- Email: [email protected]
Cooling of a heated flat plate by an obliquely impinging slot jet
International Communications in Heat and Mass Transfer 33 (2006) 372 – 380 www.elsevier.com/locate/ichmt
Cooling of a heated flat plate by an obliquely impinging slot jet☆ Haydar Eren, Nevin Celik ⁎ Department of Mechanical Engineering, Faculty of Engineering, University of Firat, 23279, Elazig, Turkey Available online 12 December 2005
Abstract Experiments were conducted to determine the effects of some parameters that were crucial in the cooling of a heated flat plate by an obliquely impinging slot jet. The inclination of the jet relative to the surface was varied from 90° to 30° (90°, 60°, 45° and 30°). For Reynolds number of 5860, 8879, and 11606, the variation of local temperatures with respect to dimensionless length (z/L), were investigated. New correlations for local temperatures in terms of Reynolds number, dimensionless distance (z/L) and oblique angle (sinϕ) were developed. The displacement region of maximum heat transfer (minimum temperature point) on the plate was measured with respect to geometrical impingement point. Results of experiments indicated that for a given position this displacement increases with increasing the inclination, and the displacement was occurred on compression side of plate. © 2005 Elsevier Ltd. All rights reserved. Keywords: Confined jet; Cooling; Heat transfer; Rectangular jet
1. Introduction Air jets have been the subjects of many theoretical and experimental investigations; their important role in many aspects of engineering has recently given a new impetus for more detailed studies of these flows. Jet impingement is frequently used in industrial practice for their excellent heat and mass transfer characteristics, where localized and controlled surface transfer is desirable. In recent years, especially because of their wide usages at industrial products and cooling of electronic devices, the subject of impinging jets has gained a great importance. The velocity profile, flow characteristics, and pressure distribution on target surface are aimed to be analyzed in jet studies. Additionally, there have been some various studies about increasing heat transfer rates and searching relationship between dimensionless numbers and heat transfer coefficients. To understand the cooling phenomena by impinging air flow to a target body, mentioning literature is unavoidable. In this field of work, the early study is from Martin [1], about heat and mass transfer between a jet and an impingement surface. That study contains only two references to inclined jets, and a further search of the archival literature failed to unearth other research papers. The other work is that of Beltaos [2], who performed a fluid mechanic study of an inclined circular jet. In those experiments, pressures were measured on the surface of the impingement plate; the point of maximum pressure was identified with the stagnation point, and its displacement from the geometrical impingement
☆
Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (N. Celik).
0735-1933/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2005.10.009
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
373
point was reported. The controlled parameters of Reynolds number ranged from 35 000 to 100 000, and the jet-to-plate distance (L/D) was in the range of 15–47. Sparrow and Lovell [3] examined the heat transfer characteristics of an obliquely impinging circular air jet on a flat surface by using the naphthalene sublimation technique. In their study while Reynolds number based on the jet orifice varied from 2500 to 10 000, jet-to-plate distance was taken to be 7–15. The oblique angle was varied from 90° to 30°. Their results indicated that the region of maximum heat transfer shifted from the geometrical impingement point along the axis of symmetry. They concluded that, both maximum and average heat transfers were not highly sensitive to the oblique angle of the jet. Goldstein and Franchett [4] used metallic foil heaters with liquid crystals to measure the local heat transfer from an oblique jet to a flat plate. The impinging jet was obtained from a square edge orifice with three Reynolds numbers (10 000, 20 000, and 30 000), and the jet-to-plate distance varied from 4 to 10. At the result, they developed a new correlation for Nusselt number as a function of jet oblique angle and jet-to-plate distance. To determine the turbulent heat transfer and flow characteristics of an oblique impinging circular jet within closely confined walls using air flow, Ichimiya [5] measured the local heat transfer distribution of an oblique jet impinging on a surface. The temperature distribution on target surface was obtained by using liquid crystal technique. Abdlmonem et al. [6] performed an experimental study to determine the effect of the inclination of a two-dimensional air jet on the heat transfer from a uniformly heated flat plate. The impingement surface was a stainless steel plate of the same width as the jet nozzle. Local Nusselt numbers were determined as a function of (i) inclination angle of the air jet relative the plate in the range of 90–40°, (ii) nozzle exit to plate spacing (z/D) in the range of 4–12 and, (iii) Reynolds number based on the hydraulic diameter of the slot nozzle in the range of 4000–12 000. The results were presented in the form of graphs showing the variation of Nusselt number as a function of these parameters. The location of maximum heat transfer region appeared to fall between 0 and 3D uphill from the geometrical impingement point, and was found to be insensitive to the Reynolds numbers in the used range. The heat transfer characteristics of a normal and oblique circular fully developed air jet impinging on a heated flat plate was experimentally analysed by Bilen [7]. In the experiments, the ranges of parameters were taken to be 10 000– 40 000 for Reynolds number, 6–14 for dimensionless jet-to-plate distance (H/D), and 45–90° for jet inclination angle. The temperature variations on the flat plate were measured by using the liquid crystal technique. It was found that, heat transfer coefficient decreased with decreasing jet inclination angle at the stagnation point. Recently, turbulent flow and heat transfer characteristics of a two-dimensional oblique wall attaching offset jet were experimentally investigated by Song et al. [8]. The local Nusselt number distributions were measured using liquid crystal technique. The mean velocity, turbulent