HN. H, E.H.

N. HN. H, E.H.

N. HN. H, E.H.

*N.H = Non heating , E.H. = electrical heating

TO

—ji

oCOto

" E.H.= electrical heating, A = air, Gly = glycerin, Stm = steam, W = water

ISO = isothermal, HT = heat transfer

Table 4 Thermocouple range and accuracy

Table 3 Range and accuracy of pressure gauges,flow meters, pump, voltmeter and ammeter

oI

Category

PressureTap

Flowmeter

Pump

Voltage

Current

Accuracy

± 0.3% FS

± 0.2% FS

± 0.2% FS

± 0.2% FS

± 0.3% FS

± 0.2% FS

± 0.2% FS

± 0.25% FS

± 0.25% FS

± 0.2% FS

Range

0-10Kgf/cm2

0 -0.3Kgf/cm2

0 -5Kg, /cm2

0 -0.2Kgf/cm2

0 -2Kgf/cm2

0 -0.3Kg, /cm2

1.2Kg,/cm2

0-2m3/h

0-15m3/h

0-10Kgf/cm2

0-60V

0 - 300 A

Location

Surface

0mm10mm20mm30mm40mm50mm60mm70mm80mm90mm100mm110mm120mm130mm140mm150mm160mm170mm180mm190mm200mm210mm220mm230mm240mm250mm

Heater

Inlet

Outlet

Thermocouple no.

TT01TT02TT03TT04TT05TT06TT07TT08TT09TT10TT11TT12TT13TT14TT15TT16TT17TT18TT19TT20TT21TT22TT23TT24TT25TT26

TT27TT28TT29

TT30TT31TT32

TT33TT34TT35

Accuracy

JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4JIS 0.4

JIS 0.4JIS 0.4JIS 0.4



Range

0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C0 - 650 °C

0 - 650 °C0 - 650 °C0 - 650 °C

0 - 650 °C0 - 650 °C0 - 650 °C

0 - 650 °C0 - 650 °C0 - 650 °C

Table 5

Fluid

Reynolds number

Flow velocity

Inlet temperature

Heat flux

System pressure

Flow direction

Flow condition

Heating condition

Experimental conditions

Water

2,414 to 98,485

up to 25 m/s

upto15°C

up to 0.4725 MW/m2

up to 1.5MPa

Vertical

Fully developed turbulent flow

Uniform heating from one side

II

ito

3

I

Appendix

Experimental data

The data points in the graphical comparisons presented in chapt.5 werecarefully taken from the referenced articles/papers [ 41 & 42 ]. In this appendix,the referenced works are first identified by the tube designations and presentworks are identified by the channel number. The physical rib andtube/channel dimensions are given in a listed form and the experimental databoth the tubes and channels are followed by the tabulated data points for theparticular tube/channel as read from the figures of the given works.

Tubes of Webb et at. (1971):

Tube designation :

Webb et al. 02/10 ( k/D=0.02,p/k=10, w/k=0.52)of Figure 7 and Figure 34

Major Parameters:

Rib width : w=0.38 mmRib height : k=0.7366 mmRib pitch : p= 7.366 mm

Tube diameter : D=36.83 mm

Experimental data :

Tables 1-W and 2-W

Narrow channel (1997)

2

Shafiqul et al.: Channel -1 (k/De=0.09, p/k=io, w/k=1.0)of Figure 7 , Figure 8, Figure 34 and Figure 35

Major parameters:

Rib width : w=0.2 mmRib height : k=0.2 mmRib pitch : p= 2 mm

Channel height :H=1.2mm

Experimental data :

Tables 1-Eand2-E

Table 1-W Friction data for Tube 02/10

IOJ

I

Point

1234567891011121314

Re

6903723486201003510153139201408425563354604805451545651196744394656

fT

0.026480.029350.029350.031440.03180.0333

0.034460.034860.035660.036490.035660.034150.036080.03446

Table 2 - W Heat transfer data for tube 02/10

Point

12345

Re

813112385222174080056597

Nu

172244390611738

Table 1

Point123456789

Table 2

Point

12345678910111213141516171819202122232425

- E Friction data for channel -1(X/De=41-to-66)

Re6887855110288123061462016440183202032823494

-E Heat

fr

0.020.01870.01760.01650.01550.01520.015

0.01450.0139

: transfer data for channel -1(X/De=29-to-71)

Re

7475749375077522754075737591762997829804982198399861990099239968118051182711845118621188511925119481199513823

