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Experimental investigation and CFD analysis of rectangular proﬁle FINS in a square channel for forced convection regimes Ece Ayli a, Ozgur Bayer b, Selin Aradag a, * a b

TOBB University of Economics and Technology, Department of Mechanical Engineering, Sogutozu, Ankara, 06560, Turkey Middle East Technical University, Department of Mechanical Engineering, Cankaya, Ankara, 06800, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 November 2015 Received in revised form 8 June 2016 Accepted 8 June 2016

Steady-state heat transfer from rectangular ﬁn arrays is examined experimentally and numerically for turbulent fully developed ﬂow. The effects of geometrical parameters on heat transfer coefﬁcient and Nusselt number are investigated. For different inter ﬁn ratios, Reynolds number and Nusselt number dependence of the results is investigated. A generalized empirical correlation for Nusselt number is developed for rectangular ﬁns for a Reynolds number range of 17 107 < Re < 2.47 108, and an aspect ratio of 0.089 < d/w < 0.0625, 0.24875 < t/L < 0.729. The correlation can predict the results with a relative rms error of 11.14%. © 2016 Elsevier Masson SAS. All rights reserved.

1. Introduction Fins with different geometries are used in a wide range of applications such as cooling of electronic equipment, turbine blades and various heat exchanger devices. Fins on a heating surface increase the heat dissipation area and may cause turbulent mixing of ﬂow. High heat ﬂux is crucial for effective cooling of surfaces with relatively small surface area, especially in military, healthcare, electronic systems and aerospace applications. Systems become more reliable and durable with effective cooling [1e3]. Several types of cooling techniques are developed in order to achieve the most efﬁcient cases. Two main types are gas and liquid cooling. Cooling with air is inexpensive and reliable. It is also easy to design and manipulate. Natural and forced convection heat transfer modes are widely used for thermal management. According to researchers, forced convection is a better choice as it results in higher heat transfer coefﬁcients and provides larger heat transfer rates. There are several studies in literature related to heat transfer and pressure drop in channel ﬂows with ﬁns that have varying geometries [1e12]. Dogan and Sivrioglu studied [4,5] mixed convection heat transfer from longitudinal ﬁns in a horizontal channel. The height and the spacing of the ﬁns are optimized to reach to the maximum

* Corresponding author. E-mail address: [email protected] (S. Aradag). http://dx.doi.org/10.1016/j.ijthermalsci.2016.06.021 1290-0729/© 2016 Elsevier Masson SAS. All rights reserved.

heat transfer. Changing ﬁn spacing does not alter heat transfer coefﬁcient, whereas increasing the ﬁn height increases the heat transfer coefﬁcient, according to their experimental ﬁndings [4,5]. Oztop et al. [6] performed simulations of heat and ﬂuid ﬂow in heated blocks at three different Reynolds numbers changing between 400 and 1300. The effect of triangular vortex promoters on heat transfer is investigated. An experimental study is carried out by Tahat et al. [7] to investigate the heat transfer from pin ﬁn arrays for staggered and in-line arrangements. Jeng and Tzeng [8], performed an experimental study to investigate pressure drop and heat transfer characteristics of a square pin ﬁn, and a circular ﬁn in different arrangements: in-line and staggered. In-line square pin ﬁn array has smaller pressure drop than that of in line circular pin ﬁns. The staggered square pin ﬁn conﬁguration has the largest pressure drop. Sahin et al. [9] investigated overall heat transfer coefﬁcient, friction factor and effects of various design parameters experimentally within a Reynolds number range of 13,500e42,000. For higher thermal performance, it is suggested that lower clearance ratio (C/H), inter ﬁn spacing ratio and Reynolds numbers are more effective. Ayli et al. [10] investigated the effect of geometrical ﬁn parameters on heat transfer characteristics and velocity for turbulent air ﬂow in square cross section duct. According to their results, triangular and rhombus vortex promoters are able to decrease

