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Enhancement of Convective Heat Transfer on A Flat Plate by Artificial

Roughness and Vibration

M. A. Saleh

Associate Professor, Mechanical Power Eng. Department Faculty of Eng., Zagazig

University, Zagazig, Egypt

Abstract :

This paper is concerned with the application of vibration simultaneously with artificial

surface roughness techniques as a combined turbulence promoter for convective heat transfer

enhancement. The study was conducted on a flat plate in parallel flow and zero external

pressure gradient for the free stream. For artificial roughness, grooves were made in the heat

transfer surface and perpendicular to flow direction. Two different groove cross-sectional

geometries were considered: V-shaped grooves and square-shaped grooves. The case of a

non-grooved surface (natural roughness case which is also referred to as “smooth surface”

case) was also considered. For vibration, two parameters were investigated; both for the

smooth plate and the artificially-roughened one, namely: the frequency ( ranging from 0 to

100 Hz) and the amplitude (ranging from 2mm to 20 mm). For a vibrated non-grooved

(smooth) plate, experiment shows that vibration is a powerful enhancement tool, the heat rate

increasing more than 2.5 fold. Frequency and amplitude of the imposed vibration both have

positive effect on heat transfer enhancement. For a vibrated artificially-roughened (grooved)

plate, the amplitude effect on heat transfer enhancement appears positive up to a certain limit.

Here, increasing the amplitude beyond a certain value produces an unexpected decrease in the

enhanced heat transfer. This phenomenon may be attributed to the formation of an overlap

boundary layer associated with large amplitudes. Moreover, the effect of frequency appears

stronger than that of the amplitude. The results show also that the non-grooved plate differsfrom the grooved one (artificially-roughened plate).

Key words: heat transfer , roughened surface, vibration.

Introduction:

The fast technological progress of

nowadays has directed the attention of

research workers to investigate possible

techniques of heat transfer augmentation in

various engineering systems. Some such

techniques resort to artificial roughening of

heat transfer surfaces, introducing vortexgenerators at inlet, applying an electrostatic

field, modifying the duct cross section and

surface, and vibrating the heat transfer

surface. These techniques result in an

increased heat transfer coefficient due to

change in the flow pattern. Considerable

attention has been focused on heat transfer

augmentation by means of vibration and

grooving of surface. The influence of

vibration on convective heat transfer has

been discussed earlier in the literature [1-8].From this survey, it is found that vibration

can be a powerful heat transfer

enhancement tool. However, most

vibration studies were carried out on

spheres and cylinders. Vibrating plates

appeared only in very few studies. The

effect of vibration on an artificially-

roughened plate has not been found in the

literature. Therefore, more work is neededin this area.

During recent years, there has been

considerable interest in the effect of

vibration on convection heat transfer

processes. Most studies in this area can be

classified into two basic categories. In one

category, oscillatory motion is applied to

the surface and this is referred to as “

surface vibration “. In the other category,

pulsating motion is imposed on the flowing

fluid, thus producing a pulsating flow.

Proceedings of the 2006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miami, Florida, USA, January 18-20, 2006 (pp69-77)



One of the practical problems,

which originally inspired interest in the

effect of vibration on heat transfer, was

encountered in rocket propulsion motors

[9]. As combustion instability of high

amplitude occurred in such motors, thelocal heat transfer to the motor walls

drastically increased and the wall

temperature rose to the point where the

motor was destroyed. On the other hand,

the application of vibration in mass transfer

was first patented byVan Dijcket et al [10]

who suggested to vibrate either the surface

or the liquid contents of an extraction

column to improve its efficiency. This is

the principle of pulsed columns which is

widely applied in the nuclear field.Vibration can be looked upon as a

powerful tool for heat transfer

enhancement. However, most of vibration

studies were carried out on non-flat

surfaces (spheres and cylinders) [11] while

vibrating plates appeared only in a very few

cases, a situation that calls for more work is

this area. Numerous works on thermo-

vibrational convection focused on

stabilizing or destabilizing effects of

vibration on convective flows and/ or heat

transfer enhancement due to vibration.

