An experimental investigation of a block moving back and forth on a heat plate under a slot jet

(1)

An experimental investigation of a block moving back

and forth on a heat plate under a slot jet

Wu-Shung Fu

a,*

, Ching-Chi Tseng

b

, Chien-Ping Huang

c

, Ke-Nan Wang

a

a_{Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 30056, Taiwan}

b_{Department of Automation Engineering, Ta-Hwa Institute of Technology, No. 1, Ta-Hwa Road, Chung-Li, Hsichu 307, Taiwan} c

Center for Environmental Safety and Health Technology, Development, Industrial Technology Research Institute, Chutung Hsinchu 310, Taiwan Received 4 March 2005; received in revised form 13 May 2005

Available online 2 April 2007

Abstract

This experimental study aims to investigate heat transfer phenomena caused by a moving block under a jet flow. The experimental apparatus includes three main systems of a jet flow, periodical movement and heating control. The work fluid is air and the data runs are performed for jet Reynolds numbers and speeds of moving block. The comparison between experimental and numerical results show good consistence, and the destruction of boundary layers discovered by previous authors’ numerical results is validated. The enhance-ment of heat transfer rate is generally accompanied with the increenhance-ment of jet Reynolds number and speed of moving block.

Keywords: Moving boundary; Convection heat transfer; Experimental

1. Introduction

Up to now, numerous methods have been proposed to enhance heat transfer rate of a heat body. These methods mainly include the passive and the active methods. The examples of the former one are treated surfaces and swirl ﬂow devices, while the examples of the active methods are surface vibration, ﬂuid vibration, injection and suction which were summarized and reviewed in detail by Bergles

[1,2]. A jet impingement which has high heat transfer rate

is one of the above active methods and widely used in the cooling apparatus for high heat ﬂux system such as electric cooling and turbine blade cooling. However, accompany-ing with the progress of semiconductor technology, the smaller and more compact device is produced indefatiga-bly. The heat generated by the new device is always several times of the former one and becomes the main defect of the failure of device. As a result, how to increase the heat

trans-fer rate of the jet impingement becomes a very important issue.

In the past, Mujumdar and Douglas[3], Martin[4], and Jambunathan et al. [5]reviewed the contemporary litera-ture. Marple et al.[6]used a flow visualization technique to study a confined water jet impingement and observed the laminar flow for jet Reynolds number up to 2300. Chou and Hung[7]studied fluid flow and heat transfers of a con-fined slot jet numerically and found that the Nusselt num-ber at the stagnation line was proportional to jet Reynolds number in a 0.5 power and the ratio of separation distance to jet width in a0.17 power. Chakroun et al.[8] investi-gated heat transfer of a round air jet impinging normally on a heated rough surface and found that the local and average Nusselt numbers of a rough surface were larger than those of a smooth surface by 8.9% to 28%. Chung et al.[9]investigated heat transfer characteristics of an axi-symmetric jet impinging on a rib-roughened convex sur-face. The average Nusselt numbers on the rib-roughened convex surface were more than those on the smooth surface by 14% to 34%. Besides, in several experimental studies, an extra mechanism in the jet impingement system was

*

Corresponding author. Tel.: +88 635 712 121x55110; fax: +88 635 720 634.

(2)

installed to enhance the heat transfer rate of the jet impingement. Zumbrunnen and Aziz [10] investigated an intermittent water jet impinging on a constant heat flux surface experimentally, and found that the enhancement due to the intermittent flow only occurred as the frequency of the intermittence was sufficiently high enough. Haneda et al.[11]enhanced heat transfer rate of a jet impingement by inserting a suspended cylinder between the jet exit and the heat plate. The mechanically oscillatory motion of the cylinder vibrated the flow field, and the maximum Nusselt number around the stagnation point was augmented by about 20% compared to that without the insertion of a cylinder.

From the above literature, the increment of heat transfer rate of the jet impingement seems to have limitation in spite of installing any extra equipment. The reason could be the stillness of velocity and thermal boundary layers on the heat plate. Consequently, as the huge enhancement of heat transfer rate is expected, the boundary layers mentioned above are necessarily destroyed.