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maximum temperature more than square promoters since they focus more air to the right wall of the heat source and cool the area between the heat sources more effectively. Akyol and Bilen [11] conducted experiments to investigate heat transfer and friction loss characteristics over a horizontal rectangular channel. Reynolds number varies between 3000 and 32,000. With the staggered array, better heat transfer is obtained than inline arrangement due to the increase of turbulence. It is also stressed that an increase in the Reynolds number causes increase in pressure drop and friction factor because of the blockage effect and it is higher in staggered arrangement than in-line. Wang et al. [12] studied the ﬂow and heat transfer characteristics inside a rectangular channel numerically and experimentally. Different shapes of ﬁns (circular, elliptical, drop shaped pins) with the same cross sectional areas, are used in the experiments. According to their results, the heat transfer rate of drop shaped pin ﬁns is weaker than circular pin ﬁns. Icoz and Jaluria [1] investigated natural convection heat transfer in a horizontal channel with two heat sources. Most appropriate boundary conditions to accurately model the transport processes are investigated. The effect of Grashof number, cavity dimensions, distance between the heat sources, heat transfer characteristics and their effects on the ﬂow are also investigated. When the channel height and the separation distance are increased, instability is observed. In this study, with the help of a fan, fully developed turbulent ﬂow is obtained. Test pieces with different ﬁn geometries are placed on the bottom surface of a square cross section channel. The ﬁnned aluminum body is heated at the test section of the set-up and constant heat ﬂux boundary condition is obtained. Other parts of the channel are insulated. The effect of geometrical parameters on heat transfer coefﬁcient and Nusselt number is investigated for turbulent ﬂow with the help of experiments. Furthermore, computational ﬂuid dynamics (CFD) studies are performed to compare the numerical and experimental studies and also to understand the ﬂow behavior in detail. A generalized empirical correlation is developed for rectangular ﬁns for a Reynolds number range of 17 107 < Re < 2.47 108, aspect ratio of 0.089 < d/w < 0.0625, and of 0.24875 < t/L < 0.729 where t/L is the ﬁn width to ﬁn length ratio and d/w is ﬁn spacing ratio.

2. Experimental set-up Fig. 1 shows the experimental test set-up which comprises a fan, honeycomb ﬁlter, hydrodynamic developing section, test section, outlet and data acquisition system. Temperature and velocity measurements are carried out with thermocouples and anemometers respectively. The square channel has an internal cross section of 225 cm2 and a total length of 227 cm. Several researchers [4,12,13] used both honeycomb ﬁlter and a hydrodynamic developing section to guarantee the uniform ﬂow ﬁeld, minimizing the turbulence effects and ﬂow separation. Honeycomb is also utilized in this study, to minimize the lateral air velocity, which is generated by the fan; so that the uniform air velocity is obtained for the inlet, and the hydrodynamic developing section is 1600 mm to ensure a fully developed ﬂow. Bottom surface of the test piece in the test section is heated with a heater that has the same dimensions with the base surface. The power input to the heater so to the test piece is controlled with a voltage adjuster. Two types of insulation materials are used to minimize the heat loss to the outer surface. At the top and sides of the channel, climaﬂex is used, whereas; glass wool is used for insulating the heater, which is located at the bottom of the ﬁnned body placed in the test section. Aluminum rectangular proﬁle ﬁns are manufactured on an aluminum plate in dimensions of 150 mm length and 400 mm width,C, as shown in Fig. 2 with the same dimensions of the heater. The ﬁnned test pieces are made from aluminum 6000 series. 36 thermocouples are ﬁtted on the test section. 27, 28, 29, 30th thermocouples are located for measuring the free stream air temperature and the air temperature just before the heated test section. 31st and 32nd thermocouples are located at the exit of the channel for measuring the air temperature. Finally, a group of thermocouples are located between the heater and the glass wool, and below the glass wool. Measured data is recorded for every 10 s. Averages of the data measured using thermocouples are taken as an average temperature of the corresponding location on the test piece. Air velocity is measured by an anemometer across the set-up at the 27, 28, 31 and 32nd points. Net heat transfer rate is calculated by the energy balance which is given

Fig. 1. Experimental set-up.

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281

Fig. 2. Thermocouple locations (a) Top view, (b) Front view, (c) Insulation material.

in Eqn. (1). Qnet is the total power input to the test section. Qvol is calculated by Ohm’s Law (Q ¼ IV) and it is the total power supplied to the heater. Qloss is the heat loss through the insulation and is calculated by equation (2) [5].

