Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes

Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes

Experimental Thermal and Fluid Science 71 (2016) 57–69 Contents lists available at ScienceDirect Experimental Thermal and Fluid Science journal home...

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Experimental Thermal and Fluid Science 71 (2016) 57–69

Contents lists available at ScienceDirect

Experimental Thermal and Fluid Science journal homepage:

Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes Hongxia Zhao a,⇑, Zhigang Liu b,⇑, Chengwu Zhang b, Ning Guan b, Honghua Zhao c a

Shandong University, School of Power and Energy, Jinan, 250061, China Energy Research Institute of Shandong Academy of Sciences, Jinan 250014, China c State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China b

a r t i c l e

i n f o

Article history: Received 9 June 2015 Received in revised form 24 September 2015 Accepted 11 October 2015 Available online 23 October 2015 Keywords: Mini pin fin Shape Friction factor Endwall effect Pin density Reynolds number

a b s t r a c t Experiments were performed on de-ionized water as working fluid, flowing across staggered mini pin fins of the same height and transverse spacing but with different pin density and different shapes of circular, elliptical, square, diamond and triangle, in a rectangular channel. The volume flow rate, pressure difference and temperature at the inlet and outlet were measured for the channel with different pin fin shapes at various Reynolds number (Re) in the range of 50–1800 to obtain the friction factor. The results showed that the friction factor for all the fins decreased with the increase of Re. At low Re (<100), the influence of the endwall effect on the flow characteristics of the test section is obvious and the friction factor weighs more; while at high Re (>300), the friction factor caused by eddy dissipation is the main part. In the intermediate range of Re (100–300), there is a transition. At different flow regimes, the shape and the fin density affects f differently. For laminar flow, the channel with triangle pin fins of the smallest density has the minimum f value while the elliptical one of the largest density has the maximum f value. On the contrary, for turbulent flow the channel with triangle pin fins has the maximum f while the elliptical one has the minimum f. Comparisons were made between experimental data and existing correlations, and results showed that there were large deviations between them. The existing correlations for the friction factor cannot correctly describe the whole flow range including laminar, transitional and turbulent zones, and new correlations are needed. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction The flow and heat transfer in micro domains has received great attentions and has been used widely in many fields, such as biomedical science [1–3], micro reactors [4,5], micro engines [6,7], micro mixers [8–10], and electronics cooling [11–13]. Micro pin fins embedded in a mini/micro channel is one of the most important micro structures. The micro pin fins can greatly enhance the active area of heat sinks; moreover, the pin fins disturb the flow and break down the boundary layer, which promotes the early flow transition, boosts the flow mixing, and drastically raises the heat transfer. They might solve the problem of high heat flux and overcome the bottle neck for rapid development of ultra-largescale integration of electronics and micro-electro-mechanical systems (MEMS). Over the years, a large amount of research work has been conducted on flow and heat transfer characteristics of ⇑ Corresponding authors. E-mail addresses: [email protected] (H. Zhao), [email protected] (Z. Liu). 0894-1777/Ó 2015 Elsevier Inc. All rights reserved.

micro pin finned channel. The focus of the current paper is on the hydraulic performance of the micro pin finned structures, so in the following, only the flow characteristics is surveyed. Many researchers chose different definitions of Reynolds number when studying the micro pin finned channels. Reynolds number and minimum cross-sectional flow area are usually calculated using different approaches depending on the pin height-todiameter ratio H/D [14]. In the first approach, for arrays with long fins (H/D > 8), ‘‘tube bundle” fins, the pressure drop is dominated by the fins while the endwall effects, i.e., thickening of boundary layer on the end walls, are secondary; the length scale for calculating Reynolds number is simply the fin hydraulic diameter D, and Reynolds number designated as Re here. In the second approach, for very short fins (H/D < 1/2) commonly used in compact heat exchangers, where the characteristic pressure drop is severely influenced by the top and bottom walls. These fin configurations are referred to as ‘‘compact heat exchanger” fins. The hydraulic diameter of the heat exchanger is used to calculate Reynolds number designated as Red. In the third approach, the minimum cross-sectional flow area has been adopted to define Reynolds


H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

Nomenclature Af a, b D C f H L Nx Nt DP Q Re REER SL ST Tf

cross-sectional area of the fin, m2 dimensional size of pin fin, m hydraulic diameter of pin fin, m tip clearance (C = H  Hf), m friction factor height, m length, m number of rows of pin fins number of total pin fins pressure difference between channel inlet and outlet, Pa flow rate, m3 s1 Reynolds number relative error longitudinal distance between pin fins transverse distance between pin fins, m characteristic temperature of the fluid, °C

number, and Rec is assigned to it [15]. In the following literature survey, Reynolds number used will be stated as Re, Red and Rec when mentioned, according to their original definitions. Peles et al. [16] performed adiabatic tests for laminar flow over micro pin fin at 10 < Re < 80. They found out that both conventional correlations and existing micro pin fin correlations fitted the experimental data fairly fell with a mean absolute error from 11.1% to 27.7%. They pointed out that for H/D smaller than some value between 1 and 2, the endwall effect is important. Later on, many researchers performed systematic studies on the flow characteristics of the micro pin finned channel. They found out that, height to diameter ratio, arrangement, pitch, endwall effect, flow regime and pin fin shapes all influenced the heat transfer and flow behavior to some extent. Kosar et al. [14] studied laminar flow across micro circular and diamond pin fins with small H/D ratio of 1 and 2, and made comparison of their experimental data with a large amount of existing conventional correlations. They found out that those correlations had large prediction errors and concluded that this was because the conventional correlations did not include the end wall effect which occurred at the micro level and low H/D ratio. They proposed a new correlation for the friction factor. They also ascertained that the staggered micro pin fins experienced a greater pressure loss than the inline ones at low Re and the difference between them disappeared as Re increased. Further, they compared circular pin fins with diamond pin fins, and found out that the diamond ones had a higher friction factor. Kosar and Peles [17] investigated the flow and heat transfer across the heat sinks with circular micro pin fins of height 243 lm and H/D = 2.43 for effective heat fluxes ranging from 3.8 to167 W/cm2 and Re from 14 to 112. The long tube correlations predicted their friction data well at high Reynolds number but over-predicted at low Reynolds number. The discrepancy of their data with the correlation from Kosar et al. [14] at low Reynolds number was attributed to the thickening of boundary layer (on the endwalls) which predominates over ‘‘flow separation delay” effects for H/D = 1 in Kosar et al. [14]. For H/D = 2.43 in their own case, ‘‘flow separation delay” prevails over boundary layer effects, resulting in a low friction factor. Prasher et al. [18] studied both staggered circular and square micro pin fins with dimensions (diameter for circular and sides for square) ranging from 50 lm to 150 lm and H/D ratio from 1.3 to 2.48, in the range of 10 < Re < 1000; they found out that the square pins led to slightly higher friction factor than the circular pins. The friction factor varied more sensibly with Re at Re < 100 but less at Re > 100; they established different correlations of friction factors for these two

