Enhancement of Convective Heat Transfer on A Flat … of Convective Heat Transfer on A Flat Plate by Artificial Roughness and Vibration M. A. Saleh Associate Professor, Mechanical

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 differs from 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 vortex generators 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 needed in 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, the local 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 typical Bridgman – 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 vibrational Grashof 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 a typical 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 swirling strips[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 present work, 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 was sated 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 surface with 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

r2uN (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 the surface. 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 quickly upon 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 radial laminar 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)) is distinctly 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 with V-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 and Re=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 to roll 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 have the 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 heat transfer.

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 frequency level 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/m2] q”g: generated heat flux [w/m2] q”loss: Heat loss [w/m2] Pr : Prantdl number [pr= γ / α] Re : Reynolds number [Re=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 Vibration Influence On The Beg Inning Of Convenction “Izvestia ANUSSR, fluid Dynamics 5, 51-55.

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

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

4- G. Z. Gershuni and E.M. Zhukho vitski, 1989 “Flat-Parallel Advective Flows In The Vibration Field” Inzhenerno-phyzicheski Zhurnal 56 (2) pp 238-242.

5- A.N. Sharifulin, 1983“Stability Of Convective Movement In The Vertical Layer With Longitudional Vibration Presence” Izvestia ANUSSR, fluid Dynamics 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 “High Frequency Vibration And Natural Convection In Bridgman -Scheme Crystal Growth” 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 Heat Transfer 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 The Six International Heat Transfer Conference”, Toronto, Canada, August 7.

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

13- Ivanova, A. A. and V. G. Kozlou, 1988 “Vibrationally Gtavitational Convection In A 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 Convective Heat Transfer In Enclosures” J. Heat transfer No. 92, pp. 429-438.

15- P.M. Gresho and R.L. Sani, 1970 “The Effects Of Gravity Modulation On The Stability Of A Heated Fluid Layer” J. fluid Mech, No. 40, pp. 783-806.

16- V. Upenskii and J. J. Favier, 1994 “High Frequency Vibration And Natural Convection In Bridgman-Scheme Crystal Growth” 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 Enclosure Induced Simultaneously By Gravity And Vibration “Int. J. Heat Mass transfer No. 35, pp 1655-1710.

18- Ftank, T. F., 1996 “Thermovibrational Convection In A Vertical Cylinder” Int. J. Heat Mass transfer, vol. 39, No 14, pp 2895-2905.

19- M.Y. Wen, K.-J. Jan, 2003 “ An Impingement Cooling on a Flat Surface By Using circular Jet With Longitudinal Swirling Strips” Internatinal J. Heat Mass Transfer Vol. 46, pp 4657-4667, 2.

20- Mohamed A. Saleh and Ahmed A. L., 2002 ”Heat Transfer Behavior of an Impinging 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 on Heat Transfer, Nov. 24-26, Koyto, Japan.

22- S.J. Kline, F.A. McClintock, 1953, “Describing Uncertainties In Single Sample 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” Heat Transfer And Flow Visualization Experiments Of Swirling Multi-Channel And 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 Motion of 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 thermometer 3- 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.

1

2

4

3

5

13

14

15

12

11 10

9

8

7

6


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)

Nuo

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

Nu

Non-vibrating flat plateVibrating flat plateVibrating square grooveVibrating V groove

Fig. (3): Effect of vibration and plate surface topography 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)

Nu

Vibrating flat plateVibrating square grooveVibrating V groove

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14 16 18 20

Z/D

Nuo

Non-vibrating flat plateNon-vibrating.square grooveNon-vibrating V grooveVibrating flat 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)

Nuo

Vibrating flat plateVibrating square grooveVibrating V groove

Fig. (5): Effect of amplitude on the stagnation Nusselt number for different shaped surfaces (at Z/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)

Nuo

Vibrating flat plate

Vibrating square groove

Vibrating V groove

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

Fig. (8): Comparison of stagnation point Nusselt number 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

Nu

Non-vibrating flat plateNon-vibrating.square grooveNon-vibrating V grooveVibrating flat plateVibrating square grooveVibrating V groove

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

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


Documents

Enhancement of Convective Heat Transfer on A Flat … of Convective Heat Transfer on A Flat Plate by Artificial Roughness and Vibration M. A. Saleh Associate Professor, Mechanical