Qnet ¼ Qvol Qloss

(1)

Qloss ¼ kinsulation Ainsulation

DTinsulation

(2)

Linsulation

Unﬁnned ﬂat plate with the same dimension of the heated section is tested ﬁrst to make sure that the heat ﬂux is uniform and the results show uniform heat ﬂux distribution. To determine the local convective heat transfer coefﬁcient and temperature distribution in rectangular ﬁn arrays, effect of ﬁn length, width and distance between the ﬁns are investigated. In all cases, the number of ﬁns is kept the same. Average air velocity is calculated by taking the average of the local measurements using the anemometer. Detailed properties of the test samples are given in Table 1. 3. Numerical methodology Numerical analyses are performed to understand the ﬂow ﬁeld in detail and computational results are compared with the experimental results. Ansys Fluent Solver [15] is used for the CFD analysis. Steady state simulations are performed. Navier-Stokes equations simulate ﬂow motion in two dimensions. Navier-Stokes equations can be shown as in equation (3).

Dðui Þ vui vu ¼r þ uj i r Dt vt vxj

!

vP v2 u þ m 2i þ Fi ¼ vxi vxj

(3)

Turbulence is simulated by Reynolds-Averaged Navier Stokes

Table 1 Fin Conﬁgurations. Test cases

Number of ﬁns

C/L

d/t

1 2 3 4 5 6 7 8 9

8 8 8 8 8 8 8 8 8

3.75 4.28 5 6 3.75 4.28 5 6 3.75

3.58 3.58 3.58 3.58 1.15 1.15 1.15 1.15 1.846

(RANS) approximation and k e ε SST turbulence model is used. As it is shown in Fig. 4, turbulence model test results are presented with the help of the heat transfer coefﬁcient at speciﬁc thermocouple positions (Fig. 3). Also in Table 2, for hydrodynamic convergence, average exit velocity values are compared for different turbulence models for several cases. When the experimental results and the results of models are compared, k-u SST turbulence model gives better results than the other models as it shows a similar trend with the experimental results. In the numerical solution, PRESTO scheme is used. Second order upwind scheme is chosen. Standard algorithm is used to discretize the pressure equation and SIMPLE algorithm is chosen to couple the velocity and pressure ﬁelds. The computations are performed with a maximum residual of 106 and a maximum number of iterations of 20,000. For all of the cases, mass ﬂow rates are the same. Simulation domain dimensions are the same with that of the experimental test section. Experimentally measured ambient temperatures and inlet velocities are used as inlet boundary condition. No slip and adiabatic wall conditions are used for the walls as boundary conditions. The whole simulation domain is illustrated in Fig. 5. The inlet is intentionally not placed very close to a solid obstruction and it is observed from the close view that the ﬂow is fully developed before entering the test section. The structured mesh proﬁles are generated in ANSYS CFX Mesh module [14]. A converged and mesh independent solution is obtained. The results of the simulation do not change with varying mesh (Fig. 6). Grid independence was achieved by increasing the number of elements and plotting convergence of heat transfer coefﬁcient for all of the cases. For all of the cases 106 number of elements are used. Both two dimensional and three dimensional simulations are performed for the preliminary numerical study. As it is seen in Fig. 7, the ﬂow structures do not change in the third dimension. Streamlines for several planes on the third dimension and the streamlines for the 2D simulations are plotted and are shown in Fig. 7. Therefore, it is concluded that the ﬂow structure is independent of the third dimension as also veriﬁed by the literature [15] where two dimensional results conﬁrm with the experimental ﬁndings. Further studies are performed only in the two dimensional domain because of these reasons presented. 4. Data processing Data obtained from the experiments are, temperature values at thermocouple positions, free stream velocity value, voltage drop

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Fig. 3. Schematic representation of test samples and thermocouple positions (a) 3D view (b) Front view.

170

Heat transfer coeﬃcient,h (W/m 2K)

150

130

110

90

70

50 0

50

100

150

Experimental

200 Distance (mm) kw sst

250

300 kw

350

400

ke

Fig. 4. Turbulence model comparison graph (Test case 1).