T1, T2 U W

temperature at channel inlet and outlet, °C velocity, m s1 width, m

Geek symbols l dynamic viscosity, kg m1 s1 q density, kg m3 e density of pin fins Subscripts c channel exp experimental f fin pred predicted

zones. They also suggested to use a log–log scale for better observation of the change of friction factor with Re. Koz et al. [19] calculated the thermal and hydrodynamic characteristics of circular micro pin–fin heat sinks with height over diameter H/D varying from 0.5 to 5 while Reynolds number and heat flux provided from the fluid interacting surfaces of the micro pin–fin are in the range of 20 < Re < 150 and 100 < q (W/cm2) < 500, respectively. They showed that the endwall effect decreased with H/D, and local Re. In addition, increasing H/D ratio while keeping ST/D ratio constant led to a less stable flow, and total force acting in the flow direction and on the micro pin–fin is proportional with H/D and Re. The ratio of viscous to total forces and the friction factor decrease with Re and increases with H/D. Liu et al. [20] conducted an experimental study on the friction factors associated with forced flow of de-ionized water over staggered and in-line micro/mini cylinder groups with hydraulic diameter of 0.5 mm and height of 1.0 mm, 0.75 mm, 0.5 mm and 0.25 mm, with Re ranging from 25 to 800. Their analysis showed that the value of fRe was approximately a constant in micro/mini cylinder group plates when the flow was purely laminar, whereas the value of fRe increased when Re > 100. They believed that some micro-scale effects, such as tip clearance effect, roughness effect, and endwall effect, resulted in obvious discrepancies between their experimental data and predictions of theoretical correlations. Liu et al. [21] experimentally obtained the resistance characteristics of de-ionized water flowing through inline and staggered arrays of micro-cylinders-group plates with different distances among micro-cylinders at 0 < Re < 300 with different heating power. They compared their data with existing correlations (Ref) and found a large deviation at low Re; they attributed this to the existence of a sluggish zone caused by micro scale and endwall effect. Selvarasu et al. [22] were concerned about the density of micro pin fins for the channel flow at 10 6 Re 6 600 and through numerical study they found that the friction factor is higher for configurations with higher pin fin density. The losses are dominated by friction drag at low Re but by form drag at high Re as wake recirculation develops. Kosar and Peles [23] performed a parametric study of pressure drop associated with the forced flow of deionized water over five micro pin fin heat sinks of different arrangements and shapes experimentally, with Reynolds numbers ranging from 14 to 720. The pin shapes are circular, hydrofoil, cone-type and rectangular. They found out that the denser arrangement brings the interaction of the wakes of the front bank pin fins with the bank next to it, which increases the flow mixing and causes a greater

H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

pressure loss. They believed that the pin fin shape was also a critical factor. The sharp point pins result in larger friction factors, because they augment wake-pin interactions and introduce more pressure drop. Qu and Siu-Ho [24] conducted both adiabatic and diabatic tests for water flowing across arrays of staggered rectangular micro pin fins with a 200  200 lm2 cross section by a 670 lm height, for Re ranged from 37.9 to 85.8. They examined six previous correlations of friction factors and found that their data were either under-predicted or overpredicted. Hence they proposed a power-law type correlation based on their adiabatic data and the new correlation predicted their diabatic data very well. In order to build a correlation for friction factor of two phase flow across micro pin fins, Konishi et al. [25] studied the single phase adiabatic flow of water across rectangular micro pin fins, and proposed a correlation to predict friction factor, applicable to 0 < Re < 300. John et al. [26] numerically studied the micro pin–fin heat sinks with circular and square pin–fin structures at 50 < Re < 500. They found that at low Re (below 300), that the pressure drop across the micro pin–fin heat sink is almost the same, irrespective of the shape of pin–fin structures. But as the magnitude of Re increases, the pressure drop across the denser or closer pin–fin structures is higher for a given Re. Whereas, for the micro pin–fin heat sink with square pin–fin structures, the pressure drop across the device with different density of pin–fin structures does not show much variation as Re increases. Liu et al. [15] performed an experimental study on liquid flow and heat transfer in micro square pin fin heat sink, with Rec ranging from 60 to 800. Their results showed that the pressure drop is inversely proportional to the size of the fin-pitch for a fixed Reynolds number, which is due to the fact that a smaller fin-pitch results in a faster flow velocity, a stronger vortex and a higher pressure drop. The laminar flow to turbulent flow transition occurs at Rec = 300, earlier than that in the conventional tube flow, because the staggered array structures in the heat sinks caused the fluid mixing between channels and the vortex evolving behind the fins more intensively and frequently. Several examined correlations all failed to predict their experimental data and a new correlation was proposed for friction factor estimation. Tullius et al. [27] designed many micro pin fins of different shapes, sizes, materials and arrangements, and analyzed their thermal and hydrodynamic performance numerically. Many existing correlations for conventional or mini/micro scales pin fins were taken to predict the friction factor for those pin fins and larger discrepancy from their calculated data were obtained. New correlation was established for each shape of the pin fins. The tip clearance also plays a significant role in affecting the flow across mini/micro pin fins. Moores and Joshi [28] examined the effect of tip clearance for water cooled staggered arrays of shrouded circular micro pin fins with H/D ranging from 0.5 to 1.1, which were exposed to a uniform heat flux of 0.02–0.26 W/mm2 and cooled with water through a nominal Reynolds number range of 100–10,000. They concluded that small amounts of tip clearance (<10% of pin height) lowered overall pressure drop. They divided the flow regime into two zones – laminar zone (Re 6 1000) and transition zone (1000 < Re < 10,000), and built correlations for the friction factor in the two zones separately, by including the tip clearance. Moores et al. [29] further studied the staggered circular micro pin fin heat sinks with and without tip clearance, and found that the tip clearance influenced pressure drop performance to the greatest extent at low Re(<5  103), while the effect being significantly diminished by Re = 1.5  104. Based on the experimental data, they proposed the correlation to predict the friction factor of the channel with circular micro pin fins including the tip clearance. Liu et al. [20] also discussed the effect of tip clearance on flow characteristics at 25 < Re < 800, and concluded that the tip clearance