Shrifulin [12] investigated the effects of

vibration on heat transfer enhancement and

flow properties. Ivanova and Kozlov [13]

conducted an experimental study of heat

transfer enhancement between two coaxial

cylinders under vibration. Forhes et al [14]

carried out a similar experimental study on

a liquid-filled rectangular cavity and noted

a marked increase in the heat transfer rate by vibration. Gresho and Sani [15]

published results of an investigation of

stabilizing / destabilizing influences of

vibration on a fluid between two infinite

planes at different temperatures. They were

interested in determining the shift due to

vibration in the critical Rayleigh number

needed to induce convective motion.

Upenskii and Favier [16] studied the

feasibility of using high frequency vibration

to suppress convection in a typicalBridgman – scheme crystal growth process.

Also, Fu and Shich [17] studied the heat

transfer rate for the classical 2D square

cavity problem. Frank [18] completed a

study of thermo-vibrational convection in a

vertical cylindrical cavity for various values

of Rayleigh number and the vibrationalGrashof number. Results indicate that

vibrational convection greatly increases

heat transfer rate over the unmodulated

case.

Most studies of jet impingement

cooling focused mainly on circular tube

with/without either decaying or continuous

swirling flow on a flat plate. The

impingement cooling on a flat surface by

means of a jet issuing through longitudinal

swirling strips had been performed. In atypical package, heat dissipation elements

are often used with the vibrating surface

since many electronic circuits are designed

to produce higher level of heat dissipation

per unit of component surface area. In

addition, Chilled tower (air-cooled type)

equipped with a mini vibrating motor is a

cooling device combined with the vibrating

surface. However, heat and fluid flow,

which are considered by engineers to

develop specifications for jet cooling or

drying systems, rarely account for surface

vibration effects. The behavior of the

impinging jet on the vibrating roughened

surface is not well known because most of

the investigations focused on impulsively

started gas jets.

The present work is a continuation

of our previous study of heat transfer

between constant-heat-flux test plate and

impinging jet with longitudinal swirlingstrips[20]. The literature apparently

contains no report of any effort, either

analytical or experimental, on the

determination of the combined effects of

vibration and artificial roughness on natural

or forced convection heat transfer of a flat

plate. This paper is apparently the first

report on this type of work. There have

been numerous published reports

(e.g.[20],[21]) concerning experimental

investigation of the convective heat transfer mechanism on roughened surfaces. The




focus of previous investigations was on

heat transfer between the stationary

roughened-surface test plate and the

impinging jet, but the combination between

roughness and vibration has hitherto not

been investigated. Here, the heat transfer between a vibrating roughened surface test

plate and an impinging jet will be

examined. With the vibrating plate, the

flow structure of an impinging jet changes

and the heat transfer characteristics of the

plate will also be affected by such change

in the flow structure. Successful predictions

and correlations of the effect of vibration on

convective heat transfer on a roughened flat

plate usually incorporate the amplitude and

frequency of the vibration. In the presentwork, the frequency of vibration was varied

from 0 to 100 Hertz and the amplitude from

2 to 20 mm. Also, the spacing ratio and the

shape of the surface were varied.

Experimental Setup

The experimental apparatus is

similar to that used by author and described

in ref.[20]( a layout is shown in fig.(1)).

However, a brief description is presented

here.

A compressor supplies the flow

which passes though a heat exchanger, a

shut-off valve, a filter, a flow meter and a

plenum chamber and finally reaches a

stainless steel injection tube. The tube is of

an internal diameter of 10 mm a wall

thickness of 1.0 mm, and 30D long (enough

to obtain fully developed flow at jet exit).

Several injection tubes were used each

having its own impingement plate. All test plates were rectangular (300mm x500mm),

each consisting of 6 mm-thick aluminum

plate, differing only in surface topography

as indicated (smooth surface, square

notches and V notches). A heat exchanger

was installed to obtain a constant

temperature flow at nozzle exit and to

reduce the temperature difference between

the ambient air and the air nozzle exit

within±0.3 °C.

A DC motor (with variable speeds) powered the drive cam-shaft (four

camshafts were used giving amplitudes

from 2 mm to 20 mm). With this system,

the oscillation frequency of the plate, f,

could be set in the range of 10 to 100 Hz. It

can be measured by using the integrating

vibration meter type 2513. This device wassated the screwdriver switch at “lin” to read

the frequency by Hz. The relative amplitude

of vibration of the flat surface ranged from

2.0 to 20 mm.