Table 2 Turbulence model comparison table. Experimental exit velocity (m/ k-ε model exit s) velocity Case 3 10.2 Case 5 14.6 Case 9 15.8

9.02 9.6 11.7

Relative error (%)

k-u model exit velocity

Relative error (%)

Kdu SST model exit velocity

Relative error (%)

11.56 34.24 25.94

9.8 13.8 14.2

3.92 5.47 10.12

9.97 14.5 15.3

2.25 0.68 3.16

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283

Fig. 5. Simulation domain (case 8).

Heat transfer coeﬃcient (h, W/m2K)

130 125 120 115 110 105 100 95 90 85 80 250000

500000

750000

1000000

1250000

1500000

1750000

2000000

Number of Elements case 1

case2

case 3

case 4

case 6

case 7

case 8

case 9

case 5

Fig. 6. Mesh Independency Study (Thermocouple position 1).

Fig. 7. Velocity streamlines at (a) z ¼ 0 (b) z ¼ 0.50 (c) z ¼ 1.00 (d) 2D domain for case 1.

and electric current. Using these parameters, Nusselt number, Reynolds Number, local convective heat transfer coefﬁcient and Prandtl number are calculated.

Hydraulic diameter which is the ratio of the open duct volume for ﬂow to the wetted surface area, is used to determine the ﬂow regime of the ﬂowing air by calculating Reynolds number. The

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Table 3 Thermal conductivity and speciﬁc heat calculation.

k Cp

Re ¼

a

b

c

d

1.5207 1011 6.78 1011

4.8574 108 1.65 107

1.0184 104 6.78 105

0.0003933 0.9703

4Vf Af

(5)

Steady state conditions are reached before the measurements are made, to be able to obtain reliable values. Steady state temperature values are used to calculate the thermophysical properties of the ﬂuid (speciﬁc heat, dynamic viscosity, thermal conductivity). Thermal conductivity and speciﬁc heat of air can be calculated by a 4th order polynomial function of temperature with a form of f(T) ¼ aT3 þ bT2 þ cT þ d . The coefﬁcients of the equation are given in Table 2 [16]. Prandtl number, deﬁned as the ratio of momentum diffusivity to thermal diffusivity, is determined by Eqn. (6).

hydraulic diameter is calculated as given in equation (4).

Dh ¼

u∞ D h v

(4)

According to Wang et al. [12], for ﬁn problems, Vf is the total ﬂuid volume inside the ﬁns array region and Af is the wetted surface area which is the area in contact with the incoming air. This convective area is the sum of the areas of the wall between the ﬁns and ﬁn areas. Reynolds number is deﬁned based on the hydraulic diameter is given below.

Pr ¼

v

a

¼

Cp m

(6)

a

The local heat transfer coefﬁcient, hlocal is deﬁned as:

Fig. 8. Steady-state temperature distribution for test case 3.

170

Heat transfer coeﬃcient,h(W/m K)

150

130

110

90

70

50 0

50

100

150

200

250

300

350

Distance (mm) case 1

case 2

case 3

case 4

Fig. 9. Variation of local heat transfer coefﬁcient with distance for different ﬁn heights (case 1e4).

400

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285

125 120

Heat Transfer Coeﬃcient (h, w/m 2K)

115 110 105 100 95 90 85 80 0

50

100

150

200

250

300

350

400

Distance (mm) case 5

case 6

case 7

case 8

Fig. 10. Variation of local heat transfer coefﬁcient with distance for different ﬁn heights (case 5e8).

Fig. 11. Nusselt number as a function of Reynolds number for case 3 (d/t ¼ 3.58) and case 7 (d/t ¼ 1.15).

5. Results and discussion

hlocal ¼

qnet ðTw Ti Þ

(7)

where qnet is the heat ﬂux on the heated surface, Tw is the temperature of the end wall, Ti is the steady state location temperature in the thermocouple positions. The local Nusselt number is calculated based on the average heat transfer coefﬁcient and hydraulic diameter as:

Nulocal ¼

hlocal Dh k

(8)

k is the conductivity which is calculated as it is given in Table 3.