Based upon the results of Fu et al.[12]that a thin block moving back and forth along a heat plate under an imping-ing jet could improve the heat transfer rate of the heat plate remarkably. In this study the boundary layer on the heat plate was destroyed by the moving thin block and the new one reformed immediately after the moving thin block which was the main mechanism to enhance the heat trans-fer rate hugely. However, the study[12]was purely numer-ical analyses and extremely short of relating experimental studies to verify its accuracy and availability.

Therefore, a further investigation of this issue will be carried out by an experimental method. The apparatus used in the experimental method includes three main sys-tems of a jet ﬂow, periodical movement and heating con-trol. The jet ﬂow system is made of a fan and a wind tunnel and provides necessary velocity distribution. The periodical movement system maintains periodical motion of a thin block moving back and forth on the heat plate

which plays a leading role. Due to the limitation of the thin block speed, a jet Reynolds number is smaller than 1500. The heating control system is combined with heat plates, thermalcouples and power supply, and is to maintain con-stant temperature condition on the heat plates which is consistent with the thermal condition used in the previous numerical study [12]. Since a stepping motor is used to drive a moving bar periodically, the acceleration and decel-eration motions of the moving bar during the initial and ﬁnal stages of periodical movement are unavoidable. The average velocity during the periodical movement is then utilized. Comparing both the numerical and experimental results, the consistence gives good agreement.

2. Physical model and experimental procedure

In order to simulate the physical model adopted in the pervious study[12]as consistently as possible, the relating experimental apparatus conducted in this study is shown in

Fig. 1, and the test section (1, 3 and 7) is equivalent to the

physical model of the previous study [12].

Air streams are sucked by a fan (without being indicated

in Fig. 1) and rectiﬁed by a wind tunnel (6). Then the air

streams could be regarded as a jet ﬂow (7) and blow uni-formly and stably at the exit of the wind tunnel. For recti-fying the air streams, the honeycomb (3) and screens (2) are then set at appropriate positions in the wind tunnel shown

in Fig. 2.

The detailed ﬁgure of the periodical movement system (11–17) shown in Fig. 1 is renewebly indicated in Fig. 3. A linkbar (7) of which one side is ﬁxed on a stepping motor (8) and the other side is connected with a connector (6). Another linkbar (5) is installed perpendicularly to the link-bar (7) and adjoins the connector (6), and a thin moving block (2) is perpendicularly inserted in the linkbar (5). For keeping the movement of the moving block (2) limited in the heating plates (1) stably and periodically, the barriers (3) and bearings (4) are used. As a result, when the stepping Nomenclature

A area [m2]

h heat transfer coeﬃcient [w m2K1]

H distance from wind tunnel exit to heat plate [m] I current [A]

k thermal conductivity [w m1K1] Nu average Nusselt number

Q heat energy [w]

R length of linkbar (Figs. 3 and 7) [m] T dimensional temperature [K] v ﬂuid velocity [m s1]

V voltage [V]

Vb dimensionless velocity of moving block [vb v1j ]

w width of wind tunnel exit [m] Dy thickness of basswood [m]

Greek symbols

h subtending angle [rad] m kinematic viscosity [m2s1] w angular velocity [rad s1] Subscripts b block h heat plate in input j jet lose lose s stagnation t theoretical value

(3)

Fig. 1. Experimental apparatus.

(4)

motor (8) revolves a small angle back and forth periodi-cally, by way of the linkbar (7), connector (6) and linkbar (5) , the moving block (2) could move short but approxi-mate horizontal distance back and forth on the heat plates (1). Since the moving block and heat plates are solid mate-rials. For avoiding damage caused by the direct contact between the moving block and heat plates, the contacting side of the moving block is made of soft material.

The heating control system is combined with heat plates, thermalcouples and power supplies. The heat plates have ﬁve pieces which are separately controlled by an individual power supply in order to maintain surface temperature of each heat plate at a constant temperature condition. The heat plates set on the left and right most sides are used as the guard plates which protect the heat energy of the other three heat plates set in the central region to dissipate from the both most sides. As a result, the data reduction of the heat energy of the central heat plate carried away by the jet ﬂow mentioned above becomes simple and accurate.

