[American Institute of Aeronautics and Astronautics 45th AIAA/ASME/SAE/ASEE Joint Propulsion...

1

American Institute of Aeronautics and Astronautics

A Study of Side Wall Heat Transfer Augmentation in a Narrow

Rectangular Duct

Carson D. Slabaugh*, An P. Le

*, J. S. Kapat

†

Center for Advanced Turbine and Energy Research, University of Central Florida, Orlando FL 32826

This paper is an investigation of the heat transfer augmentation in the fully-developed portion of a narrow

rectangular duct (R=2) characterized by dimpled geometries on the bottom wall. Testing is performed at Reynolds

numbers of 20000, 30000, and 40000. Thermal efficiency of the channel is the ultimate goal for any cooling channel

design. The purpose of the paper is to find the performance of commonly used geometries on the side walls of the

channels. Data reported includes the Nusselt Number Augmentation of the side walls of the channel and the thermal

performance of the entire duct. A better understanding of the effects produced by these geometries will help in the

design and development of more effective cooling-channel design.

Nomenclature

English Symbols

AR Aspect Ratio = (H/W)

C Specific Heat Capacity

Dh Hydraulic Diameter

f Darcy Friction Factor

fo Darcy Friction Factor, Blasius Solution

h Heat Transfer Coefficient

H Height

L Length

Nu Nusselt Number = ((h*L)/k)

Nu0 Nusselt Number from Dittus-Boelter Correlation

P Static Pressure

Pr Prandtl Number = (υ/α)

R Dimple Radius

Re Reynolds Number = ((V*Dh)/υ)

S Longitudinal Pitch

V Fluid Velocity

W Width

Greek Symbols

α Thermal Diffusivity

δ Dimple Depth

υ Kinematic Viscosity

ρ Density

η Thermal Performance Factor = (Nu/Nuo)/(( f/fo)^(1/3))

Subscripts

o Baseline Value

P Constant Pressure

Superscripts -

Averaged Value

* Graduate Research Assistant, UCF – CATER, Student Member AIAA.

† Lockheed Martin Professor of Engineering, UCF – MMAE, Associate Fellow AIAA.

45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit2 - 5 August 2009, Denver, Colorado

AIAA 2009-5377

Copyright © 2009 by Copyright © 2009 by Carson Slabaugh. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

2


I. Introduction

ptimization of internal cooling channels has been a subject of a great deal of study in past years. Methods of

passive cooling have been studied in great detail with the application of wall-surface geometries to help

promote turbulence and increase heat transfer enhancement in the channel. The added roughness of the surface

geometries break up the laminar sub-layer of the channel flow and promote mixing. The price paid for this added

mixing, however, is an increase in pressure-loss throughout the length of the channel. With ever-growing demands

for increased efficiency of turbomachinery, a variety of wall-surface geometries have been developed and tested to

improve the heat transfer augmentation in the channel, while minimizing the pressure loss. A majority of the work

that has been done and is available in the open literature is studying the effect of these geometries on the surface to

which they are applied.

The thermal conductivity values of today’s cutting edge gas turbine materials are too low to assume uniform

temperature distributions around the internal cooling channels. It is important to look at the thermal performance of

all of the channel walls and their contributions to the thermal performance of the channel as a whole. Maximizing

the participation of these surfaces is important to minimize the thermo-mechanical stresses caused by excess

temperature gradients in the component. As such it is important to choose transport enhancing geometries that

promote the advection of heat away from the cooled component.

Dimples are negative features in a surface. They are most often spherical in shape, although many variations of

this shape have been investigated and reported in the open literature. Dimples are a very attractive method of

increasing internal cooling because they trigger the formation of multiple vortex pairs that produce substantial

Nusselt number augmentation as they are swept downstream. They also have a special application in low pressure

sections of the turbine cooling system due to their characteristically low pressure drop penalties. This is partially due

to the fact that dimples are primarily a negative feature and therefore, they produce very little form drag.

