Research Innovations and Applications in Energy and Mass Transport

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International Journal of Heat and Mass Transfer 136 (2019) 851–863 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Heat transfer enhancement of turbulent channel flow using dual self-oscillating inverted flags: Staggered and side-by-side configurations Yujia Chen, Yuelong Yu, Di Peng, Yingzheng Liu ⇑ Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China a r t i c l e i n f o Article history: Received 27 December 2018 Received in revised form 5 March 2019 Accepted 8 March 2019 Keywords: Inverted flag Heat transfer Side-by-side flags Staggered flags TSP a b s t r a c t This study experimentally determined the flapping dynamics of dual self-oscillating inverted flags placed inside turbulent channel flows in side-by-side and staggered configurations and their ability to enhance wall heat removal. Three clearance-distance to channel-width ratios (Gc/W = 0.19, 0.31, and 0.5) and three streamwise-distance to channel-width ratios (Gy/W = 0, 2, and 4) were used to examine distinct flag behaviors. A single flag mounted to the heated wall with various gap clearances was chosen as the benchmark. The flags’ time-varying motions were recorded by a high-speed camera system. Three dynamic regimes were identified on the basis of the flags’ dimensionless stiffness and the channel flow’s Reynolds number: the biased mode, the flapping mode, and the deflected mode. Temperature sensitive paint (TSP) measurements demonstrated that the best cooling enhancement, with a local Nusselt number ratio of over 1.6, was achieved for the single flag system at Gc/W = 0.19. Adding another inverted flag to the side-by-side configuration at Gc/W = 0.19 further enhanced the heat removal performance on both channel walls, and the flapping period increased by nearly 50%. However, placing two side-by-side flags close to each other (Gc/W = 0.31) led to chaotic flapping motions, resulting in diminutive augmentation in heat transfer and an appreciable penalty in pressure drop. In the staggered configuration at Gy/W = 2 and 4, the two inverted flags synchronously flapped with a stable phase difference, and the flapping periods were similar to those of the single flag. The peak Nusselt number ratio was 1.9 for Gy/W = 2, which was attributed to the concerted influence of the staggered inverted flags. The system with staggered flags placed close to the heated wall had a higher thermal enhancement factor than the system with flags mounted in tandem along the channel centerline. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction The heat transfer of channel flow plays an important role in industry applications, e.g., in gas turbines and heat exchangers, and can be considerably intensified by various turbulence enhancement mechanisms (e.g., ribs, pin fins, protrusions, and dimples [1–4]). However, such strategies significantly deteriorate in turbulent channel flows with low Reynolds numbers (104), which are common in electronic products due to their highly limited effective areas and the increased cost of pressure drop. To overcome this issue, active vortex generators, such as piezo fans and magnetic fans [5,6], have been developed, but these depend ⇑ Corresponding author at: Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China. E-mail address: yzliu@sjtu.edu.cn (Y. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.048 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. on reliable external power supplies. Recent studies have shown [7] that placing a flexible flag in the channel and then forcing it into a self-oscillating motion produces substantial gains in heat transfer in the extended area [8], probably due to the flag’s instability and the highly unsteady channel flow behind the flag. A few preliminary attempts have been made to promote wall heat removal by placing a flag or multiple flags in the channel. For laminar channel flow at a very low Reynolds number (Re = 600), two vertically wall-mounted flexible flags [9,10] were forced into self-oscillating motions with a moderate amplitude to flag-length ratio, A/L > 0.35; the numerical results suggested an optimized heat transfer performance with nearly 100% enhancement in mean heat flux. However, recent experimental attempts [11] have indicated that such intense flapping is hard to generate in a turbulent channel flow. A computational study of laminar channel flow at Re < 800 [12] showed that the flow-induced vibra- 852 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 