Shown inFig. 4, a ﬁne Ni–Cr line (4) 0.1 mm in diame-ter is used as a headiame-ter during electric power applying on both ends of the line winds uniformly and tightly around an insulator of mica (2) of which the length, width and thickness are 40, 8 and 0.4 mm, respectively. Two thermal-couples (7 and 8) are installed on the upper side of the mica and prohibited to touch the Ni–Cr line. Afterward, two

pieces of thin mica (21) used as an electric insulator 0.1 mm in thickness cover both sides of the mica winded by the Ni–Cr line to prevent the direct contact between the Ni–Cr line and thin copper plate (1). Since the jet flow directly impinges on the flat heat plates assumed in the per-vious study. A piece of thin copper plate (1) then covers all materials mentioned above and the upper side of copper plate impinged by the jet flow should be adjusted as smoothly as possible. Two pairs of thermalcouples (5 and 6) are stuck on the inner side of the upper side of copper plate to indicate the surface temperature of heat plate.

A block of basswood (3) with 40, 10 and 3 mm as length, width and thickness respectively is used as a thermal insula-tor to prevent the dissipation of heat energy from the bot-tom side of heat plate. Its upper side is stuck tightly on the bottom side of heat plate mentioned above and a pair of thermalcouples (9) are installed on the bottom side of basswood. Utilizing the temperatures measured from the mica (7 and 8) and the bottom side of basswood (9), the quantity of heat energy of the heat plate transferring to the basswood by heat conduction could be calculated which means the heat loss of heat plate from the bottom side could be obtained. For flow visualization, a smoke-wire tech-niques is used to observed variations of flow field which compare with the results of numerical study [12] quali-tatively.

Fig. 3. Periodical movement system.

(5)

Each experimental data run includes three measure-ments and a brief outline is given as follows:

(1) The measurement of jet flow. Start the fan and use a hot wire anemometer to measure a velocity profile at the exit of wind tunnel. The distance from the exit of wind tun-nel to the heat plate is 50 mm. The velocity profile of f–f section shown in Fig. 2 measured at the exit is indicated

in Fig. 5. Except the regions near both walls, the velocity

distribution on most central region in which the moving block moves back and forth is ﬂat, therefore, the assump-tion of two dimensional ﬂow made in the previous study

[12] is approximately consistent with this experimental study. The jet Reynolds number Rejof jet ﬂow is deﬁned

as follows: Rej¼

vjw

m ð1Þ

vjis the ﬂuid velocity measured at the center of wind tunnel

exit, w is the width of the wind tunnel exit and m is the kine-matic viscosity of the working ﬂuid.

Adjust the revolution of fan and a designed ﬂuid veloc-ity could be obtained.

(2) The measurement of periodical movement. A step-ping motor having resolution of 36000 steps per revolution is used. The linkbar (7) shown in Fig. 3 has a length of 200 mm and the width of the exit of wind tunnel w is 20 mm which is the one-way moving distance of the

mov-ing block. The theoretical velocity of movmov-ing block vbt

could then be calculated by the following equation:

vbt¼ Rx cos h ð2Þ

R is the length of linkbar (7) (=200 mm), x is the angular velocity of stepping motor and h is the subtending angle be-tween circumferential velocity of linkbar and velocity of moving block.

As a result, the maximum clearance between the moving block and heat plates due to revolution of the linkbar is about 0.27 mm. For ﬁlling the clearance, one kind of soft material which contacts with the heat plates directly has the length to be slightly longer than 0.27 mm and is installed on the bottom side of moving block.