This geometry has been the subject of a wide variety of studies that encompass flows over a flat plate with regular

arrays of spherical pits (Afanasyev, Chudnovsky, Leontiev, & Roganov, 1993), flows in annular passages with

staggered concave dimple arrays on the inner side of a cylindrical surface (Belen'kiy, Gotovskiy, Lekakh, Fokin, &

Dolgushin, 1993), flows in hemispherical cavities(Kesarav & Kozlov, 1995) (Terekhov, Kalinina, & Mshvidobadze,

1995), flows in diverging and converging channels with hemispherical cavities (Schukin, Kozlov, & Agachev, 1995)

and flows in narrow channels with spherical dimples (Gortyshov, 1998). The most recent work on dimples is by

Glezer et al (Glezer, 2007), where they test over 30 various combinations of dimpled surfaces to enhance the heat

transfer in their heat exchanger.

Figure 1: Illustration of the Flow Structure over a Dimple

The key flow phenomena induced by the presence of dimples causing increased mixing an improvement in heat

transfer can be summarized as follows. The shedding of multiple vortex pairs from dimples arrays increases

turbulence within the flow, improves mixing and therefore improves the heat transfer performance of the channel.

Creation of strong secondary fluid motions within these vortical packets of fluid promotes this effect. Flow

reattachment inside the dimples causes an area of improved heat transfer as the fluid impinges onto the wall (see

Figure 1). Lastly, the unsteady nature of the vortex generation and ejection from the indention causes a periodic

dissipation and reformation of the thermal boundary layer downstream of the dimple over the affected area. Figure

1 illustrates the combination of flow effects observed from a flow over a spherical dimple. These effects have been

proven to produce appreciably increased performance in channel heat transfer coefficient.

O

3


It is important to note that, in a real application, more than one dimple is applied to the heat transfer surface.

Frequent arrangements can include a single row, or a large staggered array. In which case, there will be many more

vortex interactions taking place, that could be helpful or detrimental to channel performance overall. For example,

if the dimples are closely spaced in the span-wise direction, the secondary vortex formations could interact with

each other from both dimples. It is also possible to have interactions of the primary vortices in the longitudinal

direction for consecutive rows of dimples.

This project is a study of the heat transfer and pressure-loss characteristics of a rectangular duct that has an array

of dimples applied to the bottom wall-surface. Three geometries are designed based on available data in open

literature, then fabricated and installed bottom walls of the tested channels. The details of these augmentation

geometries are described in greater detail to come. Testing is performed at Reynolds Numbers of 20,000; 30,000;

and 40,000. The two goals of the study are: to understand the heat transfer effects that result from the application of

dimples to the bottom wall of a narrow rectangular channel and improving the thermal performance of the channel is

the goal of this study. Data is collected from an array of thermocouples and pressure taps and analyzed to determine

the average Nusselt Number values in the channel as well as the friction factor augmentation throughout the

channel. Nusselt Number augmentation will be compared to the correlation values established by the Dittus-Boelter

Correlation. Friction Factor augmentation will be compared to baseline values established by the Blasius solution

for turbulent flow in a duct. These augmentation values will then be combined into an overall Thermal

Performance Factor, η, which will be the basis of comparison between the tested geometries. It is the interaction of

the secondary flows, caused by the dimples, with the side walls that becomes very important in a narrow duct. This

is the contribution of this study.

II. Experimental Setup

A. Experimental Apparatus

The experimental setup used for the testing of this study is shown in Figure 2 below. The total length of the

channel is approximately thirty-five hydraulic diameters and the channel aspect ratio is 2 (AR=2). When operating

as designed, the air supply enters through the right side of the heated test section and exits to atmospheric

conditions.

Figure 2: Experimental Apparatus

The fluid used in all tests is air, supplied from an external compressor and dehumidified by an inline condenser.