had little influence on the flow resistance at low Re and dropped the flow resistance at relatively high Re (>150). Since the vortex shedding and distribution behind the pin fins are important for understanding the flow behavior, some studies are focused on this aspect. Guan et al. [30] numerically simulated the vortex distribution and their influence on the flow behavior of deionized water flowing across in-line and staggered circular pin fins with different H/D and pitches at low Re (0 6 Re 6 150). It is found that the vortex number becomes larger with the increase of pitch ratio, which may result in the increase of differential pressure resistance. Renfer et al. [31] experimentally investigated the vortex structure and pressure drop across the circular micro pin fins, and found out that the laminar flow turned into transitional flow at Re  200. The vortex shedding and flow impingement onto the pins from the post-transition flow field led to the increase of the pressure drop. The same group [32] investigated the hydrodynamics in micro cavities populated with cylindrical micro pins using dynamic pressure measurements and fluid path line visualization. They identified three different sets of flow dependent characteristic frequencies by analyzing the pressure signals: the first due to vortex shedding, the second due to lateral flow oscillation and the third due to a transition between these two flow regimes. Some researchers took mini/micro pin fins as porous media. Gunda et al. [33] tested the creep flow in a channel with micro pillars, and calculated the pressure drop by treating the micro pillars as porous media. Tamayol et al. [34] investigated the pressure drop of the nitrogen flowing through the ordered arrays of cylinders in a mini/micro channel at low Re with two methods: the porous media approach and the variable cross-section micro channel approach; they compared the predicted values with the experimental data and found out that the former method had wider applicability and smaller errors. In summary, although many researchers have made a large number of studies on the hydraulic characteristics of flow across micro pin fins of different structures and shapes, consistent conclusions have not been reached yet. The study about the complex flow structure across the micro pin fins is not sufficient: the critical Re from laminar to transitional and to turbulent flow is not yet determined; the proposed correlations are only valid under certain testing conditions, and further verification and improvement are still needed. In addition, many research focused on circular pin fins, while less attention are paid to non-circular pin fins. In order to select the optimal pin fin shape, it is necessary to compare and analyze the flow characteristics of pin fins with different shapes. With deionized water as the working fluid flowing across staggered arrays of mini pin fins, this paper tested and compared the adiabatic flow characteristics of rectangular channels with circular, elliptical, square, diamond and triangular pin fins at different flow rate and conducted in-depth theoretical analysis of the experimental results from the physics behind. The influence of shapes of mini pin fins on the flow resistance was discussed, the experimental data were compared with existing correlations for micro/mini scale pin fins, and evaluations were made on their applicability.

2. Experimental setup and procedure 2.1. Experimental setup The experimental system shown in Fig. 1a consists of the test section with the mini pin fins, the liquid supply circuit with pressure control, and data measurement and collection devices. The required pressure is supplied by a 12 MPa high-pressure nitrogen bottle. The high-pressure nitrogen goes through the gas filter and the precision regulator, and drives the deionized water to enter

H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

regulating valve quick-opening valve

test section 1iquid filter


gas storage reservoir

shutoff valve

throttling tube

liquid storage


three-layer filter

data acquisitionsystem thermocouple

pressure transducer

quick-opening valve precision pressure

graduated cylinder


Fig. 1a. Schematic of the experimental setup.

Fig. 1b. Schematic view of the flow inlet connection of the test section.

the throttle conduit. Then the deionized water flows through the pressure reducing tube and enters the test section, and finally it goes into the high precision measuring cylinder. The flow inlet connection of the test section is shown in Fig. 1b, in which the flow enters a deep plenum and then flow into the test section. The pressure port is also shown in Fig. 1b. The connection for the flow outlet of the test section is the same as the flow inlet. During the experiments, the pressure can be precisely adjusted to the experimental desired pressure (accurate to 100 Pa) by the precision regulator to meet the requirement to provide a stable flow rate and pressure parameters. The pressure reducing tube in front of the test section can reduce the pressure of the incoming flow, hence to alleviate the control difficulty of liquid pressure and the impact on the inlet pressure of the test section. The inlet and outlet of the test section is equipped with thermocouples and pressure sensors to measure the temperature T1, T2, and the pressure difference DP between the inlet and outlet. All pressure and temperature data are directly read from the data acquisition device. The liquid mass flow rate Q is measured either by the weighing method or the volume measuring method. When the flow rate is smaller, the weighing method is adopted through an electronic balance (FA2004-type); when the liquid flow rate is larger, it is measured directly by the high-precision measuring cylinder with the accuracy of 0.1 ml. When the temperature and pressure at both inlet and outlet of the test section does not vary with the flow, the electronic balance or the measuring cylinder is used to measure the mass of the flow entering the liquid storage reservoir within certain time period to obtain the flow rate. During the test, the pressure is adjusted to the required value. After both pressure and temperature is steady, the

test can then start. The same test section assembly and experimental system is also used in Ref. [20], and the readers can find more detailed information there. 2.2. Test section The test section shown in Fig. 2, is a rectangular channel with staggered mini pin fins of five different shapes, using micromachining technology, made of red copper (Fig. 3). The channel length L is 39.6 mm, width W is 5.2 mm, and height Hc is 0.5 mm. There is no tip clearance for pin fins. The test section is covered with a glass plate, sealed between them with 704 silicone rubber adhesive and connected into the experimental system with special joints. Fig. 3 shows the photo of the front of the five test sections with different fin shapes. The detailed geometrical parameters of the test sections are listed in Table 1. The pressure was measured with pressure transducers at both inlet and outlet of the test section, as shown in Fig. 1. 2.3. Experiment uncertainties The accuracies of the main measuring instruments used in the experiments are: pressure transducer accuracy of 0.1% of the maximum measurement range; thermocouple accuracy of ±0.15 °C (less than 100 °C); the accuracies of the pin fin and channel dimensions are determined by the engraving machine (YF-DA7060) with a processing accuracy of ±0.5 lm and therefore the uncertainty of their respective dimensions is less than ±0.2%. The roughness of the channel bottom and the pin fin surface is determined by the engraving machine, taking into account that the machining


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Out-let D





a=0.4 b=0.8




a=0.4 b=0.8










Fig. 2. Schematic diagram of the test section.

accuracy is ±0.5 lm, so the bottom and surface relative roughness will not exceed 0.4%. Other uncertainties are analyzed according to the literature [35] and listed in Table 2 for the inlet and outlet pressure difference DP, temperature T1 and T2, flow rate Q, Re and friction factor f.