Realistically, the moving distance 20 mm including acceleration and decelerating regions converted into the steps of stepping motor is about 600 steps or 0.11 rad in minute circumferential angle. Therefore, the velocity of moving block driven by the stepping motor maintained at a constant magnitude is impossible. The distribution of the velocity of moving block on the heat plates region of 20 mm is shown inFig. 6for a certain case. Conveniently, the average velocity of moving block vb used in the data

reduction is obtained by that the distance which is summa-tion of the moving block moving back and forth in 20 mm length 24000 times divides the waste time. Shown inFig. 6,

(6)

the moving block running through the heat plate 3 being used to calculate heat transfer rate from a heat plate almost keeps constant speed which is approximately equal to the

average velocity mentioned above. Then the average veloc-ity could be approximately regarded as a constant velocveloc-ity which is assumed in the previous study [12].

(3) The measurement of heat transfer rate of a heat plate. The heat plates mentioned above are wound tightly and uniformly by a fine Ni–Cr line and the heat plates arranged on both most sides are used as guard heaters, then as electric power is applied on heat plates, the uniform temperature distribution on the central heat plates could be obtained. The difference of two pairs of thermalcouples shown in Fig. 4 installed on the central three heat plates are not larger than 0.1°C. As a result, the condition of the constant temperature on heat plate which is assumed in the previous study [12]could almost be satisfied.

The heat transfer rate of the heat plate 3 (middle heat plate) could be calculated by the following equations:

(a) Total input heat energy

Q_in¼ I V ð3Þ

Qinis the total input heat energy (w), I, V is the current [I]

and voltage [V] of electric power, respectively.

(b) Heat energy dissipation Qlose from the basswood

installed the bottom side of heat plate.

Q_lose¼ Kb Ab DT =Dy ð4Þ

Kb is the thermal conductivity of basswood (;0.055

w m1K1), Ab is the area of basswood (0.04 m

0.01 m = 4 104m2), DT is the temperature diﬀerence between the upper and bottom sides of basswood (K) and Dy is the thickness of basswood (=0.003 m).

(c) Calculation of average Nusselt number Nu of heat plate 3. Nu¼hw k ¼ Q_con AhDT w k ð5Þ

h is the convection heat transfer coeﬃcient [w m2K1], w is the width of jet ﬂow exit [=0.02 m], k is the thermal

-8 -6 -4 -2 0 2 4 6 8 Z (cm) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 v eloci ty (m /s) -10 -5 0 5 10 X (mm) 0.0 0.2 0.4 0.6 0.8 1.0 1.2

velocity (m/s) _{present study} fully developed flow uniform flow

a

b

Fig. 5. Velocity proﬁles on the exit of jet ﬂow for Rej= 1386.

Fig. 6. Distribution of velocity of moving block versus location of heat plates.

Fig. 7. Comparison of the results of present study with previous studies. W.-S. Fu et al. / International Journal of Heat and Mass Transfer 50 (2007) 3224–3233 3229

(7)

conductivity of air [=0.025 w m1K1], Qconis the

convec-tion heat transfer energy ( = Qin Qlose), Ahis the area of

heat plate 3 [=104m2] and DT is the temperature diﬀer-ence between surface of heat plate 3 and inlet air [K].

Total pairs of thermalcouples used in the experimental system are 26, the scanning speed of temperature indicator for scanning the transient variations of total thermalcou-ples can not catch with the speed of moving block. For convenience, enough time is taken to measure the total thermalcouples and an average temperature of each ther-malcouples is used for calculating the heat transfer rate of each experimental run.

Based upon the measurements mentioned earlier, exper-imental procedures are brieﬂy indicated as follows:

(a) Start the fan to provide a designed jet velocity vjand

calculate the corresponding jet Reynolds number Rej.

(b) Start individual power supply to apply approximate power Qincomposing of current and voltage to each

heat plate.

(c) Adjust each power supply carefully to make the tem-perature of each heat plate to be the same magnitude and the temperature diﬀerence among the heat plates is not larger than 0.1°C.

(d) Take the necessary data to calculate the heat transfer rate of heat plate 3 under a pure jet ﬂow condition. (e) Start the movement system to obtain a designed

velocity of the moving block vb, the experimental

condition becomes transient. For economizing

(8)

ning time, increase an approximate quantity of power of individual heat plate according to the numerical results of the previous study[12]first. After the tem-perature variation of each heat plate becomes slight, the fine adjustment of power supply is executed sequentially until the temperation difference condi-tion is satisfied.