The flow rate of the air is regulated by the inline pressure regulator. The flow-rate is measured by the inline flow-

meter. The temperature of the inlet air is monitored with thermocouples located at the entrance of the duct. Pressure

is measured throughout the length of the channel with an array of 50 pressure taps oriented on the horizontal mid-

4


plane of the channel. In order to identify the fully developed region and to isolate the entrance and exit effects, the

duct wall is longitudinally divided into a number of identical modules each with a length of approximately 2.5

Hydraulic Diameters. Each test module contains four pieces of copper that form the walls of the internal channel.

Two thermocouples are assembled into machined holes in the back of each copper block for temperature data

collection using a Measurement Computing© data acquisition system.

Heat is supplied to the flow by an array of foil heaters that are bonded to the back of the copper blocks with high

thermal conductivity, double-sided Kapton™ tape. The heaters are manufactured to cover the surface of the copper

block exactly. Power is supplied to the heaters by an 1800 Watt DC power source. Additionally, the top bottom,

and side heaters are each controlled by an array of rheostats such that the power to each surface of each heater can

be adjusted individually to achieve constant heat flux throughout the length of the channel. It is also important to

note that the copper blocks are assembled into and acrylic housing and insulated to minimize heat leakage as shown

in Figure 3 below.

Figure 3: Cross-Section of Channel

The acrylic is shaped in a way as to provide interconnectivity between modules so that it is easy to keep the shape

of the channel under any testing condition. The acrylic is also meant to provide a structure that will allow the

copper to form a channel, but without directly linking the copper pieces. This, in effect disrupts any lateral

conduction between copper pieces. Alignment of the channel is guaranteed during the assembly process by inserting

a long aluminum alignment bar into the channel being assembled.

B. Surface-Geometries

Three different dimple geometries are tested to determine the resulting improvement in channel effectiveness. The

dimples are arranged in a staggered manner throughout the length of the channel

Table 1: Non-Dimensionalized Description of Dimple Geometries

NOTE: Dimple Radius (R) is given with respect to Hydraulic Diameter of Channel

CASE R H/d delta/d P/d S/d

A 0.533 0.946 0.236 0.775 1.001

B 0.358 1.333 0.250 1.000 1.411

C 0.358 1.010 0.189 0.758 1.069

D

5


Figure 4: Three Dimple Geometries Tested

To better understand the phenomena caused by the dimples, the three dimple arrays vary in both size as well as

shape from arrangements commonly found in literature. The first dimple shape is the largest of the three, as can be

seen in Table 1 and Figure 4(A) above. The second augmentation geometry is very similar to the first geometry in

that the axial and lateral spacing of the individual dimples is maintained. The key difference in this case is that the

difference in the radius of the dimple itself. In this case, not only is the circular ‘foot-print’ of the dimple on the

channel surface decreased, but the depth of the dimple itself is reduced as well. The final geometry is a pair of two

dimples manufactured such that there is a ridge separating the two entities at the bottom of the pit. The radius is

maintained from the second geometry as well as the lateral and axial spacing of the dimple pairs. The print diameter

of this case was determined by calculating the total print diameter of the double-dimple pair, then dividing out a

normalized dimple radius.

III. Experimental Procedure

To test the friction factor augmentation, the flow is first set to desired Reynolds number in the test section. Static

pressure measurements are taken using a Scanivalve® device throughout the length of the channel, to determine the

static pressure profile throughout the fully developed region of the channel. Heat Transfer Testing is performed

using steady-state methods for the determination of an average Nusselt Number profile as a function of hydraulic

diameter. After establishing a flow of the desired Reynolds Number through the test section, a constant heat flux is

supplied to the channel via the DC power supplies. Once the temperatures have reached a steady-state: (less then

0.5°C change per one-half hour), temperature data is taken from the thermocouples. Knowing the heat supplied to

the channel and the temperature distribution, the Nusselt Number profile throughout the channel can be determined.