Nu

169184179170167175193202187215209192190209227235206238234214210227253261220

Point

26272829303132333435363738394041424344454647484950

Re13847138641388213906139481397316261162861630416321163471639016416164671864918675186931871118738187831881018865211582118621204

Nu

260255234229245276238291281259248264300306256315308279263284324328270335324

Point

5152535455565758596061626364656667686970

Re

2122221251212972132621383233792340823427234452347523524235542704127073270922711227144271962722927294

Nu289277300342349286361345302296319374311394376326324355409407

>tn

Tubes of Webb et al, (1971):

Tube designation :

Webb et al. 02/20 (k/D=0.02, p/k=20, w/k=0.52)of Figure 7 and Figure 34

Major Parameters:



Experimental data:

Tables 3 -W and 4-W


Shafiqul et al.: Channel -2 (k/De=0.09, p/k=20, w/k=1.0)of Figure 7 , Figure 8, Figure 34 and Figure 35

Major parameters:

Rib width : w=0.2 mmRib height : k=0.2 mmRib pitch : p= 4 mm

Channel height : H=1.2 mm

Experimental data:

Tables 3-E and 4- E

Table 3 - W Friction data for tube 02/20

Point

12345678910111213

Re

651280361089013598184282383130108447995401282269101533125308142501

0.020110.022550.023610.024160.024720.025290.025880.026480.027090.027720.028040.029020.02902

>I

I


Point

12345

Re

7580139203464159306101533

Nu

1342354826971008

Table 3 - E Friction data for channel - 2(X/D.=45-to-74)

enI

Point1234567

Table

Point

1234567891011121314151617181920222324252627282930

Re10791128451467917141197922301327679

h0.013090.012370.012250.011670.011080.010830.01027

4 - E Heat transfer data for channel(X/D.= 25-to-76)

Re

1150811531115531157311687114991174011792118051181411847137311375513779138001392313696139791403514047140551409016476165011652616548166801640316739

Nu

224202165198170224173176188219215248215178216181237185191203239233270233192238196257198

Point

3132333435363738394041424344454647484950515253545556575859

Re

1679916809168151685322060220972213222163216092235021981224332251822533225442259726247262862632326355265582611526648267382675126759268173199232043

-2

Nu

204218261251326269219279323230304232241259313293357294237309250332253263283351322410329

Point

60616263646566676869

Re

32090321333132132392318553250732623326433265532729

Nu

263342390282375279293319403359

Tubes of Webb et al. (1971);

Tube designation:

Webb et al. 02/40 (k/D=0.02, p/k=40, w/k=0.52)of Figure 7 and Figure 34

Major Parameters:



Experimental data:

Tables 5-W and 6- W


8

oGOto

Shafiqul et al.: Channel - 3 (k/De=0.04, p/k=io, w/k=1.0)of Figure 7 , Figure 9, Figure 34 and Figure 36

Major parameters:

Rib width : w=0.2 mmRib height : k=0.2 mmRib pitch ; p= 2 mm

Channel height : H=3.24mm

Experimental data:

Tables 5- E and 6-E

Table 5 - W Friction data for tube 02/40

Point

123456789101112131415161718

Re

651269038323832385201101813758180022355424395308204427844799515457943499187125308140845

fT

0.014930.015280.015630.016370.015630.016550.016740.016370.016740.016940.017130.017130.016940.017330.017730.017940.018350.01878


Point

12345

Re

794314084214523384159306

Nu

111185270385569

Table 5

Point

123456789

- E Friction data channel(X/D,=17-to-28)

Re

454655016300737784709750120391458417339

fT0.02340.02170.02070.01940.0190.01850.01750.01720.0167

Point

1011121314151617

-3

Re

2226325524327933920747113549636335877508

fT0.01590.01580.01590.01540.0150.01510.0150.0143

Table 6 - E Heat transfer data for channel -3(X/D,=17-to-26)

Point Re Nu Point Re Nu12345678910111213141516171819202122232425262728

4673467846834689469346998828883588438851885788658870151801518915200152121521915230152372654426586266122662826636266584971349727

165164157154164153249253236229242221249341365337321349302363479445470432464496596698

29303132333435363738

49750497724978149809829848314183188832348326083325

675608650707864940940824814909

IoCOCO

Table 7 - E Friction data for channel - 4(X/De=18-to-29)


Shafiqul et al. : Channel - 4 (k/De=0.04, p/k=20, w/k=1.0)of Figure 7 , Figure 9, Figure 34 and Figure 36

Major parameters:

Rib widthRib heightRib pitchChannel height

Experimental data:

Tables 7- E and 8- E

: w=0.2 mm: k=0.2 mm: p= 4 mm: H=3.24mm

Point

1234567891011121314151617

Re3790477057746932818499511209314994185322205626109326843908546221577386976283886

fT0.023220.019460.018780.017390.017000.016180.015590.015120.014640.014370.014100.013930.013670.013470.013210.013050.01285

Table 8

Point

123456789101112131415161718

- E Heat transfer data for channel - 4

Re

638363946422643964856497650865176526653265387891790579397960801780328046

(X/D,=11-to-29)

Nu

180185165174158163166165154172178205212186198179184186

Point

192021222324252627282930313233343536

Re

80578068807680831321913235132861331413387134041342113432134431344813453234692355823606

Nu

185172194202280294251277243255257252226263273404362391

Point

3738394041424344454647484950

Re

2372923757237852380223827238344354643627438324387543918439424397243977

Nu

339361367353370388497576487519524491517551

I

I* « .ooI

Narrow channel (Smooth, 1997)

Channel designation:Shafiqu! et a l . : Channel - 5 Figure 8 and Figure 35

Major parameter:

Channel height : H=1.2mm

Experimental data:

Tables 9-E and 10-E

Table 9

Point

123456789101112131415

Table 10

- E Friction data for channel - 5

Re

241527913254398247415528708679679529120491604319901246952884733480

(X/D,=41-to-67)

fT

0.01340.01240.01170.01080.01030.00970.00880.00840.0080.00730.00670.00610.00570.00540.0052

- E Heat transfei

Point

12345678910111213141516171819

0.01130.01090.01050.00990.00950.00920.00860.00840.008

0.00750.007

0.00660.00630.00610.0058

Uh.-1.416/Re

0.022400.018670.016000.014000.012440.011200.008960.00747

• data for channel -5(X/De=42-to-62)

Re

4263427842864301430976477666767576947704130661309113103131271314021719217302174421759

Nu

53545352538690888486129139137124131196169168188

2

Table 11 -E Friction data for channel - 6(X/D,=18-to-30)

to

I

Narrow channel (Smooth , 1997)

Channel designation:

Shafiqul et al. : Channel -6 Figure 9 and 36

Major parameter:

Channel height : H=2.97 mm

Experimental data:

Tables 11-E and 12-E

Point

123456789101112131415

Table 12

Point

123456789101112131415161718

Re

48265824680882421018112297143512015124381301712806736292413385413898458

-E Heat

Re

470147124717472747318566858886028608144191442814446144542382623859238712389823908

fT0.0086930.0085790.0084070.0081410.0078420.0076260.0074500.0068670.0067300.0062300.0035910.0060920.0061060.0057730.005202

transfer data

fblasius

0.0094780.0090430.0086970.0082910.0078650.0075020.0072180.0066310.0063220.0059940.0061040.0057240.0055400.0051790.004460

for channel(X/De=18-to-27)

Nu

6666656464111112109112176169166169247257248233243

Point

192021222324252627

Uin,r=1.4*16/Re

0.022400.018670.014000.011200.00747

-6

Re

410824115641201412177245072550725887266972700

Nu

353357335356489538511472512

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ft

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7

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sAK

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rad

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lR=2.58xlO'C/kg

1 rad = lcGy=10"2Gy

1 rem= 1 cSv= 10 !Sv

10"10"10"10*

10*

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102

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7.03070 x 10'1

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9.86923

0.967841

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mmHg(Torr)

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735.559

760

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14.2233

14.6959

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1.35582

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1

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0.426858

107.586

0.138255

1.63377 xlO"20

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2.72407 x 10"'

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1.16279x10-'

2.93072 x 10''

3.76616 x 10'7

4.45050 x 10-"

cald+ftjt)0.238889

2.34270

8.59999 x 10 s

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252.042

0.323890

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9.29487 x 1 0 3

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1.51857x10-"

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0.737562

7.23301

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3.08747

778.172

1

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eV

6.24150x10"

6.12082x10"

2.24694x10"

2.61272 x 10"

6.58515 x 10"

8.46233 x 10"

1

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= 735.499 W

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Gy

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100

1

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3876

1

tt3ft

Sv

1

0.01

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100

1

(86 if 12 fl

EXPERIMENTAL STUDY ON HEAT TRANSFER AUGMENTATION FOR HIGH HEAT FLUX REMOVAL IN RIB-ROUGHENED NARROW CHANNELS

experimental study on heat transfer augmentation …

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