intensity, and wall static pressure coefficient profiles were measured at the constant value of jet Reynolds number of 53 200, for the dimensionless ratio (H/D) from 2.5 to 10 and the oblique angle α from 0° to 40°. It was observed that the time averaged reattachment point nearly coincided with the maximum value of Nusselt number for all oblique angles, but the maximum pressure point did only for α = 0°. Heat transfer from an obliquely impinging circular air jet to a flat plate was performed by Yan and Saniei [9]. Liquid crystal technique was used to measure the local Nusselt number. In the experiments the oblique angles were selected to be 90°, 75°, 60°, and 45°. The parameters such as Reynolds number (Re) and the ratio of dimensionless jet-to-plate distance (H/D) were taken to be in the range of 10 000 and 23 000, and 2–10 respectively. Local heat transfer coefficients were given as a function of the mentioned parameters and discussed in relation to the asymmetric wall jet upon impingement of the jet flow. They showed that for a given situation, the point of maximum heat transfer shifts away from the geometrical impingement point toward the compression side of the jet. After a literature survey about the jet impingement works, it can be clearly seen that to obtain impingement heat transfer people normally use an infinite plate (or sufficiently large plate) on the target surface. The flow impinges to target surface at laboratory conditions (ambient air). However current paper dealt with a set up inside a wind tunnel where the flow is driven by the axial pressure gradient in the entire flow field. It is well known that, in reality the target surface which is desired to be cooled is usually operated in closed mediums (i.e. electronic devices). From this point of view the authors aimed to see the heat transfer of jet impingement when the impingement work is occurred in the closed fields instead of free ambient. This study contains the heat transfer characteristics of impinging air jet to an oblique flat plate in a closed field. But to complete the study it is necessary to measure the axial pressures before and after the impingement. The authors desire to compile both heat transfer and flow characteristics in future studies. In present study, cooling of a heated flat plate, fixed with various angles of 90°, 60°, 45° and 30° in a wind tunnel test room was analyzed experimentally. In order to check the experimental results, one of the oblique angle of flat plate was
374
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 1. Experimental set-up, jet flow facility.
chosen to be 90°, since the data for oblique angle of 90° are available in the literature. The experiments were conducted for Reynolds number (11 806, 8879, and 5860), and dimensionless distance (z/L); here (z/L) is the ratio of the distance measured from initial surface side (z = 0) to whole plate length (Fig. 2). Contrary to literature the jet-to-plate distance was constant (H/D = 8). In this connection, local temperatures and the displacement of maximum heat transfer point from geometrical impingement point were measured for various positions of plate. Consequently, new correlations were developed for the dimensionless temperature as a function of Reynolds number, dimensionless ratio, and oblique angle. 2. Experimental study The slot jet experiments were performed in a wind tunnel. In order to produce a parallel jet flow, a rectangular slot of 30 × 300 mm2 was constructed in the contraction cone of the wind tunnel by increasing the contraction ratio (Fig. 1). The dimensions of flat plate were 300 × 136 mm2, and the target surface was roughness. A copper resistance wire was placed behind the plate that its whole surfaces except front surface were covered with a special sticky thermal isolation paper. The thermocouples were glued on the behind surface of aluminum plate through drilled holes (Fig. 2), and the void space was completely filled with thermal epoxy. The heater was an electrical insulated resistance wire having a length of 0.3 mm. The beading of wire was well done to supply perfect insulation. The beaded wires were wholly assembled to the backside of aluminum (Fig. 2). A big care
Fig. 2. Coordinate system and heating style of impingement plate.
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
375
Fig. 3. Positions of flat plate in the wind tunnel test room in front of jet flow.
was shown when covering the wires to plate backside, since a little gap between wires may cause non-uniformity of the heating on the plate. The flat plate was heated using a power supply variac. The air was supplied from a sucking fan and the flow rate was controlled by an inverter. After reaching steady state, the electric power input, the inverter, surface temperatures, and air temperatures at jet exit were recorded for each run. Both the jet exit velocity and temperature data were reported by Campbell CR10X data logger with a computer system. In the case of velocity measurement, an air velocity transducer (TSI Model 8455) was used. The temperatures were measured by T type thermocouples. The impingement plate was placed in test room with various oblique angles of 90°, 60°, 45° and 30° (Fig. 3). The surface temperatures were measured with respect to these various positions of plate for different Reynolds numbers as 5860, 8879, and 11606. Re number was defined base on hydraulic diameter of jet exit (Dh) and jet exit mean velocity (V). To estimate Reynolds number, first the uniformity of velocities issuing from jet exit must be proved. In this case another study of co-authors was used [10]. In the present experiments, the temperature measurements were accurate to within ± 1.25%, jet exit air velocity measurement ± 2%, and those of Re number for the ranges of parameters studied in the steady-state period is 3.8%. Uncertainty of copper wire resistance is 0.5% and based on pre-experiment calibration the uncertainties were about ± 3.99% in total heat obtained from the power supply. 3. Experimantal results and discussions For all inclination angles less than 90°, the point of maximum cooling/minimum temperature decreases dramatically with increasing inclination angles as evidenced in Fig. 4. The displacement distance is denoted by S (Fig. 2). The 0,14
[7] H/D=10 [3] H/D=7 [2] H/D=15 present H/D=8
0,12
S/H
0,1 0,08 0,06 0,04 0,02 0 30
60
90
120
φ (deg)
Fig. 4. Displacement distance between the point of maximum heat transfer and the geometrical impingement point.