These values are compared to a correlation values established by the Dittus-Boelter Correlation for the specific

Reynolds number to yield an augmentation profile throughout the channel.

IV. Data Reduction

A. Pressure Profile Testing

For the analysis of the pressure profile data taken, the following procedure was followed:

�� 0.316 ��

�

(1)

� �

��

��

0.5 � ��

(2)

where ��

�� is measured across the fully developed portion of the channel. This criteria is known to be met by

examining the pressure profile data collected from the array of pressure taps placed along the stream-wise direction

of the channel side walls. This is necessary to give an accurate representation of the thermal performance of the

channel, where friction factor augmentation is compared to Nusselt number augmentation in the fully developed

portion.

(C) (B) (A)


6

B. Heat Transfer Testing

To determine the average Nusselt number of the channel first the power generated by the foil heaters was found

knowing that

��

(3)

where V is measured for each test and adjusted such that constant heat input is always achieved throughout the

length of the channel. The resistance of each heater is known, as a function of temperature and is therefore

calculated for each test as well. The heat leakage from each wall of each heating module is also known as a function

of temperature and is therefore calculated for every test. It is then known that the power actually added to the flow

is the difference between the total heat generated the heat lost.

�!" �!� � �� # ��%&&

(4)

It is important to note that the effects of lateral conduction between the modules were calculated and found to be

less than two percent of the actual heat conducted through the channel walls to the flow itself. It is, therefore,

considered negligible for the purposes of these calculations. Also, due to the very low Biot number of the copper

blocks forming the channel walls of each module, the channel wall temperature-profile is assumed to a step function,

where the temperature of each wall of each module is the average of the measured values taken by the two

thermocouples. This assumption is verified by the fact that the temperatures measured by the two thermocouples are

invariably with 1.5°C of each other, which is within the ±1°C range of accuracy for the thermocouples being used.

It is therefore assumed that the wall temperature of each wall of each module is the temperature at the center-point

of that surface.

Due to the location of the thermocouples, this power calculation must be modified slightly in order to correctly

find the amount of power added before the point where the wall temperature is assumed to be taken. The power

added to the flow from one thermocouple location to the next is that which should be considered for determination

of the heat transfer coefficient. This value is found to be the sum of the heat transferred to the flow from the second

half of the preceding copper block and the first half of the down-stream copper block where the specific

thermocouple is located.

�!��'�(� 0.5 �!" �!�()

* 0.5 �!" �!�(

(5)

This idea is also applied to the calculation of the local bulk mean temperature of the flow where:

+,��-�� +,��-��.

*�

/0 1�

(6)

And

� � 0.5 2� %�() �,% %3()

�&��'() 4 * 0.5 2� %�(

�,% %3( �&��'(

4

(7)

Knowing the Bulk temperature throughout the flow and the exact value of the power added to the flow at each

point of temperature measurement, the heat transfer coefficient can be calculated and Nusselt number. The

experimental results for Nusselt number are compared to correlation values established by the Dittus-Boelter

correlation to establish the heat transfer augmentation value for each case. Bulk temperature change throughout the

channel was maintained at approximately 20°C. The temperature different between the wall and the fluid was

maintained at approximately 50°C.

The Thermal Performance of the duct is calculated by finding the span-wise average of the Nusselt number

augmentation values for each wall the fully-developed section of the channel.

5 �

6767�

��

./9 (8)


7

The Nu/Nuo is found by taking the area-weighted average of the Nusselt number for each wall in the fully

developed portion of the channel. This form is used to normalize the change in the heat transfer performance of the

channel that would results from a change in Reynolds number that would be the effect of a change in the friction

factor of the channel given a constant value for pumping power driving the flow.

C. Uncertainty

The calculated uncertainty for the final results was performed using the procedures described by Kline and

McClintock (Kline & McClintock, 1953). The overall uncertainties for the channel Reynolds Number were

approximately ±3.7% (with higher uncertainty being at lower Reynolds number). The average Nusselt number

uncertainty was found to be ±7.6%.