3. Results and discussions In the experiment, the temperature T1, T2 and pressure P1, P2 at the inlet and outlet were measured. The pressure loss DP for flow across the pin finned channel was evaluated by subtracting the local resistance loss for the sudden change of area at both inlet and outlet, which is about 1.1–4.5% of total pressure difference (P1 - P2), corresponding to different flow rates. The average temperature at the fluid inlet and outlet is taken as the characteristic temperature Tf. Since the H/D ratio is between 1 and 2, the proper choice for Reynolds number is not clear. Hence three definitions of Reynolds numbers were used. In the tube bundle approach [14], the equivalent diameter De of pin fin is the characteristic length, and Re, therefore, can be expressed by the following equation:

Re ¼

qU max De l


where Umax is the maximum flow velocity at the minimum cross-sectional area, m/s. De is the equivalent diameter De ¼

4Af , Lf

where Af is the cross sec-

tion of the pin fin, and Lf is the perimeter of the cross section of the pin fin.

For circular pin fin; U max ¼


and for pin fin of other shapes; U max ¼

ð2aÞ QST WHðST  aÞ


In the compact heat exchanger approach [14],

Red ¼

qU max Dh l



Dh ¼

4Amin L A



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where W is the width of the channel and L is the length of the channel. For staggered pin fin configuration:

Amin ¼

(a) Circle

   w c þ ðST  Dh Þ H ST


The third Reynolds number is based on the minimum crosssectional flow area [15], and the equivalent diameter Dc is defined as:

For circular pin fin; Dc ¼


2HðST  DÞ H þ ST  D

For the other shape pin fin; Dc ¼

(b) Ellipse

Rec ¼

2HðST  aÞ H þ ST  a

qU max Dc l




The friction factor can be obtained by the following:

f ¼

(c) Square

2Dp N x qU 2max


The relative error between the experimental and predicted values by existing correlations of friction factor is defined as REER:


jf exp  f pred j  100% f exp


3.1. Flow rate and friction factor

(d) Diamond

(e) Triangle Fig. 3. Front photos of the test section with pin fins of five shapes.

Table 1 Geometrical size of mini pin fin groups.

Circle Ellipse Square Diamond Triangle

H (mm) Dimension (mm) H/D

ST (mm) SL (mm)

e ¼ WAcfLc Nx

0.5 0.5 0.5 0.5 0.5

0.8 0.8 0.8 0.8 0.8

0.114 0.228 0.145 0.145 0.073

0.4 a = 0.4, b = 0.8 a = b = 0.4 a = 0.4, b = 0.8 a = b = 0.4

1.25 1.02 1.25 1.40 2.02

1.2 1.2 1.2 1.2 1.2

34 34 34 34 34

Table 2 Experimental uncertainties. Parameters


DP Q Reynolds number f

±0.2% ±1.1% ±2.9% ±5.8%


A ¼ pDHN t þ 2 WL 

pD2 4

! Nt


During the experiments, the flow characteristics of the five pin fin groups were tested separately. The pressure difference between the channel inlet and outlet, and the channel flow rate were measured to calculate and obtain the relations of pressure drop vs. flow rate (Fig. 4) and f vs. Re (Fig. 5). Fig. 4 shows the pressure drop vs. flow rate for the five test sections with mini pin fin groups of different shapes. It can be seen that the pressure drop increases with growing flow rate for all the test sections; at low flow rate (0–20 ml/min), it only shows a slight difference in pressure drops for the five pin fin groups. As flow rate (>20 ml/min) continuingly increases, the pressure drop of the five pin fin groups takes on an accelerating trend, and the acceleration rate demonstrates as circle > triangle > square > diamond > ellipse; this fact, from the authors’ opinion, mainly comes from the endwall effect and the cross section shape of the pin fin. When flow rate is small (<20 ml/min), the velocity is low, the fluid viscosity and the roughness of the machined pin fins causes the boundary layer to form between pin fins very easily. The fluid does not pass through all the passages between the pin fins [21], the endwall effect is significant and the wall shear stress is large, which are the main factors to cause pressure drop. At this time, the influence of the pin fin shape on the pressure drop is negligible and no much difference among the five pin fin groups. As the flow rate increases constantly, the fluid velocity near the wall is large and the endwall effect weakens gradually; the viscous and blocking effects on the fluid exerted by the upper, lower and side walls of the pin fins, rise rapidly, which caused the boundary layer to separate from the wall of pins, and vortex forming in the wake starts to shed [23]. There must be a most suitable flow rate, at which the endwall effect can be completely ignored. After this flow rate, the pressure drop increases fast in a gradient-ascent trend because of the interaction between vortex and pin fins [21,23]. At this stage, it can be thought, the influence of the pin fin shape on the pressure drop is dominant.

H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69


Fig. 4. Relationship of DP vs. Q for the five pin fin groups of different shapes.

The density of the pins also plays a role in affecting pressure drop at large flow rate. Even though the elliptical pin fins have the largest density ðe ¼ 0:228Þ, but possess the lowest pressure drop. The diamond and square pin fins have the same density ðe ¼ 0:145Þ and almost the same intermediate pressure drop. The triangular pin fins have the smallest fin density ðe ¼ 0:073Þ but the second largest pressure drop. It seems that the pressure drop is inversely related with the fin density, except the circular pin fins. The circular pin fins have a fin density almost one and half times of that of triangular pin fins, but have the largest pressure drop. From the above statements, it can be seen that the flow across pin fins has a quite complex nature. Both shape and fin density is important in determining pressure drop at large flow rate. Fig. 5(a)–(c) gives the change of f vs. different Reynolds numbers for the five kinds of pin fins with different shapes. The log scale is used for f for better illustration. Comparing these plots, it shows that the way that f changes differently with different Reynolds number. Comparing with Fig. 4, only in Fig. 5(a), the trend of friction factor f vs. Re is consistent with that of pressure drop vs. flow rate. Hence Re, based on the pin fin diameter, is a more appropriate choice for this study. Fig. 5(a) shows, in the range of all Re, the friction factor of pin fins of different shapes all decreases with Re increasing; when Re reaches a certain value, f keeps almost constant, but there are gaps between the decreasing trends of the pin fins with different shapes. When Re < 100, the elliptical pin fin group has the largest friction factor, the circular one the second, the square and the diamond are about the same, and the triangular one the smallest. When 100 < Re < 300, as Re increases, the elliptical pin fin group has the biggest drop of friction factor, the diamond and the square pin fin groups with the same drop of friction factor as the second, the circular the third, while the triangle one the smallest. Hence when Re > 300, the elliptical one has the smallest friction factor, the square and the diamond have about the same value of friction factor. From the tested range of Re, it seems that the circular has a larger friction factor than the triangular. However, it can tell from the trend that the triangle will have the largest friction factor as Re grows even larger. When Re < 100, because the triangular pin fin heat sink has the smallest fin density, the friction produced by the flow around the fins is also smaller; hence the friction factor is the smallest, which agrees with Kosar et al. [22,23]. The drop of friction factor within the range of Re (100–300) means that the flow experiences a transition. It can be judged that the channel with triangular pin fins changes from flow transitional regime into turbulence quickly, while the one with the elliptical pin fins enters