376
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380 0,14 Re 11606 Re 8879 Re 5860
0,12
S/H
0,1 0,08 0,06 0,04 0,02 0 0
30
60 φ (deg)
90
120
Fig. 5. Reynolds number effects on the displacement of maximum heat transfer.
measured displacements were normalized by jet-to-plate separation H and were plotted in Fig. 4 as a function of the inclination angle ϕ. The inclination angle 30° was not placed in this figure, as the authors mentioned in literature survey did not perform experiments at this angle. So to compare the results obtained in the present work with the given literature only data for 90°, 60°, and 45° and Reynolds number 5860 are shown in this figure. As can be seen in the figure the displacement increases monotonically as the jet becomes more and more inclined. The displacement of the maximum heat transfer for inclined jets appears to have been previously measured by some investigators. But since the experimental conditions are not same a direct comparison of the results of Fig. 4 with the literature are not possible. Balteos [2] measured static pressures on the surface of an impingement plate and designated the point of maximum pressure taking place at the stagnation point. In that study, both the Reynolds numbers and the separation distances were significantly larger than those of the present investigation (35 000 ≤ Re ≤ 100 000 and 15 ≤ H/D ≤ 47). Furthermore, Belteos operated in the blowing mode to induce airflow through an orifice, and the jet was delivered through a converging nozzle fed by a circular tube. It is likely that this arrangement affected both the jet velocity profile and the turbulence level at exit. It is clearly seen that the displacements measured by Balteos are markedly smaller than those found by both Sparrow and Lovell [3], and Bilen [7]. The displacements found here are not as great as those given in Ref. [3] and Ref [7]. The deviations might well be explainable in terms of the differences in the experimental setups and operating ranges noted above. Fig. 5 shows the displacement of maximum heat transfer for three Reynolds numbers: 11 606, 8879, and 5860. The effect of oblique angles on the shift of maximum cooling is found to be sensitive to Re numbers. Increasing Re number can increase the distance of displacement. For example, the displacement of minimum temperature point is 9.12 mm for ϕ = 60°, 19.2 mm for ϕ = 45° and 24.24 mm for ϕ = 30° at Re = 5860. In the case of Re = 8879, these distances are 10.08 mm for ϕ = 60°, 20.64 mm for ϕ = 45° and 26.16 mm for ϕ = 30°. At last for Re = 11606, these values are 12.48 mm for ϕ = 60°, 21.6 mm for ϕ = 45°, and 27.6 mm for ϕ = 30°. In Fig. 6, minimum temperature/maximum cooling points on impingement plate with respect to oblique angles were plotted at different Reynolds numbers. Increasing the Reynolds number causes an increment on cooling of plate directly. Here, the best cooling is obtained at Re 11 606 as in the literature. Fig. 6 also shows the effect of oblique angle on minimum temperature. Decreasing the angle from 90° to 30° (it means increasing the inclination from jet exit) causes a poorer cooling than that of a conventional normal jet does. Figs. 7, 8, and 9 show the detailed surface local temperature distributions for four different oblique angles, ϕ = 90°, 60°, 45°, and 30° at three different Reynolds numbers. The inclination angle of 90° is well known conventional jet 340
Re 11606 Re 8879 Re 5860
T0 (K)
335 330 325 320 315 15
30
45
75 60 φ (deg)
90
105
120
Fig. 6. Variation of minimum temperature point with respect to oblique angles at three different Re number.
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 7. Temperature distribution with respect to z/L at different inclination angles for Re = 5860.
Fig. 8. Temperature distribution with respect to z/L at different inclination angles for Re = 8879.