Nomenclature A B C* E F f fT Gc Gx Gy Hc H h I KB L Lp Nu Nu* P Dp R ReW S T t* Dt* U0 V flapping amplitude [m] ^  m] flexural rigidity [NA length to channel width ratio C* = L/W young’s modulus of the inverted flag [GPa] friction factor flapping frequency of the inverted flag [Hz] TSP function gap clearance between the flag and wall [m] separation distance between two flags in the transverse (x) direction [m] separation distance between two flags in the streamwise (y) direction [m] height of the wind channel [m] height (or span) of the inverted flag [m] thickness of the inverted flag [m] luminescence intensity of the TSP dimensionless bending stiffness length of the inverted flag [m] distance between two pressure taps [m] Nusselt number Nusselt number ratio electronic power applied to the heating foil [W] pressure drop between two pressure taps [Pa] results calculated from variables Reynolds number (based on the width of the channel) area of the heating foil [m2 ] temperature [K] dimensionless time dimensionless flapping period ^  s1 ] free stream velocity [mA measured variables tion of a conventional flag (clamped at the leading edge and free at the trailing edge) resulted in an appreciable convective heat transfer augmentation of over 60%. Unfortunately, the extremely soft flag used in the numerical study was nearly unavailable in engineering applications. A real flag in the conventional configuration can be experimentally excited by the channel flow at a high Reynolds number, up to 105 [13,14]; however, this is challenging for Re  104 [15]. A single inverted flag (free at the leading edge and fixed at the trailing edge) with a length to channel-width ratio of C* = 0.5 was excited to an intense flapping motion at the channel laminar flow (Re < 800) by Park et al. [16], who reported heat transfer enhancement of 150%, but with a penalty of nine times the mechanical energy loss. Subsequently, Yu et al. [17] experimentally examined the heat transfer enhancement performance of three inverted flags of different lengths (C* = 0.125, 0.25, and 0.375) in the range of Re = 1.2  104 –2.3  104 . They found the local Nusselt number increased by 20% for a short flag (C* = 0.125), and the pressure drop increased by 69%. As the longest flag (C* = 0.375) was in flapping mode, it achieved the best cooling performance, with a remarkable augmentation of up to 70%, but at a substantial cost in pressure drop, which increased by a factor of 3.17. This increase in pressure drop was attributed to the energetic vortex shedding process behind the flag, and was confirmed by the time-resolved particle image velocimetry (TR-PIV) measurement of the unsteady flow [17]. Using tandem flags (C* = 0.25) along the channel centerline, Chen et al. [8] successfully doubled the local Nusselt number for the extended streamwise area, but the total pressure drop still exceeded the smooth channel without flags by a factor of four. In these studies [8,17], the considerable penalty in pressure drop was the result of a large blockage of the long flag W x y z X Y Z* width of the channel [m] transverse direction [m streamwise direction½m spanwise direction½m normalized transverse coordinate normalized streamwise coordinate normalized spanwise coordinate Greek symbols thickness of the turbulent boundary layer [m] d99 g thermal enhancement factor t Poisson’s ratio of the inverted flag k thermal conductivity of the air [Wm1  K1 ] qf fluid density [kg  m3 ] qs density of the inverted flag [kg  m3 ] Subscripts 0 smooth channel ref reference air, in inlet air Abbreviation CCD charge coupled device CMOS complementary metal oxide semiconductor FFT fast fourier transform TSP temperature sensitive paint TR-PIV time-resolved particle image velocimetry UV-LED ultraviolet light-emitting diode to the high-speed mainstream, which is needed for a flag placed in the channel centerline to generate a large flapping motion and sweep out the thermal boundary layer. It is well established that placing short inverted flags in proximity to a heated wall introduces strong disturbance to the near-wall flow, intensifying wall heat removal at a reduced pressure drop across the entire channel, and that the effective heat transfer enhancement area can be extended by different configurations of the paired flags. Building on Chen et al. [8], this study quantified the coupling flapping dynamics of dual inverted flags in proximity to the wall and the resultant heat transfer enhancement. Using a single flag as a benchmark, two representative configurations of the paired flags, staggered and side-by-side, were compared. A total of three clearance-distance to channel-width ratios (Gc/W = 0.19, 0.31, and 0.5) and three streamwise-distance to channel-width ratios (Gy/W = 0, 2, and 4) were varied to examine their distinct behaviors. In the experiment, a high-speed camera was installed to identify the flags’ flapping motions; the spatially varying temperature field on the heated wall surface was determined using the temperature sensitive paint (TSP) technique. 