V. Results

Baseline tests were first run to validate the heat transfer and friction factor results from the experiment by

installing smooth-surface copper blocks on the bottom wall of the channel. All testing parameters were held

constant, including inlet conditions, channel Reynolds numbers, and all other channel dimensions. Baseline results

yielded acceptable Nusselt number values, within the uncertainty of the experiment, with respect to the Dittus-

Boelter correlation in the fully-developed region of the duct for all three Reynolds numbers being tested (Figure 5).

Similarly, the experimental friction factor fell within about 2% of the value predicted by the Blasius solution at a

Reynolds number of 20000, and approximately 10% for the 30000 and 40000 Reynolds number cases. These results

provide an idea of the bias present in the remainder of the cases with flow augmenting surface features present.

From Figure 5, it can be seen that the small dimples have only a very minor effect on the performance of the

channel. This is thought to be because of the relatively high Reynolds numbers being tested. The footprint of the

dimple is thought to be too small to provide any appreciable effect on the side walls of the channel with such high

fluid momentum in the channel.

Figure 5: Block-by-Block Nusselt Number Ratio

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

10 15 20 25 30

Nu

/N

uD

B

X/DH

Reynolds Number = 20,000

Large Dimples

Small Dimples

Double Dimples

Smooth Wall

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

10 15 20 25 30

Nu

/N

uD

B

X/DH


Large Dimples

Small Dimples

Double Dimples

Smooth Wall

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 15 20 25 30

Nu

/Nu

DB

X/DH


Large Dimples

Small Dimples

Double Dimples

Smooth Wall


8

An interesting phenomenon was found from the large dimple case at approximate 20Dh downstream from the

channel entrance. There is a rise in the heat transfer coefficient over a range of approximately 3 copper blocks. To

confirm the existence of this phenomenon, a repeatability study was performed. To expose any changes in the

experimental rig, the order of the modules was changed in a random manner in a series of 4 repeated tests. Testing

was also performed by a different individual for two of the repeated tests, yielding to a total number of varied factors

of 3. In this work, the existence of this peak was confirmed at a 90% confidence interval with an variation of only

13% in the calculated heat transfer coefficient along the length of the channel for the repeated tests.

Figure 6 illustrates a sharp increase in the Nusselt number augmentation caused by the large dimples at a channel

Reynolds number of 30000. This graph shows the average Nusselt number augmentation over the fully-developed

portion of the channel as a function of Reynolds number. The existence of this peak is indicative of a high level of

turbulence transport that is generated, which can be understood when one considers the considering the momentum

of the fluid through the channel. For this particular dimple geometry, a Reynolds number of 30000 represents an

optimal value of fluid momentum for fluid to enter the concave feature and an escape, producing a very high

turbulence intensity and vortex shedding that spreads to advect heat from the side-wall surfaces as they are swept

downstream. In contrast, at a Reynolds number of 20000, the flow is hypothesized to not have enough energy to

produce the intense vortices created by the 30000 Reynolds number case. Additionally, at a Reynolds number of

40000, the flow is thought to have too much momentum for this dimple size and, in this case, rather than dropping

into the feature, then being swept back up into the mainstream to improve mixing the fluid may simply be flowing

right over the dimple. Figure 1 provides a greater understanding of this concept.

Figure 6: Summary of Nusselt Number Augmentation Results

The testing of the double dimple surface feature revealed a very interesting result. From Figure 5 it can be seen

that the Nusselt number augmentation on the channel side walls resulting from the application of double dimples to

the bottom wall of the channel was the highest of any tested geometry for all of the Reynolds numbers tested. The

beauty of this feature is further exaggerated by the relatively small pressure drop that was also seen for all of the

Reynolds numbers tested. Similar results were also discovered by Afanasyev et al. who concluded that, in a

Reynolds number range of approximately 10000 to 30000, heat transfer performance of a channel with dimpled

wall-surfaces could be enhanced by as much as 30-40% with only a negligible increase in friction factor.