377
378
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 9. Temperature distribution with respect to z/L at different inclination angles for Re = 11 606.
position. The minimum temperature is measured at ϕ = 90°, on the geometrical impingement point for all Re number values. Than at ϕ = 60°, 45° and 30° the point of minimum temperature/maximum cooling shifts away from the geometrical impingement point toward the compression side on the principal axis. As drawn in Fig. 3, the down side of plate is compression side. When an inclination angle is given to plate (90–30°), the upper side of plate goes far away from jet exit, so this side is not cooled as good as down side. To obtain a correlation for temperature distribution with respect to variable parameters of Reynolds number, dimensionless distance (z/L), and oblique angle (sinϕ), the multiple regression method was used. The ratio of local temperatures (Tw) to minimum temperature (T0) on impingement surface was used as the constant parameter for correlations. Thus the correlation is obtained as follows: Tw =T0 ¼ aReb ðz=LÞc ðsin/Þd
ð1Þ
The coefficients a, b, c, and d were calculated for four different oblique angle, and the results were given in Table 1. At the oblique angle ϕ = 90°, inclination parameter does not effect the temperature distribution. Hence the coefficient d was not included for this configuration. While local temperature increase with decreasing angle (90–30°), that decreases with the dimensionless distance (z/L) (Fig. 2). It can be also said that; at ϕ = 90°; Re number is more effective
Table 1 Correlation coefficients ϕ (°)
a
b
c
d
90 60 45 30
0.289 0.862 0.854 0.840
0.1225 0.0040 0.0044 0.0050
− 0.1837 − 0.1461 − 0.1560 − 0.1727
– − 0.0003 − 0.0002 − 0.0001
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
379
than dimensionless distance. However, in the inclined positions of plate the dominant parameter on temperature variations is the dimensionless distance. 4. Conclusions Summarizing the results some conclusions may be listed. In present work, local temperature distributions from an obliquely impinging slot air jet to a flat plate were obtained experimentally. The effects of oblique angle (ϕ) on the local temperature was investigated for different Reynolds numbers of 5860, 8879 and 11 606. The parameter ranges are ϕ = 90°, 60°, 45° and 30°. In the range of parameters taken in this investigation, the region of maximum cooling shifts from the geometrical point toward the compression side of the plate. The point of maximum cooling is displaced from the geometrical point of the jet with the extent of displacement increasing as the inclination increases. The largest displacement encountered during the experiments is about 0.92 D. Conventional type jet shows a symmetric position (ϕ = 90°) as it is thought, but the distribution of temperatures on inclined surface shows a non-axisymmetric pattern. It is apparent that future work of surface pressure, velocity field and heat transfer for the same oblique impinging jet configuration is needed to resolve the issue of the relation between the point of maximum pressure, point of maximum heat transfer and the stagnation point for an obliquely impinging jet. It is clear that at same conditions (Re number, oblique angle ϕ, and jet-to-plate distance H/D), the air jet in a nonconfined room will cause better cooling than present one done. But operating conditions of devices are not as same as laboratory conditions. Especially the electronic devices are operated in confined positions. As mentioned above, in present study heated plate is in a test room of a wind tunnel. The authors hope that this study may help the investigators in this point of view. Nomenclature Dh hydraulic diameter [Dh = 4Ac/P] (m) G geometrical impingement point H jet-to-plate distance (m) L length of flat plate (m) Re Reynolds number based on jet exit velocity and the jet hydraulic diameter S shift of point of maximum heat transfer from the geometrical impingement point (m) T0 minimum temperature on the plate surface (°C) Tw local temperature on plate surface (°C) V velocity (m/s) z coordinate along jet issuing direction (m) ν kinematics viscosity (m2/sn) ϕ oblique angles of plate (°) Subscripts w wall 0 point of minimum temperature References [1] H. Martin, Heat and mass transfer between impinging gas jets and solid surfaces, Advances in Heat Transfer 13 (1977) 1–60. [2] S. Beltaos, Oblique impingement of circular turbulent jets, Journal of Hydraulic Research 14 (1976) 17–36. [3] E.M. Sparrow, B.J. Lovell, Heat transfer characteristics of an obliquely impinging circular jet, Journal of Heat Transfer 102 (1980) 202–209. [4] R.J. Goldstein, M.E. Franchett, Heat transfer from a flat surface to an oblique impinging jet, Journal of Heat Transfer 110 (1988) 84–90. [5] K. Ichimiya, Heat transfer and flow characteristics of an oblique turbulent impinging jet within confined walls, Journal of Heat Transfer 117 (1995) 316–322. [6] H.B. Abdlmonem, A.S. Michel, D.P. Chandrakant, The effect of inclination on the heat transfer between a flat surface and an impinging twodimensional air jet, International Journal of Heat and Fluid Flow 21 (2000) 156–163.
380
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
[7] K. Bilen, An Experimental Investigation of Heat Transfer Characteristics of a Normal and Oblique Air Jet Impinging on Heated Flat Plate, Doctoral thesis, KTU, Trabzon, Turkey, 1994. [8] H.B. Song, S.H. Yoon, D.H. Lee, Flow and heat transfer characteristics of a two-dimensional oblique wall attaching offset jet, International Journal of Heat and Mass Transfer 43 (2000) 2395–2404. [9] X. Yan, N. Saniei, Heat transfer from an obliquely impinging circular air jet to a flat plate, International Journal of Heat and Fluid Flow 18 (1997) 591–599. [10] H. Eren, N. Celik, Experimental investigation of the jet flow in a wind tunnel test room which tries to suck, Proceedings of the Third GAP Engineering Congress, Sanliurfa, Turkey, 2000, pp. 17–23.