5.1. Experimental results Experiments are conducted to obtain heat transfer rate across ﬁns and temperature distribution of the system. To get reliable values, steady state condition is achieved before the measurements are taken. For ﬁns with 35 mm height, the system reaches equilibrium after approximately 84 min and the temperature distribution for the eighth (8th) node is shown in Fig. 8. In Fig. 9, convective heat transfer coefﬁcient values for ﬁrst four cases are shown. In the ﬁrst case (40 mm high ﬁn), which is the longest ﬁn conﬁguration, the heat transfer coefﬁcient reaches to its maximum value. When the ﬁn is shorter (case 4), the heat transfer coefﬁcient also decreases. This is why the maximum temperature

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Fig. 12. Nusselt number as a function of Reynolds number for case 3 (C/L ¼ 13.33) and case 4 (C/L ¼ 16).

150

Heat Transfer Coeﬃcient (h,W/m 2K)

140 130 120 110 100 90 80 70 0

50

100 case 1

150

200 Distance (mm) case 5

250

300

350

400

case 9

Fig. 13. Local heat transfer coefﬁcient versus inter ﬁn distance ratio.

values are observed in the shortest ﬁn for all types of ﬁn groups. In shorter ﬁns the area which is in contact with the coolant decreases and this is why the temperature values are greater than the temperatures for the longer ﬁn conﬁgurations. In Fig. 10, local heat transfer coefﬁcient variation with streamwise distance is shown for cases 5 to 8. The maximum local heat transfer coefﬁcient is obtained for the smallest value of the clearance ratio (C/L). This trend is observed by other researchers, as well [17,18]. In Fig. 11, Nusselt number versus Reynolds number graph is shown for fully developed and turbulent ﬂow. Nusselt number increases with increasing inter-ﬁn distance, d. This pattern is also observed in Figs. 9 and 10. In Fig. 12, clearance ratio effect is given

for Nusselt number. Nusselt number increases with rise of d/t and decrease of clearance ratio, C/L. As expected, increase in the Reynolds number generates more turbulence and Nusselt number increases because of the turbulence effect. Cases 1, 5 and 9, which have same clearance ratio, should be compared (Fig. 13) to investigate the effect of inter-ﬁn distance ratio in detail. It is again observed that larger d/t ratio provokes larger heat transfer rates. When the distance between the ﬁns is extended, more incoming air gets between the ﬁns and more turbulence is generated in this region. As hot and cold ﬂuids mix, the maximum temperature values decrease and heat transfer rate and Nusselt number increase. This pattern is also proved with CFD analysis as it is seen in Fig. 13.

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287

Fig. 14. Temperature contours for (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4 (e) Case 5 (d) Case 6 (f) Case 7 (g) Case 8.

0.675 0.67

Prandtl Number

0.665 0.66 0.655 0.65 0.645 0.64 0.635 700

750

800

850

900

950

1000

Nusselt Number experimental numerical Fig. 15. Comparison of Prandtl and Nusselt Numbers for case 5.

1050

1100

288

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Fig. 16. Comparison of the correlation obtained from the data set and experimental results.

5.2. Computational ﬂuid dynamics (CFD) results Velocity values are close to zero and turbulence forms in this region when ﬁn spacing is not enough for incoming air to enter this zone, between the ﬁns. When inter-ﬁn distances are large enough for entering of cold ﬂuid between the ﬁns, cold ﬂow enter to this zone, hot ﬂuid mixes with the incoming air which decreases the maximum temperature values and increases heat transfer rate. As it is seen in Fig. 14, inter ﬁn temperature values are larger when d/t ratio is smaller. Fig. 15 shows comparison of Nusselt versus Prandtl numbers for experimental and numerical results. As the Nusselt number increases Prandtl number also increases. As Prandtl number rises, thermal boundary layer becomes thinner and heat transfer rate increases. The maximum difference between experimental and numerical results is 2.8%.

Nu ¼ aReb

c d d t w L

(10)

d t þ d log log Nu ¼ log a þ b logðReÞ þ c log w L

(11)

By performing least squares linear regression [19], equation (12) is obtained for Nu number a given range.