0

0.5

1

1.5

2

2.5

15000 20000 25000 30000 35000 40000 45000

Bottom Wall

Large Dimples

Small Dimples

Double Dimples

0

0.2

0.4

0.6

0.8

1

1.2

1.4

15000 20000 25000 30000 35000 40000 45000

Top Wall

Large Dimples

Small Dimples

Double Dimples

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

15000 20000 25000 30000 35000 40000 45000

Side Wall

Large Dimples

Small Dimples

Double Dimples

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

15000 20000 25000 30000 35000 40000 45000

Overall Channel (Averaged)

Large Dimples

Small Dimples

Double Dimples


9

Figure 6 presents the averaged side-wall Nusselt number augmentation in the fully-developed portion of the

channel, represented in the local plots Figure 5. As expected, the featured wall exhibited the highest level of Nusselt

number augmentation, followed by the side walls. The increase in Nusselt number on the side walls is indicative of

the induced participation created by the surface features on the bottom wall. Side wall effects were found to be very

important in the overall performance of the channel in the Large and Double dimple cases.

The level of the area-weighted average Nusselt number augmentation values (presented in Figure 6) were compared

to similar studies available in the open literature. In many of these cases, the fluid mixing and vortex interactions

caused by a much wider array of dimples led to significantly higher values for heat transfer and friction

augmentation. This is to be expected because of the narrow channel width and the limited number of surface

features that could be applied for this study. Chyu, et al. tested a staggered array of hemispherical and tear-drop

dimples at Reynolds numbers of 10000 to 50000. The dimples tested were very similar in size and shape to those

tested in this study but were arranged in a broader array. The friction factor results varied from 1.5 to 5 and his

overall Nusselt Number enhancement was found to be 2.5. In another study, Hwang et al. studied internal channels

with dimples and protrusions applied to one and two walls of the channel. At a Reynolds number of 10000, this

work concluded that a channel with dimple of similar concavity to those of this study, yielded a heat transfer and

friction augmentation of 2.0 and 2.2, respectively for a staggered dimple array 6/7 dimples in the span-wise

direction. While these results vary from those obtained in this study, it is logical to say that the number of dimples

present and the vortex interactions between them could be the cause of the discrepancy.

As would be expected, the friction factor augmentation of the channel is significantly higher for the channel with

the larger augmentation geometries than that of the smaller geometries. The small dimples were found to exhibit no

appreciable increase in the friction factor of the channel. This fact, in conjunction with the negligible increase in

Nusselt number augmentation gives the understanding that shows no major increase in the thermal performance of

the channel side-walls with the small dimple geometry. The large dimples tested showed an increase in friction

factor of as much as 50%. The double dimple feature exhibited an increase in the channel friction factor of

approximately 10% over the fully developed portion of the channel for all of the Reynolds numbers tested.

Figure 7: Friction factor augmentation as a function of Reynolds number

As was stated, thermal performance of the channel is the goal of the design. The calculated thermal performance

factor of the channel as a whole is given in

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

15000 20000 25000 30000 35000 40000 45000

f/f 0

Reynolds Number

Friction Factor Augmentation vs. Reynolds Number

Smooth Wall

Large Dimples

Small Dimples

Double Dimples


10

Table 2, below, for each test run. Note that the same trend is present as was seen in the side-wall Nusselt number

values where the large dimples run at a Reynolds number of the 30,000 shows the highest thermal performance of

any combination by more than 15%.

Table 2: Thermal Performance Values for Entire Channel

Reynolds

Number

Case 1

Large Dimples

Case 2

Small Dimples

Case 3

Double Dimples

20,000 1.192 1.163 1.343

30,000 1.367 1.058 1.403

40,000 1.187 1.192 1.398

VI. Conclusions

The application of dimples to the bottom wall of a narrow rectangular channel does in fact have a marked effect

on the heat transfer performance of the channel side walls. It is also apparent that the sides are impacted differently

than the dimpled bottom surface or non-dimpled top surface of the channel.