Cooling of a heated flat plate by an obliquely impinging slot jet☆ Haydar Eren, Nevin Celik ⁎ Department of Mechanical Engineering, Faculty of Engineering, University of Firat, 23279, Elazig, Turkey Available online 12 December 2005
Abstract Experiments were conducted to determine the effects of some parameters that were crucial in the cooling of a heated flat plate by an obliquely impinging slot jet. The inclination of the jet relative to the surface was varied from 90° to 30° (90°, 60°, 45° and 30°). For Reynolds number of 5860, 8879, and 11606, the variation of local temperatures with respect to dimensionless length (z/L), were investigated. New correlations for local temperatures in terms of Reynolds number, dimensionless distance (z/L) and oblique angle (sinϕ) were developed. The displacement region of maximum heat transfer (minimum temperature point) on the plate was measured with respect to geometrical impingement point. Results of experiments indicated that for a given position this displacement increases with increasing the inclination, and the displacement was occurred on compression side of plate. © 2005 Elsevier Ltd. All rights reserved. Keywords: Confined jet; Cooling; Heat transfer; Rectangular jet
1. Introduction Air jets have been the subjects of many theoretical and experimental investigations; their important role in many aspects of engineering has recently given a new impetus for more detailed studies of these flows. Jet impingement is frequently used in industrial practice for their excellent heat and mass transfer characteristics, where localized and controlled surface transfer is desirable. In recent years, especially because of their wide usages at industrial products and cooling of electronic devices, the subject of impinging jets has gained a great importance. The velocity profile, flow characteristics, and pressure distribution on target surface are aimed to be analyzed in jet studies. Additionally, there have been some various studies about increasing heat transfer rates and searching relationship between dimensionless numbers and heat transfer coefficients. To understand the cooling phenomena by impinging air flow to a target body, mentioning literature is unavoidable. In this field of work, the early study is from Martin [1], about heat and mass transfer between a jet and an impingement surface. That study contains only two references to inclined jets, and a further search of the archival literature failed to unearth other research papers. The other work is that of Beltaos [2], who performed a fluid mechanic study of an inclined circular jet. In those experiments, pressures were measured on the surface of the impingement plate; the point of maximum pressure was identified with the stagnation point, and its displacement from the geometrical impingement
☆
Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (N. Celik).
0735-1933/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2005.10.009
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
373
point was reported. The controlled parameters of Reynolds number ranged from 35 000 to 100 000, and the jet-to-plate distance (L/D) was in the range of 15–47. Sparrow and Lovell [3] examined the heat transfer characteristics of an obliquely impinging circular air jet on a flat surface by using the naphthalene sublimation technique. In their study while Reynolds number based on the jet orifice varied from 2500 to 10 000, jet-to-plate distance was taken to be 7–15. The oblique angle was varied from 90° to 30°. Their results indicated that the region of maximum heat transfer shifted from the geometrical impingement point along the axis of symmetry. They concluded that, both maximum and average heat transfers were not highly sensitive to the oblique angle of the jet. Goldstein and Franchett [4] used metallic foil heaters with liquid crystals to measure the local heat transfer from an oblique jet to a flat plate. The impinging jet was obtained from a square edge orifice with three Reynolds numbers (10 000, 20 000, and 30 000), and the jet-to-plate distance varied from 4 to 10. At the result, they developed a new correlation for Nusselt number as a function of jet oblique angle and jet-to-plate distance. To determine the turbulent heat transfer and flow characteristics of an oblique impinging circular jet within closely confined walls using air flow, Ichimiya [5] measured the local heat transfer distribution of an oblique jet impinging on a surface. The temperature distribution on target surface was obtained by using liquid crystal technique. Abdlmonem et al. [6] performed an experimental study to determine the effect of the inclination of a two-dimensional air jet on the heat transfer from a uniformly heated flat plate. The impingement surface was a stainless steel plate of the same width as the jet nozzle. Local Nusselt numbers were determined as a function of (i) inclination angle of the air jet relative the plate in the range of 90–40°, (ii) nozzle exit to plate spacing (z/D) in the range of 4–12 and, (iii) Reynolds number based on the hydraulic diameter of the slot nozzle in the range of 4000–12 000. The results were presented in the form of graphs showing the variation of Nusselt number as a function of these parameters. The location of maximum heat transfer region appeared to fall between 0 and 3D uphill from the geometrical impingement point, and was found to be insensitive to the Reynolds numbers in the used range. The heat transfer characteristics of a normal and oblique circular fully developed air jet impinging on a heated flat plate was experimentally analysed by Bilen [7]. In the experiments, the ranges of parameters were taken to be 10 000– 40 000 for Reynolds number, 6–14 for dimensionless jet-to-plate distance (H/D), and 45–90° for jet inclination angle. The temperature variations on the flat plate were measured by using the liquid crystal technique. It was found that, heat transfer coefficient decreased with decreasing jet inclination angle at the stagnation point. Recently, turbulent flow and heat transfer characteristics of a two-dimensional oblique wall attaching offset jet were experimentally investigated by Song et al. [8]. The local Nusselt number distributions were measured using liquid crystal technique. The mean velocity, turbulent intensity, and wall static pressure coefficient profiles were measured at the constant