Fig. 5. Relationship of f vs. different Re for the five pin fin groups.

the turbulent regime the slowest and at a higher Re. The other three are in between. As Re increases, the decline trends are not consistent for the five pin fin groups; the gaps of friction factor f among them gradually increase and reach constants finally. The author thinks that this is possibly due to the mutual influence caused by different forces. From the view point of mechanics, the force exerted by liquid on the flow around body can be divided into two classes: the shear


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stress tangent to the body surface and the dynamic pressure force perpendicular to the body surface. Based on the boundary layer theory, the friction force is the projection of the tangential shear stress on the body surface along the flow direction. Because the vortex shedding in the wakes of the body leads to the asymmetric distribution of pressure along the body surface, there is pressure difference along the flow direction, which can be called the eddy resistance. Therefore the friction factor can be divided into the friction resistance coefficient f1 and the eddy resistance coefficient f2. At very low Re (<100), the velocity is very small, the flow between the fin pins are seriously influenced by the endwall effect, causing a thicker boundary layer, and the flow is mainly a smooth flow attached to the wall, which can be treated as purely laminar. At this stage there is no vortex, and the resistance is mainly friction resistance of flow around body; while the eddy resistance is very small, hence f1 > f2. As Re increases gradually, f drops slowly. During the transition zone (Re = 100–300), the friction resistance becomes less and the eddy resistance becomes more; together they contribute to the whole friction factor. When Re further increases, the friction factor decreases more slowly and reaches a constant at certain Re, which is possibly due to the influence of the inertia force. When the fluid flows across staggered pin fins at a larger speed, the flow changes its direction frequently, and generates vortex and flow disturbance under the inertia force. Meanwhile with the interaction between mini pin fins, the flow reaches full turbulence at certain Re, and the flow resistance is eddy resistance dominantly, f1 < f2. Considering the influence of the pin fin shape on the eddy resistance, it will cause flow across different pin fins to enter turbulence at different Re, which is consistent with the above conclusions. Since the five types of pin fins with different shapes have the same transverse dimension on the upwind face, the upwind resistance force of flow impacting on pin fins will keep the same. The difference of the friction factors among the pin fins are mainly affected by the eddy resistance. From Fig. 5(a) it can tell that eddy resistance has the biggest impact on the triangular pin fins, and the smallest on the elliptical pin fins when Re > 300. The difference among the other three pin fins is not apparent. This may come from the smaller pin density of the triangular pin fins and the more disturbance of flow brought by its shape, compared to the elliptical one. From the tail of the front row of pin fins to the front of the row next to it, the pressure will rise. The distribution of the downstream pressure greater than the upstream pressure is called the inverse pressure gradient. Because of the action from the inverse pressure gradient and the wall viscous shear, boundary layer separation will occur at the back of the pin fins, vortex will be generated and carried away by the bulk flow, and a wake zone will form behind the pin fins. Since the triangular pin fin is the least streamlined, and the smallest in longitudinal dimension, the sudden narrowing of its cross section brings even greater inverse pressure gradient, and leads to the earlier boundary layer separation and vortex shedding. In addition, because of the small density of the triangular pin fins, the wakes formed due to boundary layer separation will evolve and more vortexes will shed from the fins, which amplifies the viscous dissipation, and enlarges the pressure loss [23]. Therefore the triangular pin fins have a larger f than all the other pin fins. As the circular pin fin also has the smallest longitudinal dimension, the velocity gradient on the perpendicular direction of its surface is larger, and the inverse pressure gradient is the largest, so the vortex structure in its wake is distinct. The separation point of the boundary layer is approximately at the middle of the pin fin, and the streamlines become detached from the wall more easily. The streamline of the elliptical pin fin is better than the circular, the boundary layer separation is delayed, the largest fin density confines the evolution of the vortex shedding from the pin fins within limited space, the small wake zone results in less viscous dissipation, and all lead to a smaller f

than the circular pin fin. The streamline of the elliptical pin fin is also better than the square pin fin and the diamond pin fin; both are less streamlined, but their longitudinal dimension is larger, their boundary layer separation is delayed, the vortex shedding at their wake is less than the circular, the wake zone is smaller, and hence their f is greater than the elliptical pin fin and less than the circular. In summary, at different flow regimes, the shape and the density affect the friction factor differently. At low Re (<100), the influence of the endwall effect on the flow characteristics of the test section is obvious, and the friction factor weighs more. So the density of pin fins will increase the pressure drop. While at high Re, the friction factor caused by eddy dissipation due to pin fin shape is the dominant part. The density of pin fins will decrease the pressure drop, since vortex shedding will be restrained. Therefore, at low Re (<100), the channel with triangle pin fins of the least density has the smallest f while the elliptical one with the biggest density has the largest f; but the trend is reversed at larger Re (>300). 3.2. Comparison of correlations and experimental data For flow across mini/micro pin fins in a channel, many researchers [14,15,18,22,24,27–29,34] pointed out that correlations obtained from conventional pin fins are not applicable to mini/ micro pin fins, and they proposed new correlations for mini/micro pin fins. On account of limited pin fin shape and flow regime they studied, this paper investigated the adiabatic flow across staggered pin fin groups of circular, elliptical, square, diamond and triangular shape in the range of 50 < Re < 1800. Comparisons were made on experimental and predicted values of friction factors by existing correlations for mini/micro pin fins. Their prediction errors and applicability were examined and discussed. The correlations used in this paper are listed in Table 3, all based on Re defined ‘‘tube bundle approach” [14], except Cor1 and Cor6, where both Re and Red are used. Although the correlations used were originally developed for certain pin fin shape and certain flow regime, they are extended to predict all the pin fins studied in this paper. The compared results are shown in Figs. 6–15. Fig. 6 shows comparison of experimental and predicted values of f vs. Re for circular pin fins, and Fig. 7 displays the relative error REER vs. Re between predicted values and experimental values. It can be seen that, at Re > 300, experimental values are close to the values predicted by Cor2 developed by Moores and Joshi [28] for mini pin fins and REER is within 20%. They are also close to Cor5 from Qu and Siu-Ho [24] for micro square pin fins at very low and limited Re number, and REER is within 15%; but there are large deviations between these values at Re < 300, and both underpredict experimental values. The lower Re, the higher REER. Taking into account that the correlation from Moores and Joshi [28] includes the effect of the tip clearance, the bias may be caused by part of the flow passing through the crevice. Even though Cor5 is originally developed for square pin fins at low Re (37.9 < Re < 85.8), its good estimation for circular pin fins at large Re (>300) is surprising. When comparing these two correlations, one finds that they are very similar, and they even have close values for the exponential number of Re, except that the former includes a factor of H/D. Its poor applicability at low Re (<300) may come from the scaling effect since it is developed for micro pin fins. Another correlation (Cor3) proposed by Moores et al. [29] over-predicts the experimental data, and has a large value of REER (>50%). When comparing this correlation (Cor3) with the correlation developed by the same authors (Cor2), one finds that the difference lies in the constant coefficient, the exponential numbers for both H/D ratio and Re. Since Cor3 was originally proposed for use in a very large Re range from 100 to 20,000, it may be not very accurate for the transitional and early turbulent flow regimes