Experimental Procedure

Three test cases of a jet impinging

normal to a vibrating surface were

considered. In one case, a plate with

smooth surface (non-grooved surface) was

examined, in the second case, a surfacewith V-shaped grooves was tested. The

third case considered a surface with square-

shapes grooves. The experiments were

conducted for various Reynolds numbers

(500 to 26000), vibration frequencies f (0 to

100 Hz) and relative amplitudes (2 mm to

20 mm). The distances from jet exit to

impingement point [z/D] had values

(changed from 5 to 15). In each test run,

after a steady state was secured, the

temperature distribution on the test plate

was measured with power connected to

heater coils. A steady state was usually

reached in approximately 3h.

Calculation

The gross heat flux (q”g) in the

heating foil was controlled by varying the

output voltage by a varic and this heat was

measured by a Wattmeter. The convective

heat flux q” cov can be calculated

q”cov= q”g –q”loss (1)The term q”loss is a small correction

for conduction and radiation loss from the

element. This correction never exceeded

2% of q”g in the present study.

The local heat transfer coefficient

was determined from:

h= q”con/(Tw-Tad) (2)

Experimental results for heat

transfer will be presented in terms Nusselt

number (Nu=hD/K) distributions for various

conditions.




Also, the local Nusslet number at the

stagnation point was calculated by using the

local heat transfer coefficient at such point.

The average Nusslet number is

calculated by numerical integration as

follows:

∫=− r

o2

dr . Nur r

2u N (3)

Uncertainty Analysis: The uncertainty analysis was based

on the methods suggested by Kline and Mc

Clintock [22] and Moffat [23]. The

maximum measurement uncertainties were:

Heat flux: ± 1.7%; Heat transfer coefficient:

± 5.22%; Nusselt number: ± 5.5%,

Reynolds number: ± 2.53%, frequency: 3%and amplitude: 3.2%.

Results and Discussion

The flow field, extending from jet

tube exit to impingement surface under

vibration can be divided into six distinct

regions as shown in Fig.(2) for the three

plate configurations (smooth surface (non-

grooved), square-grooved surface, and V-

grooved surface). These regions are : (1)

free jet region; (2) impinged area region;

(3) cross flow region; (4) separated flow

region; (5) entrainment region; and (6)

region of axial oscillation of surface flow.

This methodology is consistent with those

of other studies similar, with a slight

difference shown in Fig.(2), (e.g. Huang

and Genk [24] and Shleen and Gussain

[25]). Before hitting the surface, the air

flow exiting the jet tube a free jet flow

(region 1). This free jet is turbulent but not

fully developed upon impinging thesurface. Just below the free jet flow, resides

the impingement area (region 2). This

impingement area in the vicinity of the

stagnation point has a diameter of 1.5d to

3.0d, depending on jet to-plate distance and

Reynolds number, upon impinging the

surface, the greater part of the flow kinetic

energy is converted into a static pressure

energy, forcing the air to flow in a

boundary layer along the surface (region 3).

The cross flow region decelerates quicklyupon away from the stagnation point due to

increase in the flow cross-sectional area and

the entrainment of surrounding air. As the

boundary layer flow becomes laminar and

thicker, the flow kinetic energy becomes

too low to sustain radial flow.

Subsequently, the combined effect of radiallaminar flow and entrainment (region 5)

causes the formation of vortices (separated

flow) at some distance from the stagnation

point (region 4). In addition, vortex

formation from shear layers is modified by

plate acceleration when the plate is forced

to vibrate (region 6). This modification

process caused by the plate acceleration is

synchronized with the outward radial

movement of the vortex. The flow field for

the square-grooved surface (Fig.(2b)) isdistinctly different from that of smooth

surface as shown in Fig.(2a). The square

groove stimulates more entrainment of

surrounding air. The impingement area

(region2) of the square groove is

significantly layer than that of the smooth

surface at the same conditions. These

grooves also break the laminar flow and

converts it to turbulent flow with some

vortices forming in the grooves. The flow

model developed for V-grooved surface in

fig.(2c).