value of jet Reynolds number of 53 200, for the dimensionless ratio (H/D) from 2.5 to 10 and the oblique angle α from 0° to 40°. It was observed that the time averaged reattachment point nearly coincided with the maximum value of Nusselt number for all oblique angles, but the maximum pressure point did only for α = 0°. Heat transfer from an obliquely impinging circular air jet to a flat plate was performed by Yan and Saniei [9]. Liquid crystal technique was used to measure the local Nusselt number. In the experiments the oblique angles were selected to be 90°, 75°, 60°, and 45°. The parameters such as Reynolds number (Re) and the ratio of dimensionless jet-to-plate distance (H/D) were taken to be in the range of 10 000 and 23 000, and 2–10 respectively. Local heat transfer coefficients were given as a function of the mentioned parameters and discussed in relation to the asymmetric wall jet upon impingement of the jet flow. They showed that for a given situation, the point of maximum heat transfer shifts away from the geometrical impingement point toward the compression side of the jet. After a literature survey about the jet impingement works, it can be clearly seen that to obtain impingement heat transfer people normally use an infinite plate (or sufficiently large plate) on the target surface. The flow impinges to target surface at laboratory conditions (ambient air). However current paper dealt with a set up inside a wind tunnel where the flow is driven by the axial pressure gradient in the entire flow field. It is well known that, in reality the target surface which is desired to be cooled is usually operated in closed mediums (i.e. electronic devices). From this point of view the authors aimed to see the heat transfer of jet impingement when the impingement work is occurred in the closed fields instead of free ambient. This study contains the heat transfer characteristics of impinging air jet to an oblique flat plate in a closed field. But to complete the study it is necessary to measure the axial pressures before and after the impingement. The authors desire to compile both heat transfer and flow characteristics in future studies. In present study, cooling of a heated flat plate, fixed with various angles of 90°, 60°, 45° and 30° in a wind tunnel test room was analyzed experimentally. In order to check the experimental results, one of the oblique angle of flat plate was
374
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 1. Experimental set-up, jet flow facility.
chosen to be 90°, since the data for oblique angle of 90° are available in the literature. The experiments were conducted for Reynolds number (11 806, 8879, and 5860), and dimensionless distance (z/L); here (z/L) is the ratio of the distance measured from initial surface side (z = 0) to whole plate length (Fig. 2). Contrary to literature the jet-to-plate distance was constant (H/D = 8). In this connection, local temperatures and the displacement of maximum heat transfer point from geometrical impingement point were measured for various positions of plate. Consequently, new correlations were developed for the dimensionless temperature as a function of Reynolds number, dimensionless ratio, and oblique angle. 2. Experimental study The slot jet experiments were performed in a wind tunnel. In order to produce a parallel jet flow, a rectangular slot of 30 × 300 mm2 was constructed in the contraction cone of the wind tunnel by increasing the contraction ratio (Fig. 1). The dimensions of flat plate were 300 × 136 mm2, and the target surface was roughness. A copper resistance wire was placed behind the plate that its whole surfaces except front surface were covered with a special sticky thermal isolation paper. The thermocouples were glued on the behind surface of aluminum plate through drilled holes (Fig. 2), and the void space was completely filled with thermal epoxy. The heater was an electrical insulated resistance wire having a length of 0.3 mm. The beading of wire was well done to supply perfect insulation. The beaded wires were wholly assembled to the backside of aluminum (Fig. 2). A big care
Fig. 2. Coordinate system and heating style of impingement plate.
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
375
Fig. 3. Positions of flat plate in the wind tunnel test room in front of jet flow.
was shown when covering the wires to plate backside, since a little gap between wires may cause non-uniformity of the heating on the plate. The flat plate was heated using a power supply variac. The air was supplied from a sucking fan and the flow rate was controlled by an inverter. After reaching steady state, the electric power input, the inverter, surface temperatures, and air temperatures at jet exit were recorded for each run. Both the jet exit velocity and temperature data were reported by Campbell CR10X data logger with a computer system. In the case of velocity measurement, an air velocity transducer (TSI Model 8455) was used. The temperatures were measured by T type thermocouples. The impingement plate was placed in test room with various oblique angles of 90°, 60°, 45° and 30° (Fig. 3). The surface temperatures were measured with respect to these various positions of plate for different Reynolds numbers as 5860, 8879, and 11606. Re number was defined base on hydraulic diameter of jet exit (Dh) and jet exit mean velocity (V). To estimate Reynolds number, first the uniformity of velocities issuing from jet exit must be proved. In this case another study of co-authors was used [10]. In the present experiments, the temperature measurements were accurate to within ± 1.25%, jet exit air velocity measurement ± 2%, and those of Re number for the ranges of parameters studied in the steady-state period is 3.8%. Uncertainty of copper wire resistance is 0.5% and based on pre-experiment calibration the uncertainties were about ± 3.99% in total heat obtained from the power supply. 3. Experimantal results and discussions For all inclination angles less than 90°, the point of maximum cooling/minimum temperature decreases dramatically with increasing inclination angles as evidenced in Fig. 4. The displacement distance is denoted by S (Fig. 2). The 0,14
[7] H/D=10 [3] H/D=7 [2] H/D=15 present H/D=8
0,12
S/H
0,1 0,08 0,06 0,04 0,02 0 30
60
90
120
φ (deg)
Fig. 4. Displacement distance between the point of maximum heat transfer and the geometrical impingement point.