H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69 Table 3 Correlations for friction factor of flow across mini/micro scale pin fins. Number and Reference


Cor1, Kosar et al. [14]

f ¼ p1 þ p2 0:3  1:1  1739 H=D ST SL p1 ¼ 1:7 Af H=D þ 1 Re 0:3  2:0  345 1 ST SL p2 ¼ Af Red H=D þ 1 Cor2, Moores and Joshi [28]

0:505  0:742  H C þ Hc f ¼ 19:04 Re0:502 Hc D Cor3, Moores et al. [29]

 0:28þð1j1 Þ H f ¼ 10:52j1 Re0:39þð1j2 Þ D

Fluid, flow regime,




Arrangement, shape and scale

Water, Re < 130, adiabatic


1, 2


Staggered, circle, micro

Water, 100 < Re < 1000, diabatic


0.5, 0.8, 1.1


Staggered, circle, mini

0.0036–0.513 0.5, 0.8, 1.1 Water, 200 < Re < 20,000, diabatic


Staggered, circle, mini

j2 ¼ exp0:8ðC=HÞ j1 ¼ exp4:3ðC=HÞ Cor4, Prasher et al. [18]

Re < 100

 0:64  0:258  0:283 H SL  D ST  D f ¼ 169:82 Re1:35 D D D Re > 100 f ¼ 0:295

Water, Re < 1000, diabatic

0.0606–0.136 1–2.5


Staggered, circle, square, micro

Water, 37.9 < Re < 85.8, adiabatic and diabatic




Staggered, square, micro

Water, Re < 130, adiabatic


1, 2


Staggered, diamond, micro

 1:249  0:7  0:36 H SL  D ST  D Re0:1 D D D

Cor5, Qu and Siu-Ho [24]

f ¼ 20:09Re


Cor6, Kosar et al. [14]

f ¼ p1 þ p2 0:4  1:5  1126 H=D ST SL p1 ¼ 1:1 Af H=D þ 1 Re 1  1:7  6:6 1 ST SL p2 ¼ 0:7 Af H=D þ 1 Red

Fig. 6. Comparison of f vs. Re between experimental and predicted values for circular mini pin fins.

Fig. 7. Relation of REER vs. Re for circular mini pin fins.


H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

Fig. 8. f vs. Re between experimental and predicted values for elliptical mini pin fins.

Fig. 11. Relation of REER vs. Re for square mini pin fins.

Fig. 9. Relation of REER vs. Re for elliptical mini pin fins.

Fig. 12. f vs. Re between experimental and predicted values for diamond mini pin fins.

Fig. 10. f vs. Re between experimental and predicted values for square mini pin fins.

Fig. 13. Relation of REER vs. Re for diamond mini pin fins.

H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

Fig. 14. f vs. Re between experimental and predicted values for triangle mini pin fins.

Fig. 15. Relation of REER vs. Re for triangle mini pin fins.

in the current study. The large values of REER also prove that it is not appropriate to use a single correlation to cover the whole laminar, transitional and turbulent flow range. However, the correlation developed by Kosar et al. [14] (Cor1) seriously underestimates the experimental value, and REER is very large, more than 80%. Their correlation is deduced from the laminar flow for micro pin fins at very low Re (0–130) in a very complex form, which includes many influencing factors, such as ST, SL, and two different Reynolds numbers. All these limit their applications and large deviations can be expected. The REER of the correlation by Prasher et al. [18] (Cor4) is large at small Re, REER more than 40% at Re < 300, but it decreases as Re increases. It shows good estimation at Re > 300, with REER < 30%. The REER changes drastically with Re and the overall values are larger than Cor2 and Cor5. By examining Cor4, it is similar to Cor2 and Cor5, except that it includes ST and SL, and also has a different exponential number for Re. Cor4 is also derived for micro scale pin fins, while the current pin fins are mini scale, and the scaling difference may lead to different friction factors at small Re. In addition, they investigated diabatic flow while the current is adiabatic flow; the temperature will influence the physical properties of the fluid, and hence the flow, which causes the deviation of the friction factor at low Re number. There are few experimental studies focused on mini/micro scale elliptical pin fins and no empirical correlations exist. Here the