2. Experimental setup 2.1. Flag dynamics measurement apparatus Fig. 1(a) presents a schematic diagram of the experimental setup to measure the flag flapping dynamics. Two rectangular and flexible inverted flags made of transparent polyethylene terephthalate (density qs ¼ 1:38  103 kg=m3 , Young’s modulus E = 2:2GPa;and Poisson’s ratiot ¼ 0:39) were set parallel to the Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 853 Fig. 1. Flag flapping dynamics: (a) schematic diagram of experimental setup; (b) single flag configuration; (c) side-by-side flags configuration; and (d) staggered flags configuration. flow. The flags shared the same thickness (h = 0.025 mm), height (or span) (H = 60 mm), and length (L = 7.5 mm, C* = 0.19). These dimensions led to a high aspect ratio (H/L = 8) that guaranteed two-dimensional flapping motions near the mid-span position. The inverted flag was clamped at its trailing edge with two pieces of carbon fiber plate that were 3 mm in length and 0.5 mm in thickness. The right-hand coordinate origin was situated at the mid-span of the upstream flag trailing edge, and the x, y, and z axes denoted the transverse, streamwise, and spanwise orientations, respectively. All of the coordinates were normalized by the channel width W, i.e., X* = x/W, Y* = y/W, and Z* = z/W. The measurements were conducted in a subsonic open-circuit wind tunnel with an 80 mm (height, Hc)  40 mm (width, W) cross section that had been previously installed by Chen et al. [8]. The wind tunnel was equipped with a contraction section (contraction ratio 7:1) to straighten the air flow entering the test segment. The top-hatted inlet velocity profile, with a turbulent boundary layer thickness of d99 = 0.25 W, was measured by moving the hot-wire probe along the normal-wall (x) direction; the turbulence intensity was below 2% for the current free-stream velocity range U0 = 5:8  9:4 m/s 854 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 (ReW = qf U0W/lf ranged from1:55  104 to2:52  104 ). The dimen2 3 f U0 L , which characterizes the sionless bending stiffness [7] KB=B=q relative magnitude of the bending force to the fluid inertial force exerted on the flag, ranged from 0.198 to 0.075. Herein, qf = 1.2 kg/m3 denotes the air density (1 atm, 395 K) 3 andB ¼ Eh =12ð1  t2 ) is the flexural rigidity of the flag. To visualize the flag motions, a 5 W continuous-wave semiconductor laser (532 nm) was used to illuminate the mid-span of the flags, as shown in Fig. 1(a). A 12-bit high-speed CMOS camera (dimax HS4, PCO, USA) was installed on the top of the wind channel to record the flapping dynamics of the inverted flags. The camera was operated at a speed of 2000 fps (the flag flapping frequency, f, was around 100 Hz for all of the experiments) with a resolution of 1500  600 pixels (0.1375 mm/pixel), allowing the instantaneous flag profiles of the two inverted flags to be captured simultaneously. Inspired by the side-by-side and staggered flag systems proposed by Cerdeira et al. [18], Ryu et al. [19], and Huang et al. [20], three configurations were tested, as shown in Fig. 1(b)– (d): (b) a single flag, (c) side-by-side flags, and (d) staggered flags. In Fig. 1, Gc is the gap clearance between the flag and the wall, Gx is the separation distance in the transverse (x) direction, and Gy denotes the separation distance in the streamwise (y) direction. To improve the clarity of the discussion of the results in following sections, the upper and lower walls in Fig. 1(b)–(d) are marked as wall side 1 and wall side 2, respectively. 