1) It was found that, for the given parameters of the Large dimple case, there is a peak in the side wall

participation as well as the overall channel performance at a Reynolds number of 30000.

2) The Double dimple surface feature exhibited very effective heat transfer enhancement and drastically

improved the heat transferred from the channel side walls for all of the tested Reynolds numbers. This

is accompanied by a relatively low increase in pressure drop through the channel.

3) In a narrow channel the effects of the channel are weighted for more heavily than in a channel with a

comparatively larger aspect ratio.

Acknowledgments

This work was completed at the Laboratory for Turbine heat Transfer and Aerodynamics with the support of the

Center for Advanced Turbine and Energy Research at the University of Central Florida.

References

Afanasyev, V. N., Chudnovsky, Y. P., Leontiev, A. I., & Roganov, P. S. (1993). Turbulent Flow Friction and Heat

Transfer Characteristics for Spherical Cavities on a Flat Plate. Experimental Thermal and Fluid Science , 7, 1-8.

Belen'kiy, M. Y., Gotovskiy, M. A., Lekakh, B. M., Fokin, B. S., & Dolgushin, K. S. (1993). Heat Transfer

Augmentation Using Surfaces Formed by a System of Spherical Cavities. Heat Transfer Research , 25 (2), 196-203.

Griffith, T. S., Al Hadhrami, L., & Han, J.-C. (2003). Heat Transfer in Rotating Rectangular Cooling Channels

(AR=4) With Dimples. Journal of Turbomachinery , 125, 555-563.

Han, J.-C., Dutta, S., & Ekkad, S. V. (2000). Gas Turbine Heat Transfer and Cooling Technology. New York, New

York, United States of America: Taylor and Francis.

Jorgensen, S. W., & Leahy, J. H. (2003). Patent No. 6568187. United States of America.

Kesarav, V. S., & Kozlov, A. P. (1995). Heat Transfer Research , 25, 156.

Kline, S. J., & McClintock, F. A. (1953). Mechanical Engineering , 75, 3-8.

Mahmood, G. I., & Ligrani, P. (2002). Heat Transfer in a Dimpled Channel: Combined Influences of Aspect Ratio,

Temperature Ratio, Reynolds Number, and Flow Structure. International Journal of Heat and Mass Transfer , 45,

2011-2020.

Mahmood, G. I., Hill, M. L., Nelson, D. L., Ligrani, P. M., Moon, H. K., & Glezer, B. (2001). Local Heat Transfer

and Flow Structure on and Above a Dimpled Surface in a Channel. ASME Journal of Turbomachinery , 123, 115-

123.

Moon, H. K., O'Connell, T., & Glezer, B. (2000). Channel Height Effect on Heat Transfer and Friction in a Dimpled

Passage. Journal of Engineering Gas Turbine and Power , 122, 307-313.

Patrick, W. V. (2005). Computations of Flow Structures and Heat Transfer in a Dimpled Channel at Low to

Moderate Reynolds Number. Masters Thesis, Virginia Polytechnic University, Blacksburg, VA.


11

Schukin, A. V., Kozlov, A. P., & Agachev, R. S. (1995). Study and Application of Hemispherical Cavities for

Surface Heat Transfer Augmentation. 44th International Gas Turbine and Aeroengine Congress and Exposition,

(pp. 1-6). Houston, TX.

Terekhov, V. I., Kalinina, S., & Mshvidobadze, Y. (1995). Russian Journal of Engineering Thermophysics , 5, 11.

[American Institute of Aeronautics and Astronautics 45th AIAA/ASME/SAE/ASEE Joint Propulsion...

Documents

Transcript of [American Institute of Aeronautics and Astronautics 45th AIAA/ASME/SAE/ASEE Joint Propulsion...