The local Nusselt number

distribution along the plate with and

without the vibration( for f=50Hz,

am=10mm, Re=17000 and z/D=6) is shown

in Figure (3) for three surfaces of different

topographies. It is shown that in all cases,

the local Nusselt number decreases with by

the radial distance measured from the

stagnation point. However, Nu values withV-grooves are much higher than with

square grooves and smooth surface,

particularly at and around the stagnation

point. It appears that Nu for a vibrated

smooth plate, compared with a non-vibrated

plate, increases by 2.5 fold.

Fig.(4) shows the effect of the

vibration frequency on the stagnation

Nusslet number Nuo. This figure shows Nuo

versus vibration frequency with a relative

amplitude am =10 mm at z/D=6 andRe=17000 for three surface topographies.




with different shapes. It is noted that Nuo

increases with vibration frequency. The

waves generated by the vibrating device

appear to be reflected at the top of the

plate. However in the case of v-grooves,

these reflected waves cause the air film toroll up, resulting in a forced convection

region that is characterized by convection

and conduction together at the solid-air

interface. Consequently, the heat transfer

coefficient increases.

Fig.(5) presents the effect of

vibration amplitude on the stagnation

Nusselt number Nuo. From Fig.(5), it is

observed that for a given vibration

frequency (f=50 Hz), Nuo increases with

the amplitude of vibration up to maximum, beyond which with amplitude. This

phenomenon may by attributed to the

formation of an overlap boundary layer

associated with large amplitudes.

Fig(6) shows the variation of Nusslet

number average , Nu, with vibration

frequency. As expected, Nu increases with

frequency with a trend similar to that of the

stagnation (Nuo). It was found to be shown

in Fig(4). These results tend to suggest that

with high vibration frequencies, the

interface between the solid wall and the air

becomes more turbulent. The reflected

waves from the vibrating device lead to

cool air film hold-up resulting in a forced

convection region. The effect of surface

topography is clear.

Fig(7) shows the effect of the

amplitude on the average Nusselt number .

The result shows a similar behavior as with

Nuo (Fig(5)).Fig(8) shows the variation of the

stagnation Nusselt number (Nuo) ) with

nozzle-to-plate distance(z/D) for three

surface topographies considered the with

and without vibration. These is a slight

dependence of Nuo on Z/D when the plate

is non-vibrated bat. A significant

dependence appears with vibration and Nuo

decreasing with Z/D.

Fig.(9) is a repetition of Fig(8) but

for the averaged Nusselt number. We havethe same trend here also.

Conclusion

The present investigation leads to

the following conclusions:

1- Increasing the amplitude beyond a

certain limit produces an unexpected

decrease in the enhancement of heattransfer.

2- The effect of vibration frequency is

stronger than that of the amplitude.

3- The enhancement of heat transfer is

strongly dependent on of both

roughness and vibration compared

with a non -vibrated the smooth

surface.

4- Roughness can save vibration energy,

since the same heat transfer rate can

be obtained with a lower frequencylevel than needed for may be a

smooth surface.

Nomenclature

A : Surface area of the test plate[m2]

am: Surface vibration amplitude[mm]

D :Inner diameter of the tube [mm]

f : Frequency of plate vibration [mm]

G : Acceleration of gravity [mm/sec2]

g :Groove depth, mm

Gr: Grashof Number(Gr=λ g L3/µ2)

h : Heat transfer coefficient w/m2

k]

Z : Jet to plate distance.

k : Thermal conductivity of the fluid [w/m

k]

L : Length of surface active area [mm]

Nu : Local Nusslet number [Nu=h L/α]

Nu : Average Nusslet number [Nu=h L/α]

Nuo : Local Nusslet number at stagnation

point [Nu=h L/α]

q”cov: convective heat flux [w/m

2

]q”g: generated heat flux [w/m2]

q”loss: Heat loss [w/m2]

Pr : Prantdl number [pr= γ / α]

R e : Reynolds number [R e=u L/ γ]

Taw : Adiabatic wall temperature [k]

Tw: Wall temperature [k]

Greek Symbol

α : Thermal diffusion coefficient[mm2/s]

γ :Kinematic viscosity [mm2/s]

ρ : Fluid density [g/mm2]

ω : Circular frequency of vibration 2л f [s-1

]




Subscripts:

f: with vibration.

n: without vibration.

o: stagnation point value

References

1- S.M. Zenkovskaya and I.B. Simonenko,1966 “On The High Frequency VibrationInfluence On The Beg Inning Of Convenction “Izvestia ANUSSR, fluidDynamics 5, 51-55.

