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Experimental investigation and CFD analysis of rectangular profile FINS in a square channel for forced convection regimes
International Journal of Thermal Sciences 109 (2016) 279e290
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
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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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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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).
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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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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
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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
[10] [11] [12]
[13]
[14] [15]
[16] [17] [18] [19]
equipment as an undergraduate design project. Comput Appl Eng Educ 2012;20:103e13. Ayli E, Kiyici F, Bayer O, Aradag S. Experimental investigation of heat transfer and pressure drop over rectangular profile fins placed in a square channel. In: International Symposium of convective heat and mass Transfer,7-15 july, 2014; 2014. lu M. Experimental Investigation of mixed convection heat Dogan M, Sivriog transfer from longitudinal fins in a horizontal rectangular channel: in Natural convection dominated flow regimes. Energy Convers Manag 2009;50: 2513e21. lu M. Experimental investigation of mixed convection heat Dogan M, Sivriog transfer from longitudinal fins in horizontal rectangular channel. Int J Heat Mass Transf 2010;53:2149e58. Oztop H, Varol Y, Alnak Dogan E. Control of heat transfer and fluid flow using a triangular bar in heated blocks located in a channel. Int Commun Heat Mass Transf 2009;39:878e85. Tahat M, Kodah ZH, Jarrah BA, Probert SD. Heat transfers from pin-fin arrays experiencing forced convection. Appl Energy 2000;67:419e42. Jeng Tzer-Ming, Tzeng Sheng-Chung. Pressure drop and heat transfer of square pin-fin arrays in in-line and staggered arrangements. Int J Heat Mass Transf 2007;50:2364e75. Sahin B, Demir A. Performance analysis of a heat exchanger having perforated square fins. Appl Therm Eng 2008;28:621e32. Ayli E, Turk C, Aradag S. Experimental investigation of cooling of electronic equipment. Int J Material, Mech Manuf 2013;1:153e7. Akyol U, Bilen K. Heat transfer and thermal performance analysis of a surface with hollow rectangular fins. Appl Therm Eng 2009;26:209e16. Wang F, Zhang J, Wang S. Investigation on flow and heat transfer characteristics in rectangular channel with drop-shaped pin fins. Propuls Power Res 2012:64e70. Pandit J, Thompson M, Ekkad SV, Huxtable ST. Effect of pin fin to channel height ratio and pin fin geometry on heat transfer for flow in rectangular channels. Int J Heat Mass Transf 2014;77:359e68. ANSYS Fluent. Version 15.0, user manual. 2015. Jouhara H, Axcell B. Modelling and simulation techniques for forced convection heat transfer in heat sinks with rectangular fins. Simul Model Pract Theory 2009;17:871e82. Incropera FP, DeWitt DP. Introduction to heat transfer. New York: John Wiley & Sons; 1996. Sara ON. Performance analysis of rectangular ducts with staggered square pin fins. Energy Convers Manag 2003;44:1787e803. Sara ON, Yapici S, Yilmaz M. Second law of rectangular channels with square pin-fins. Int Comm Heat Mass Transf 2001;28(5):617e30. Chapra SC, Canale RP. Numerical methods for engineering. sixth ed. McGrawHill; 2010.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
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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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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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
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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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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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equipment as an undergraduate design project. Comput Appl Eng Educ 2012;20:103e13. Ayli E, Kiyici F, Bayer O, Aradag S. Experimental investigation of heat transfer and pressure drop over rectangular profile fins placed in a square channel. In: International Symposium of convective heat and mass Transfer,7-15 july, 2014; 2014. lu M. Experimental Investigation of mixed convection heat Dogan M, Sivriog transfer from longitudinal fins in a horizontal rectangular channel: in Natural convection dominated flow regimes. Energy Convers Manag 2009;50: 2513e21. lu M. Experimental investigation of mixed convection heat Dogan M, Sivriog transfer from longitudinal fins in horizontal rectangular channel. Int J Heat Mass Transf 2010;53:2149e58. Oztop H, Varol Y, Alnak Dogan E. Control of heat transfer and fluid flow using a triangular bar in heated blocks located in a channel. Int Commun Heat Mass Transf 2009;39:878e85. Tahat M, Kodah ZH, Jarrah BA, Probert SD. Heat transfers from pin-fin arrays experiencing forced convection. Appl Energy 2000;67:419e42. Jeng Tzer-Ming, Tzeng Sheng-Chung. Pressure drop and heat transfer of square pin-fin arrays in in-line and staggered arrangements. Int J Heat Mass Transf 2007;50:2364e75. Sahin B, Demir A. Performance analysis of a heat exchanger having perforated square fins. Appl Therm Eng 2008;28:621e32. Ayli E, Turk C, Aradag S. Experimental investigation of cooling of electronic equipment. Int J Material, Mech Manuf 2013;1:153e7. Akyol U, Bilen K. Heat transfer and thermal performance analysis of a surface with hollow rectangular fins. Appl Therm Eng 2009;26:209e16. Wang F, Zhang J, Wang S. Investigation on flow and heat transfer characteristics in rectangular channel with drop-shaped pin fins. Propuls Power Res 2012:64e70. Pandit J, Thompson M, Ekkad SV, Huxtable ST. Effect of pin fin to channel height ratio and pin fin geometry on heat transfer for flow in rectangular channels. Int J Heat Mass Transf 2014;77:359e68. ANSYS Fluent. Version 15.0, user manual. 2015. Jouhara H, Axcell B. Modelling and simulation techniques for forced convection heat transfer in heat sinks with rectangular fins. Simul Model Pract Theory 2009;17:871e82. Incropera FP, DeWitt DP. Introduction to heat transfer. New York: John Wiley & Sons; 1996. Sara ON. Performance analysis of rectangular ducts with staggered square pin fins. Energy Convers Manag 2003;44:1787e803. Sara ON, Yapici S, Yilmaz M. Second law of rectangular channels with square pin-fins. Int Comm Heat Mass Transf 2001;28(5):617e30. Chapra SC, Canale RP. Numerical methods for engineering. sixth ed. McGrawHill; 2010.