(f) Take the necessary data to calculate the heat transfer rate of heat plate 3 of a moving block under a jet ﬂow condition.

(g) Change the parameters of vj, vband Qin, and repeat

the above procedures.

As for the uncertainty analysis, the relative uncertainty proposed by Kline [13] being used to analyze the results and the uncertainties for Nusselt and Reynolds numbers are about 7% and 5%, respectively.

3. Results and discussion

In the situation of conﬁned impinging system, the rela-tionship between the Nusselt number Nus at stagnation

point and jet Reynolds number Rej could be expressed as

the following equation: Nus¼ cRe0:5j ðH =wÞ

0:17

ð6Þ c¼ 0:574

The solid line shown inFig. 7is obtained from Eq.(6), both dashed lines are 15% deviation from the solid line. The previous studies of Chou and Hung [7] Heiningen

[14], and both numerical [12] and experimental results of the authors’ studies are consistent well with the results of Eq.(6).

A flow visualization is shown qualitatively inFig. 8. A fine metal line used as a heater and applied by paraffin is set at a top angle of a white triangle shown in Fig. 8. The fine metal line can generate white smoke within a short time when the electric power is on. The figures of (a)–(e) are experimental results and the figures of (1)–(5) are obtained by the numerical method. Shown in (a) as the moving block moves toward the left, the fluid on the right side of moving block is sucked by the moving block, the fluid then flows toward the left which causes white smoke also flowing toward the left. The direction of vectors of fluid velocities close to the wall shown in (1) is to the left which is consis-tent with the result of (a). When the moving block moves toward the left further shown in (b), the white smoke forms a circulation zone on the right of the moving block, simi-larly the vectors of fluid velocities in (2) indicate a circula-tion region on the right of the moving block. In (c), the moving block moves to the left most side, the distance between the moving block and fine metal line becomes large, and a part of white smoke close to the wall continu-ously moves toward the left and a part of white smoke forms a larger circulation zone. These results are similar to the numerical results shown in (3). In (d), the moving

block starts to move toward the right and the fluids are pushed by the moving block. As a result, the white smoke flows to the right side of fine metal line, and the remnant white smoke from the above motion (c) appears on the left side of the moving block. In the meanwhile, the direction of the corresponding fluid velocities is also toward the right and indicated in (4). The moving block continuously moves to the right which results in both white smoke and fluid velocities flowing to the right and being shown in (e) and (5), respectively.

Variations of the experimental and numerical results obtained from [12] with time for Rej= 515, Vb= 1.12

and 0.0 are shown in Fig. 9. During the experimental run, a minute increment of electric power is necessary, and the experimental run consumes much time to reach the stable state which means the variation of the heat sur-face temperature is smaller than 0.1°C. During the exper-imental run, the electric power is sometimes increased excessively which causes the monotous increment of the variations of Nu to be diﬃcult. Due to the existence of

Fig. 9. Variations of average Nusselt numbers with time for Rej= 515,

Vb= 0.0 and 1.12 conditions.

(9)

destruction of thermal and velocity boundary layers by a moving block, from the running of moving block the Nu is always larger than that of the situation without moving block (Vb= 0). Finally both experimental and numerical

results become consistent, and the enhancement of heat transfer rate is about 60%.

Fig. 10 indicates the time development of both

experi-mental and numerical results for Rej= 722, Vb= 0.45

and 0.0 situations. Similarly, the experimental run takes up much time and the experimental and numerical results are gradually close to the same value. The enhancement of heat transfer rate is about 45%.

Fig. 11 indicates the time development of both

experi-mental and numerical results for Rej= 1054 and Vb=

0.31 and 0.0 situations. Accompanying with the decrement of Vb, the enhancement generally decreases and is about

23%.

Shown inFigs. 12 and 13, there are the variations of Nu of experimental results with time for Rej= 1262, Vb= 0.26

and 0.0 and for Rej= 1471, Vb= 0.22 and 0.0, respectively.