2- G.Z. Gershuni and E. M. Zhukhovitski,1979 “On The Free Heat Convection InVibration Of Field In MicrogravityConditions “Dok ladi ANUSSR 249 (3),580-584.

3- G.Z. Gershuni, E. M. Zhukhovitski, andA. Nepomniashi, 1989 “Stability of Convective Flows” P. 109, Navka,Moscow.

4- G. Z. Gershuni and E.M. Zhukho vitski,1989 “Flat-Parallel Advective Flows InThe Vibration Field” Inzhenerno-

phyzicheski Zhurnal 56 (2) pp 238-242.5- A.N. Sharifulin, 1983“Stability Of

Convective Movement In The VerticalLayer With Longitudional VibrationPresence” Izvestia ANUSSR, fluidDynamics 2, pp 186-188.

6- M.P. Zavarikin, S.V. Zorin and G. Fipution,1985 “Experimental Study Of Vibro-

Converction” Dokladi ANUSSR 281 (4),815-816.

7- V. Uspenskii and J.J. Favier, 1994 “HighFrequency Vibration And NaturalConvection In Bridgman -Scheme CrystalGrowth” Int. J. heat Mass brans for, vol.37. No4. pp. 691-698.

8- C.F.Ma, 2002 ”Impingement Heat Transfer With Meso-Scale Fluid Jets” in:Proceedings of 12 th International HeatTransfer Conference.

9- Bargles, A.E., 1969,”Progree in Heat and

Mass Transfer” 1, 331.10- Van Dijck W.J.D., U.S. Patent, Aug. 13 th, 1935 No. 2011186.

11- Bergles, A. E., 1979 “Procedoings Of TheSix International Heat Transfer Conference”, Toronto, Canada, August 7.

12- Shairfulin, A. N., 1986 “Super CriticalVibration Induced Thermal Convection InA Cylindrical Cavity” Fluid Mech. Sov.Res 15, pp. 28-35.

13- Ivanova, A. A. and V. G. Kozlou, 1988“Vibrationally Gtavitational Convection InA Horizontal Cylinderical Layer Heat

Transfer” Sov., Res 20, pp. 235-247.

14- R.E., Forbes, C.T. Carkey and C.J. Bell,1970 “Vibration Effects On ConvectiveHeat Transfer In Enclosures” J. Heattransfer No. 92, pp. 429-438.

15- P.M. Gresho and R.L. Sani, 1970 “TheEffects Of Gravity Modulation On The

Stability Of A Heated Fluid Layer” J. fluidMech, No. 40, pp. 783-806.

16- V. Upenskii and J. J. Favier, 1994 “HighFrequency Vibration And NaturalConvection In Bridgman-Scheme CrystalGrowth” Int. J. Heat, Mass Transfer No.37, pp 691-698.

17- W.S.Fu and J. Shieh, 1992 “A Study Of Thermal Convection In An EnclosureInduced Simultaneously By Gravity AndVibration “Int. J. Heat Mass transfer No.35, pp 1655-1710.

18- Ftank, T. F., 1996 “ThermovibrationalConvection In A Vertical Cylinder” Int. J.Heat Mass transfer, vol. 39, No 14, pp2895-2905.

19- M.Y. Wen, K.-J. Jan, 2003 “ AnImpingement Cooling on a Flat SurfaceBy Using circular Jet With LongitudinalSwirling Strips” Internatinal J. Heat MassTransfer Vol. 46, pp 4657-4667, 2.

20- Mohamed A. Saleh and Ahmed A. L.,2002 ”Heat Transfer Behavior of anImpinging Jet Along Rib-Groove-Roughened Walls” World Renewable

Energy Congress VII, 29 June- 5 July,Germany.