correlations for circular and square pin fins were used to predict the friction factor of elliptical pin fins. The experimental and predicted values vs. Re are shown in Fig. 8, and REER between them shown in Fig. 9. As can be seen from the graphs, the correlation underestimates the experimental data at low Re but overestimates at high Re except Cor1. The REER between predicted and experimental values for the elliptical pin fins shows an opposite trend from the circular pin fins. Cor1, Cor3 and Cor4 outperformed Cor2 and Cor5. The REER values for the latter two correlations are small (<60%) at low Re (<300) and much larger (>60%) at high Re (>300). Though Cor5 successfully predicts the circular pin fins, it fails in the elliptical pin fins, and the difference in pin density is possibly the primary reason. The elliptical pin fins have a much larger pin density, two times of the circular pin fins. As discussed previously, the pin density is an important factor affecting the pressure drop. The denser pins the less pressure drop at large Re (>300) since vortex shedding are restrained to a confined space. Overall, Cor3 from Moores et al. [29] performs best at large Re (>300), REER less than 25%; Cor1 and Cor4 are about the same at large Re (>300), REER about 50%. Such large deviations may come from the difference in flow regime, shape, pin density, etc. Fig. 10 shows the comparison of the predicted and experimental values of f vs. Re for the square pin fins, and Fig. 11 shows the REER between them vs. Re. As can be seen from Fig. 11, at Re < 200, all correlations under-predict the experimental data. The curves in the figure cross at a certain Re; this is possibly due to the flow changes into turbulence from transitional region, hence resulting in great decrease of friction factor in the transitional region. Cor5 over-predict the experimental data at Re > 200, while the other three under-predicts. There are large deviations between Cor5 and the experimental data at large Re. The REER for Cor5 drops at first and then rises as Re increases. Since Cor5 is derived for micro square pin fins within pure laminar flow at Re < 100, extending it to mini square pin fins in transitional and turbulent region may bring errors. In addition, they studied micro pin fins, however, the current study focused on mini pin fins. The size difference will lead to different flow behavior, hence the prediction errors. On the other hand, the H/D ratio in Qu and Siu-Ho [24] is 3.35, larger than that in the current study, which may be another factor that brings the prediction error. It is known that H/D ratio plays a significant role in affecting the pressure drop. Large H/D ratio at low Re will weaken the endwall effect, hence the underestimation of the present data; large H/D ratio at high Re allows more space for vortex shedding and evolving, and hence enlarges the pressure drop, which may explain the overestimation of the experimental data at high Re. Cor1 shows largest REER because it is derived for micro circular pin fins and has a very complex form with two different Reynolds numbers, which may produce big errors beyond its experimental conditions. The other correlations also show high REER values, so they are not applicable for estimating friction factor for mini square pin fins. Kosar et al. [14] studied laminar flow across micro diamond pin fins experimentally and proposed correlations for friction factors Cor6. The other correlations are also extended to predict the friction factor for diamond pin fins. Fig. 12 shows the comparison of the predicted and experimental values of f vs. Re for the diamond pin fins. Fig. 13 shows REER between them vs. Re. It can be seen that the experimental values are much greater than the corresponding predicted ones at low Re (<200), and the REER between them rises as Re lowers. The REER of Cor1 for circle pin fins is the largest among them, with values varying from 0.8 to 0.9. The prediction of Cor3 is not good either, with REER as high as 87% at low Re and minimum 40% at large Re. Cor6 proposed by Kosar et al. [14] for diamond shows no better prediction. The average REER is about 40%. The deviation may be due to the fact that the correlation is for micro diamond pin fins at laminar flow, and not applicable for mini


H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69

pin fins at transitional and turbulent flow. Cor4 from Prasher et al. [18] performs best at large Re (>350) with REER < 20% but performed poor at low Re (<350). The smaller REER of Cor4 proves its better applicability, since it derives from both adiabatic and diabatic data for both circular and square micro pin fins with H/D close to the current study. The deviation at low Re may be attributed to the scaling effect and the shape difference. Although the triangular pin fin at conventional scale is very commonly used as flow perturbation elements, there is little research done on mini/micro scale. Correlations for other shaped pin fins are applied to triangular mini pin fins. The predicted and the experimental values are compared, and the results are shown in Fig. 14, the REERs between them shown in Fig. 15. As can be seen from the graphs, all the correlations, except Cor5, underestimate the experimental data. The predicted values of Cor5 and Cor2 are close to the experimental data, but large deviations are found at low Re (<100). The largest REER comes from Cor1 for circular pin fins. When Re > 100, Cor5 performs best among them with REER < 25%. The REER from Cor4 is also large, but it drops quickly as Re increases. The deviations are partly attributed to the shape of the triangle, less streamlined and more perturbation for the flow. Other factors are pin scale, pin density and flow regime, etc. Based on the above analysis, it can be concluded that all the existing correlations cannot predict the friction factor well for the five pin fin groups (circular, elliptical, square, diamond, and triangular) at low Re (<300), while part of them perform better at high Re (>300). The bias mainly is due to the difference in flow regime, pin fin scale, H/D, and shape. Further studies are still needed to completely understand the complex flow across the mini/micro pin fin groups, to differentiate different flow regimes and the transition. New correlations are needed to include more factors and provide more accurate estimations for the experimental data.

4. Conclusions The pressure drop and friction factor of de-ionized water flowing across staggered mini pin fins of the same height and transverse spacing but with different pin density and different shapes of circular, elliptical, square, diamond and triangle, in a rectangular channel were studied experimentally. The experimental data are compared with predicted values by existing friction correlations for mini/ micro pin groups and the following conclusions were reached. (1) At low Re (<100), the endwall effect is obvious and the viscous friction force is dominant. At high Re (>300), the eddy force produced by the vortex shedding takes the main part. In the transition zone (100 < Re < 300), both endwall effect and eddy force contribute to the friction factor. (2) For the current study, with H/D ratio from 1 to 2, Reynolds number based on ‘‘tube bundle approach” is a proper choice for comparing friction factors of pin fins with different shapes. (3) The friction factor of five pin fin groups with different shapes drops as Re increases, and finally reaches a constant value. At large Re (>300), the influence on the eddy resistance by the pin fin shape will lead to the difference in friction factors among different pin fin groups. The elliptical pin fin is the best streamlined, and hence the lowest flow resistance; the triangular pin fin is the least streamlined and hence the largest resistance. (4) At different flow regimes, pin density affects friction factor differently. At low Re (<300), the channel with triangular pin fins of the lowest density has the smallest f while the elliptical one of the greatest density has the largest f. The trend is reversed at large Re (>300).

(5) Because of the limited range of their original testing conditions, existing correlations for mini/micro scale pin fins cannot correctly cover flow in laminar, transitional and turbulent region. There are large deviations between experimental and predicted values, especially at low Re (<300). The extension of the correlations from pin fins of one shape to another shape also produces large errors, especially at low Re (<300). The factors affecting the flow resistance are mainly flow regime, pin fin shape, pin density, scale, and H/D ratio, which should be taken into account when deriving new correlations.

Acknowledgements The authors acknowledge the support of National Science Foundation of China under Grant No. 51306107 and Shandong Provincial Natural Science Foundation of China under Grant No. ZR2011EEQ015.