Nu ¼ 4:69822 107 Re1:11986

0:2151597 0:20729137 d t w L (12)

where;

9:17 107 < Re < 2:47 108 0:089 < 5.3. Development of Nusselt number correlation Convective behavior of the steady state, turbulent, rectangular ﬁn is assumed as a function of Reynolds number, Prandtl number, ﬁn span ratio, d/w, and ﬁn length ratio, t/L.

d t Nu ¼ f Re; Pr; ; w L

(9)

General form of the correlation function is given in equation (10). This equation is transformed by taking its logarithm to yield equation (11). The logarithm of the dependent variable is linearly dependent on the logarithms of the independent variables.

d < 0:0625 w

t 0:24875 < < 0:729 L In Fig. 16, comparison of generalized heat transfer correlation for rectangular ﬁn and experimental results are given. The average deviation between correlation equation and experimental data is less than ±17.79 %. Root mean square (rms) error is calculated which measures the differences between values predicted by correlation and the values taken from the experiments. For correlation and experiment the root mean square error (rmse) is. ±11.14 %. In Fig. 17, Nusselt number distribution with the streamwise direction and in Fig. 18, Nusselt number variation with t/L is given for

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289

Fig. 17. Nusselt number distribution with the streamwise direction and comparison of data with correlation.

Fig. 18. Variation of Nusselt number with t/L and comparison of data with correlation. Table 4 Relative Errors and Root Mean Square Errors for the data shown in Figs. 14e16.

Correlation equation vs Experimental Values Nusselt number versus distance comparison Nusselt number versus t/L comparison

both correlation and experimental values. Error calculations are given in Table 4. The results in Fig. 18 demonstrate that at high t/L ratios, t/L effect on Nusselt number is weak. 6. Conclusions In this combined experimental and computational work, the effects of geometrical ﬁn parameters on heat transfer characteristics are investigated for turbulent air ﬂow in square cross section duct. A correlation for Nusselt number is developed and presented

Relative error (%)

Relative RMS error (%)

17.79 10.32 16.35

11.14 6.12 14.81

for steady state, turbulent, rectangular ﬁn array. Experimental results are presented for different ﬁn spacing, ﬁn height, Reynolds number and effects of these parameters is investigated. Furthermore, the ﬂow phenomenon is further examined with CFD analysis to examine the effects of inter ﬁn distances. The conclusions are summarized as: (1) For the smallest value of the clearance ratio, C/L, maximum local heat transfer coefﬁcient is obtained.

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(2) Because of the boundary layer effect, when d/t (inter-ﬁn distance) ratio gets smaller maximum temperature values increase. (3) Increase of the Reynolds number produces more turbulence and Nusselt number increases because of the turbulence effect. (4) Nusselt number increases with an increase of inter-ﬁn distance, d/t and with a decrease of ﬁn clearance ratio, C/L. (5) Computational results are in good agreement with the experimental ﬁndings. Computational ﬂuid dynamics technique is helpful for predicting heat transfer characteristics of the turbulent ﬂow of rectangular ﬁn. (6) Steady state data set correlation is obtained which can predict the characteristics of turbulent ﬂow of rectangular ﬁns.

[3]

[4]

[5]

[6]

[7] [8]

Acknowledgments [9]

The construction of the set-up is ﬁnancially supported by METUBAP project (BAP-08-11-2013-035) and the experiments were performed at METU Department of Mechanical Engineering Heat Transfer Laboratory. The computations are performed using the facilities of TOBB ETU Hydro Energy Research Center CFD Laboratory supported by Turkish Ministry of Development. Some of the results presented here are also presented brieﬂy at International Symposium of Convective Heat and Mass Transfer in July 2014. The authors would like to thank to undergraduate student Firat Kiyici, MS student Gizem Demirel and lab technician Mustafa Yalcin for their help during data collection and the construction of the setup. References [1] Icoz T, Jaluria Y. Design of cooling systems for electronic equipment using both experimental and numerical inputs. J Electron Packag 2004;126(4):465e71. [2] Aradag S, Olgun U, Akturk F, Basibuyuk B. CFD Analysis of cooling of electronic

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