21- Mohamed A. Saleh, 2004 “A Study of Heat Transfer On A Roughened Surface-Entrainment and Subsonic Mech Number Effects” The First International Fourm onHeat Transfer, Nov. 24-26, Koyto, Japan.

22- S.J. Kline, F.A. McClintock, 1953,“Describing Uncertainties In SingleSample Experiment “Mech Eng., Vol. 175,

pp. 3-8.23- Moffat, R. J., 1985, “Describing The

Uncertainties In Experimental Results”Experimental Therm. Fluid Sci., vol. 1, pp.3-17.

24- Huang,L.,M.S.El.Genk,1980” HeatTransfer And Flow VisualizationExperiments Of Swirling Multi-ChannelAnd Conventional Impinging Jets” Int. J.Heat&Mass Transfer Vol.41, PP. 583-600.

25-Shlien, D.J., Hussain, A.K.M.F., 1983”Visualization of The Large Scale Motionof A Plane Jet, Flow Visualization” in:Proceeding of The 3 rd International

Symposium of Flow Visualization.




1- Compressor 5- U tube manometer 9- Vibrating mech. 13- Wattmeter

2- Heart exchanger 6- Plenume chamber 10- Elec. Motor 14- Digital thermom3- Air filter 7- Tested plate 11- Thermo couples 15- Selector switch

4- Orifice meter 8- Cam shaft 12- Auto transformer

Fig. (1): Layout of the experimental setup.

4

5

13

14

15

12

1110

9

8

7

6

Proceedings of the 2006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miami, Florida, USA, Januar



z/d = 6, Re = 17000 and am

= 10 mm

0

100

200

300

400

500

600

700

800

900

10 30 50 70 90 110

f (Hz)

N u o

Non-vibrating flat plateVibrating flat plateVibrating square grooveVibrating V groove

Fig. (2): Schematic Illustrations of Expected Flow Patterns of Impingement on (a) a flat

plate, (b) a square-grooved plate, and (c) a V-grooved plate.

z/d = 6, Re = 17000, f = 50Hz and am

= 10 mm

0

100

200

300

400

500

600

0 5 10 15 20 25

r/ro

N u

Non-vibrating flat plate

Vibrating flat plate

Vibrating square groove

Vibrating V groove

Fig. (3): Effect of vibration and plate surfacetopography on local Nusselt number distribution (at

Z/D=6, Re = 17000, f=50Hz and am = 10 mm).

Fig. (4): Effect of vibration frequency on stagnation Nusselt number for different shaped surfaces (at Z/D

= 6, Re = 17000 and am = 10 mm).

(a) Flat plate

(b) Square-grooved plate

(c) V-grooved plate




z/d = 6, Re = 17000 and am

= 10 mm

0

50

100

150

200

250

300

10 30 50 70 90 110

f (Hz)

N

u



Vibrating V groove

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14 16 18 20

Z/D

N u o

Non-vibrating fl at plateNon-vibrating.square grooveNon-vibrating V grooveVibrating fl at plateVibrating square grooveVibrating V groove

z/d = 6, Re = 17000 and f = 50Hz

0

100

200

300

400

500

600

700

0 5 10 15 20 25

am (mm)

N u o


Vibrating square grooveVibrating V groove

Fig. (5): Effect of amplitude on the stagnation Nusselt number for different shaped surfaces (atZ/D = 6, Re = 17000 and f = 50Hz).

Fig. (6): Effect of vibration frequency on the average Nusselt number for different shaped surfaces (at Z/D= 6, Re = 17000 and am = 10 mm).

z/d = 6, Re = 17000 and f = 50Hz

0

50

100

150

200

250

300

0 5 10 15 20 25

am (mm)

N u o



Vibrating V groove

Fig. (7): Effect of amplitude on the average Nusseltnumber for different shaped surfaces (at Z/D = 6, Re= 17000 and f = 50Hz).

Fig. (8): Comparison of stagnation point Nusseltnumber for Re = 17000, am=10 mm and f = 50Hz).

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16

Z/D

N u

Non-vibrating fl at plateNon-vibrating.square grooveNon-vibrating V grooveVibrating fl at plateVibrating square grooveVibrating V groove

Fig. (9): Comparison of average Nusselt number for

Re = 17000, am = 10 mm and f = 50Hz).


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