The jet Reynolds numbers are larger in these situations, the criteria of convergence of numerical calculation is hardly satisﬁed which causes the numerical results to be absent. As the moving block starts to move, the heat transfer rate is accompanied with increment in both situations. The enhancements of heat transfer rate are about 30%. 4. Conclusions

This experimental study employs a moving block to enhance heat transfer rate of a heat plate on which the moving block moves back and forth. Diﬀerent combina-tions of jet Reynolds numbers and moving block velocities are taken into consideration and the conclusions are sum-marized as follows:

(1) The enhancement of heat transfer rate caused by the destruction of velocity and thermal boundary layers is validated experimentally.

(2) The larger moving block velocity is, the more remark-able enhancement of heat transfer rate becomes. (3) Due to direct contact between the moving block and

heat plate, time consuming is unavoidable.

(4) Good agreement is found between the experimental and numerical results.

Acknowledgement

The support of this work by National Science Council, Taiwan, ROC, under contract NSC 89-2212-E-009-072 is gratefully acknowledged.

References

[1] A.E. Bergles, Recent development in convective heat-transfer aug-mentation, Appl. Mech. Rev. 26 (1973) 675–682.

[2] A.E. Bergles, Survey and evaluation of techniques to augment convective heat and mass transfer, Progr. Heat Mass Transfer 1 (1969) 331–424.

(10)

[3] A.S. Mujumdar and W.J.M. Douglas, Impingement heat transfer: a literature survey, TAPPI Meeting, New Orleans, 1972, SM 8603.7, pp. 107–136.

[4] H. Martin, Heat and mass transfer between impinging gas jets and solid surfaces, in: T. Irvine, J.P. Harnett (Eds.), Advances in Heat Transfer, vol. 13, Academic Press, New York, 1977, pp. 1–60. [5] K. Jambunathan, E. Lai, M.A. Moss, B.L. Button, A review of heat

transfer data for single circular jet impingement, Int. J. Heat Mass Transfer 13 (2) (1992) 106–115.

[6] V.A. Marple, B.Y.H. Liu, K.T. Whitby, On the ﬂow ﬁelds of inertial impactors, J. Fluids Eng. Trans. ASME 96 (1974) 394–400. [7] Y.J. Chou, Y.H. Hung, Impingement cooling of an isothermally

heated surface with a conﬁned slot jet, ASME J. Heat Transfer 116 (1994) 479–482.

[8] W.M. Chakroun, A.A. Abdel-Rahman, S.F. Al-Fahed, Heat transfer augmentation for air jet impinged on a rough surface, Appl. Thermal Eng. 18 (1998) 1225–1241.

[9] Y.S. Chung, D.H. Lee, J.S. Lee, Heat transfer characteristics of an axisymmetric jet impinging on the rib-roughened convex surface, Int. J. Heat Mass Transfer 42 (1999) 2101–2110.

[10] D.A. Zumbrunnen, M. Aziz, Convective heat transfer enhancement due to intermittency in an impinging jet, ASME J. Heat Transfer 115 (1993) 91–98.

[11] Y. Haneda, Y. Tsuchiya, K. Nakabe, K. Suzuki, Enhancement of impinging jet heat transfer by making use of mechano-ﬂuid interac-tive ﬂow oscillation, Int. J. Heat Fluid Flow 19 (1998) 115–124. [12] W.S. Fu, K.N. Wang, W.W. Ke, An investigation of a block moving

back and forth on a heat plate under a slot jet, Int. J. Heat Mass Transfer 44 (2001) 2621–2631.

[13] S.J. Kline, The purpose of uncertainty analysis, ASME J. Fluid Eng. 117 (1955) 153–160.

[14] A.R.P. van Heiningen, A.S. Mujumdar, W.J.M. Douglas, Numerical prediction of the ﬂow ﬁeld and impingement heat transfer caused by a laminar slot jet, ASME J. Heat Transfer 98 (1976) 654–658. W.-S. Fu et al. / International Journal of Heat and Mass Transfer 50 (2007) 3224–3233 3233