References [1] Y.-L. Park, B.-R. Chen, R.J. Wood, Design and fabrication of soft artificial skin using embedded microchannels and liquid conductors, IEEE Sens. J. 12 (8) (2012) 2711–2718. [2] E.W.M. Kemna, R.M. Schoeman, F. Wolbers, et al., High-yield cell ordering and deterministic cell-in-droplet encapsulation using Dean flow in a curved microchannel, Lab Chip 12 (16) (2012) 2881–2887. [3] J. Sun, M. Li, C. Liu, et al., Double spiral microchannel for label-free tumor cell separation and enrichment, Lab Chip 12 (20) (2012) 3952–3960. [4] D. Mei, M. Qian, B. Liu, et al., A micro-reactor with micro-pin-fin arrays for hydrogen production via methanol steam reforming, J. Power Sources 205 (2012) 367–376. [5] O.H. Laguna, E.M. Ngassa, S. Oraa, et al., Preferential oxidation of CO (CO-PROX) over CuOx/CeO2 coated microchannel reactor, Catal. Today 180 (1) (2012) 105– 110. [6] X.-Q. Zhang, X.-L. Wang, R. Liu, et al., Modeling and analysis of micro hybrid gas spiral-grooved thrust bearing for microengine, J. Eng. Gas Turb. Power – Trans. ASME 135 (12) (2013). [7] W.G. Gardner, J.W. Jaworski, A.P. Camacho, et al., Experimental results for a microscale ethanol vapor jet ejector, J. Micromech. Microeng. 20 (4) (2010) 045019. [8] X. Mao, B.K. Juluri, M.I. Lapsley, et al., Milliseconds microfluidic chaotic bubble mixer, Microfluid. Nanofluid. 8 (1) (2010) 139–144. [9] M. Nabavi, Steady and unsteady flow analysis in microdiffusers and micropumps: a critical review, Microfluid. Nanofluid. 7 (5) (2009) 599–619. [10] T. Tofteberg, M. Skolimowski, E. Andreassen, et al., A novel passive micromixer: lamination in a planar channel system, Microfluid. Nanofluid. 8 (2) (2010) 209–215. [11] O.O. Adewumi, T. Bello-Ochende, J.P. Meyer, Constructal design of combined microchannel and micro pin fins for electronic cooling, Int. J. Heat Mass Transf. 66 (2013) 315–323. [12] S. Gururatana, Heat transfer augmentation for electronic cooling, Am. J. Appl. Sci. 9 (3) (2012) 436–439. [13] M.R. Sohel, R. Saidur, M.F.M. Sabri, et al., Investigating the heat transfer performance and thermophysical properties of nanofluids in a circular microchannel, Int. Commun. Heat Mass Transfer 42 (2013) 75–81. [14] A. Kosßar, C. Mishra, Y. Peles, Laminar flow across a bank of low aspect ratio micro pin fins, J. Fluids Eng. – Trans. ASME 127 (3) (2005) 419–430. [15] M. Liu, D. Liu, S. Xu, et al., Experimental study on liquid flow and heat transfer in micro square pin fin heat sink, Int. J. Heat Mass Transf. 54 (25–26) (2011) 5602–5611. [16] Y. Peles, A. Kosar, C. Mishra, et al., Forced convective heat transfer across a pin fin micro heat sink, Int. J. Heat Mass Transf. 48 (17) (2005) 3615–3627. [17] A. Kosar, Y. Peles, Thermal-hydraulic performance of MEMS-based pin fin heat sink, J. Heat Transf. – Trans. ASME 128 (2) (2006) 121–131. [18] R.S. Prasher, J. Dirner, J.-Y. Chang, et al., Nusselt number and friction factor of staggered arrays of low aspect ratio micropin-fins under cross flow for water as fluid, J. Heat Transf. – Trans. ASME 129 (2) (2007) 141–153. [19] M. Koz, M.R. Ozdemir, A. Kosßar, Parametric study on the effect of end walls on heat transfer and fluid flow across a micro pin-fin, Int. J. Therm. Sci. 50 (6) (2011) 1073–1084. [20] Z. Liu, C. Zhang, N. Guan, Experimental investigation on resistance characteristics in micro/mini cylinder group, Exp. Therm. Fluid Sci. 35 (1) (2011) 226–233. [21] Z. Liu, Z. Wang, C. Zhang, et al., Flow resistance and heat transfer characteristics in micro-cylinders-group, Int. J. Heat Mass Transf. 49 (5) (2013) 733–744.

H. Zhao et al. / Experimental Thermal and Fluid Science 71 (2016) 57–69 [22] N.K.C. Selvarasu, D.K. Tafti, N.E. Blackwell, Effect of pin density on heat-mass transfer and fluid flow at low Reynolds numbers in minichannels, J. Heat Transf. – Trans. ASME 132 (6) (2010) 061702. [23] A. Kosar, Y. Peles, TCPT-2006-096.R2: micro scale pin, fin heat sinks – parametric performance evaluation study, IEEE Trans. Compon. Packag. Technol. 30 (4) (2007) 855–865. [24] W. Qu, A. Siu-Ho, Liquid single-phase flow in an array of micro-pin-fins-Part II: pressure drop characteristics, J. Heat Transf. – Trans. ASME 130 (12) (2008) (124501(1-4)). [25] C.A. Konishi, W. Qu, F.E. Pfefferkorn, Experimental study of water liquid-vapor two-phase pressure drop across an array of staggered micropin-fins, J. Electron. Packag. 131 (2) (2009) 021010. [26] T.J. John, B. Mathew, H. Hegab, Parametric study on the combined thermal and hydraulic performance of single phase micro pin-fin heat sinks Part I: square and circle geometries, Int. J. Therm. Sci. 49 (11) (2010) 2177–2190. [27] J.F. Tullius, T.K. Tullius, Y. Bayazitoglu, Optimization of short micro pin fins in minichannels, Int. J. Heat Mass Transf. 55 (15–16) (2012) 3921–3932. [28] K.A. Moores, Y.K. Joshi, Effect of tip clearance on the thermal and hydrodynamic performance of a shrouded pin fin array, J. Heat Transf. 125 (2003) 999–1007.


[29] K.A. Moores, J. Kim, Y.K. Joshi, Heat transfer and fluid flow in shrouded pin fin arrays with and without tip clearance, Int. J. Heat Mass Transf. 52 (25–26) (2009) 5978–5989. [30] N. Guan, Z.-G. Liu, C.-W. Zhang, Numerical investigation on heat transfer of liquid flow at low Reynolds number in micro-cylinder-groups, Heat Mass Transf. 48 (7) (2012) 1141–1153. [31] A. Renfer, M.K. Tiwari, T. Brunschwiler, et al., Experimental investigation into vortex structure and pressure drop across microcavities in 3D integrated electronics, Exp. Fluids 51 (3) (2011) 731–741. [32] A. Renfer, M.K. Tiwari, F. Meyer, et al., Vortex shedding from confined micropin arrays, Microfluid. Nanofluid. 15 (2) (2013) 231–242. [33] N.S.K. Gunda, J. Joseph, A. Tamayol, et al., Measurement of pressure drop and flow resistance in microchannels with integrated micropillars, Microfluid. Nanofluid. 14 (3–4) (2012) 711–721. [34] A. Tamayol, J. Yeom, M. Akbari, et al., Low Reynolds number flows across ordered arrays of micro-cylinders embedded in a rectangular micro/ minichannel, Int. J. Heat Mass Transf. 58 (1–2) (2013) 420–426. [35] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17.