376
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380 0,14 Re 11606 Re 8879 Re 5860
0,12
S/H
0,1 0,08 0,06 0,04 0,02 0 0
30
60 φ (deg)
90
120
Fig. 5. Reynolds number effects on the displacement of maximum heat transfer.
measured displacements were normalized by jet-to-plate separation H and were plotted in Fig. 4 as a function of the inclination angle ϕ. The inclination angle 30° was not placed in this figure, as the authors mentioned in literature survey did not perform experiments at this angle. So to compare the results obtained in the present work with the given literature only data for 90°, 60°, and 45° and Reynolds number 5860 are shown in this figure. As can be seen in the figure the displacement increases monotonically as the jet becomes more and more inclined. The displacement of the maximum heat transfer for inclined jets appears to have been previously measured by some investigators. But since the experimental conditions are not same a direct comparison of the results of Fig. 4 with the literature are not possible. Balteos [2] measured static pressures on the surface of an impingement plate and designated the point of maximum pressure taking place at the stagnation point. In that study, both the Reynolds numbers and the separation distances were significantly larger than those of the present investigation (35 000 ≤ Re ≤ 100 000 and 15 ≤ H/D ≤ 47). Furthermore, Belteos operated in the blowing mode to induce airflow through an orifice, and the jet was delivered through a converging nozzle fed by a circular tube. It is likely that this arrangement affected both the jet velocity profile and the turbulence level at exit. It is clearly seen that the displacements measured by Balteos are markedly smaller than those found by both Sparrow and Lovell [3], and Bilen [7]. The displacements found here are not as great as those given in Ref. [3] and Ref [7]. The deviations might well be explainable in terms of the differences in the experimental setups and operating ranges noted above. Fig. 5 shows the displacement of maximum heat transfer for three Reynolds numbers: 11 606, 8879, and 5860. The effect of oblique angles on the shift of maximum cooling is found to be sensitive to Re numbers. Increasing Re number can increase the distance of displacement. For example, the displacement of minimum temperature point is 9.12 mm for ϕ = 60°, 19.2 mm for ϕ = 45° and 24.24 mm for ϕ = 30° at Re = 5860. In the case of Re = 8879, these distances are 10.08 mm for ϕ = 60°, 20.64 mm for ϕ = 45° and 26.16 mm for ϕ = 30°. At last for Re = 11606, these values are 12.48 mm for ϕ = 60°, 21.6 mm for ϕ = 45°, and 27.6 mm for ϕ = 30°. In Fig. 6, minimum temperature/maximum cooling points on impingement plate with respect to oblique angles were plotted at different Reynolds numbers. Increasing the Reynolds number causes an increment on cooling of plate directly. Here, the best cooling is obtained at Re 11 606 as in the literature. Fig. 6 also shows the effect of oblique angle on minimum temperature. Decreasing the angle from 90° to 30° (it means increasing the inclination from jet exit) causes a poorer cooling than that of a conventional normal jet does. Figs. 7, 8, and 9 show the detailed surface local temperature distributions for four different oblique angles, ϕ = 90°, 60°, 45°, and 30° at three different Reynolds numbers. The inclination angle of 90° is well known conventional jet 340
Re 11606 Re 8879 Re 5860
T0 (K)
335 330 325 320 315 15
30
45
75 60 φ (deg)
90
105
120
Fig. 6. Variation of minimum temperature point with respect to oblique angles at three different Re number.
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 7. Temperature distribution with respect to z/L at different inclination angles for Re = 5860.
Fig. 8. Temperature distribution with respect to z/L at different inclination angles for Re = 8879.
377
378
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
Fig. 9. Temperature distribution with respect to z/L at different inclination angles for Re = 11 606.
position. The minimum temperature is measured at ϕ = 90°, on the geometrical impingement point for all Re number values. Than at ϕ = 60°, 45° and 30° the point of minimum temperature/maximum cooling shifts away from the geometrical impingement point toward the compression side on the principal axis. As drawn in Fig. 3, the down side of plate is compression side. When an inclination angle is given to plate (90–30°), the upper side of plate goes far away from jet exit, so this side is not cooled as good as down side. To obtain a correlation for temperature distribution with respect to variable parameters of Reynolds number, dimensionless distance (z/L), and oblique angle (sinϕ), the multiple regression method was used. The ratio of local temperatures (Tw) to minimum temperature (T0) on impingement surface was used as the constant parameter for correlations. Thus the correlation is obtained as follows: Tw =T0 ¼ aReb ðz=LÞc ðsin/Þd
ð1Þ
The coefficients a, b, c, and d were calculated for four different oblique angle, and the results were given in Table 1. At the oblique angle ϕ = 90°, inclination parameter does not effect the temperature distribution. Hence the coefficient d was not included for this configuration. While local temperature increase with decreasing angle (90–30°), that decreases with the dimensionless distance (z/L) (Fig. 2). It can be also said that; at ϕ = 90°; Re number is more effective
Table 1 Correlation coefficients ϕ (°)
a
b
c
d
90 60 45 30
0.289 0.862 0.854 0.840
0.1225 0.0040 0.0044 0.0050
− 0.1837 − 0.1461 − 0.1560 − 0.1727
– − 0.0003 − 0.0002 − 0.0001
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
379
than dimensionless distance. However, in the inclined positions of plate the dominant parameter on temperature variations is the dimensionless distance. 4. Conclusions Summarizing the results some conclusions may be listed. In present work, local temperature distributions from an obliquely impinging slot air jet to a flat plate were obtained experimentally. The effects of oblique angle (ϕ) on the local temperature was investigated for different Reynolds numbers of 5860, 8879 and 11 606. The parameter ranges are ϕ = 90°, 60°, 45° and 30°. In the range of parameters taken in this investigation, the region of maximum cooling shifts from the geometrical point toward the compression side of the plate. The point of maximum cooling is displaced from the geometrical point of the jet with the extent of displacement increasing as the inclination increases. The largest displacement encountered during the experiments is about 0.92 D. Conventional type jet shows a symmetric position (ϕ = 90°) as it is thought, but the distribution of temperatures on inclined surface shows a non-axisymmetric pattern. It is apparent that future work of surface pressure, velocity field and heat transfer for the same oblique impinging jet configuration is needed to resolve the issue of the relation between the point of maximum pressure, point of maximum heat transfer and the stagnation point for an obliquely impinging jet. It is clear that at same conditions (Re number, oblique angle ϕ, and jet-to-plate distance H/D), the air jet in a nonconfined room will cause better cooling than present one done. But operating conditions of devices are not as same as laboratory conditions. Especially the electronic devices are operated in confined positions. As mentioned above, in present study heated plate is in a test room of a wind tunnel. The authors hope that this study may help the investigators in this point of view. Nomenclature Dh hydraulic diameter [Dh = 4Ac/P] (m) G geometrical impingement point H jet-to-plate distance (m) L length of flat plate (m) Re Reynolds number based on jet exit velocity and the jet hydraulic diameter S shift of point of maximum heat transfer from the geometrical impingement point (m) T0 minimum temperature on the plate surface (°C) Tw local temperature on plate surface (°C) V velocity (m/s) z coordinate along jet issuing direction (m) ν kinematics viscosity (m2/sn) ϕ oblique angles of plate (°) Subscripts w wall 0 point of minimum temperature References [1] H. Martin, Heat and mass transfer between impinging gas jets and solid surfaces, Advances in Heat Transfer 13 (1977) 1–60. [2] S. Beltaos, Oblique impingement of circular turbulent jets, Journal of Hydraulic Research 14 (1976) 17–36. [3] E.M. Sparrow, B.J. Lovell, Heat transfer characteristics of an obliquely impinging circular jet, Journal of Heat Transfer 102 (1980) 202–209. [4] R.J. Goldstein, M.E. Franchett, Heat transfer from a flat surface to an oblique impinging jet, Journal of Heat Transfer 110 (1988) 84–90. [5] K. Ichimiya, Heat transfer and flow characteristics of an oblique turbulent impinging jet within confined walls, Journal of Heat Transfer 117 (1995) 316–322. [6] H.B. Abdlmonem, A.S. Michel, D.P. Chandrakant, The effect of inclination on the heat transfer between a flat surface and an impinging twodimensional air jet, International Journal of Heat and Fluid Flow 21 (2000) 156–163.
380
H. Eren, N. Celik / International Communications in Heat and Mass Transfer 33 (2006) 372–380
[7] K. Bilen, An Experimental Investigation of Heat Transfer Characteristics of a Normal and Oblique Air Jet Impinging on Heated Flat Plate, Doctoral thesis, KTU, Trabzon, Turkey, 1994. [8] H.B. Song, S.H. Yoon, D.H. Lee, Flow and heat transfer characteristics of a two-dimensional oblique wall attaching offset jet, International Journal of Heat and Mass Transfer 43 (2000) 2395–2404. [9] X. Yan, N. Saniei, Heat transfer from an obliquely impinging circular air jet to a flat plate, International Journal of Heat and Fluid Flow 18 (1997) 591–599. [10] H. Eren, N. Celik, Experimental investigation of the jet flow in a wind tunnel test room which tries to suck, Proceedings of the Third GAP Engineering Congress, Sanliurfa, Turkey, 2000, pp. 17–23.