2.2. Heat transfer performance measurement apparatus The heat transfer measurements were conducted in the same wind tunnel. The spatially varying temperature field on the heated wall was quantified using the temperature sensitive paint (TSP) [21] technique. TSP is a molecular temperature sensor consisting of luminescent molecules and a binder. When illuminated by light of a certain wavelength (385 nm in this study), the luminescent molecules in the TSP layer are excited into an unstable elevated energy state, which is susceptible to shifting to a ground state through two mechanisms: thermal deactivation and luminescent deactivation (i.e., luminescence wavelength around 600 nm). As the temperature rises, thermal deactivation increases and luminescent deactivation decreases, leading to attenuated luminescence intensity. The temperature field, accurately indicated by the luminescence intensity, can be determined by examining their relationship, which is generally described by the function fT in the following equation:   Iref ¼ f T T; T ref ; I Fig. 2. Schematic diagram of the heat transfer experimental setup. ð1Þ where Iref is the luminescence intensity at a specified reference temperature Tref (usually room temperature) and I is the luminescence intensity at arbitrary temperature T. The process for calibrating function fT is discussed below. Fig. 2 shows the schematic diagram of the heat transfer experiment apparatus. To produce the TSP layer, an oxygenimpermeable automobile clearcoat (Dupont ChromClear HC7776S) was used as a binder, and Ru (dpp) (GFS Chemical, Inc.) was selected as the temperature sensor [22–24]. The TSP sensor was dissolved in methanol and mixed with the clearcoat binder. Then, the TSP solution was air-sprayed onto a thin stainless steel plate (500 mm in length, 40 mm in width, and 0.5 mm in thickness), and left for several hours until dry. To provide an adjustable and uniform heat flux, the whole upper surface of the stainless steel plate was covered with a heating foil (0.1 mm thick, Backer Calesco, Sweden). A direct current (DC) source provided continuous and stable electronic power to the heating foil; the electronic power could be measured by the built-in voltmeter and ammeter inside the DC source. A suitable cavity in the upper channel wall (made of Plexiglas) was carefully designed to embed the heated plate so that the flow distortion would be eliminated. A thermal insulation layer (10 mm thick, thermal conductivity < 0.025 W/mK) was used to minimize heat loss from thermal conduction; heat loss through the insulated wall was estimated to be less than 1% of the power input. Eighteen T-type thermocouples were attached to the heating foil to monitor the plate temperature. Their locations in relation to the inverted flags are plotted in Fig. 2. Two additional thermocouples were installed at the channel inlet and outlet to obtain the airflow temperature. The experiments were conducted in a constant-temperature room in which the air conditions and inlet air temperature was kept at around 295 K. All of the temperature signals were simultaneously captured by a data acquisition system (Fluke 2638A, USA). The pressure drop was measured by a manometer placed between the two pressure taps situated on the lower transparent Plexiglas wall (accessible as a light path) at Y* = 3.5 and 6, respectively. Under excitation by the 385 nm UV-LED (UHP-T-LED-385, Prizmatix), the TSP layer emitted luminescent signals, which were captured by a 14-bit CCD camera (PCO 1600, USA) with a resolution of 1600  1200 pixels (0.1837 mm/pixel). The camera lens (Nikon 35 mm f/2.8) was equipped with a band-pass filter (575 25 nm) to exclude any excitation light from the UV-LED. The local Nusselt number Nu is widely used as a dimensionless index to measure cooling performance, and is defined as follows: Nu ¼ PW  ; Sk T  T air;in ð2Þ where S denotes the heating foil area, P is the power of DC source, k is the thermal conductivity of air, and T and T air;in represent, respectively, the local wall temperature and inlet airflow temperature measured after the heat-balanced state was established. The stainless steel plate was under the dual influence of the electronic heating, with constant power P, and cold air cooling, which depended on surface temperature T; as T gradually increased, a heat-balanced state was eventually reached when the heating power was equivalent to the heat convection toward the cold air, guaranteeing a fully development of the heat transfer before measurement. The stainless steel plate was deemed to be in the heat-balance state when the maximum variation in temperature measured by every single thermocouple was less than 0.1 K over a 5-min period, with a calculated diversity of 0.045% between the heat input and heat transferred to the cold air. The temperature difference T  Tair,in in the heatbalanced state was maintained at 15–30 K for all of the experimental cases. Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 The TSP measurement procedure and the in-situ calibration process for the function fT were performed simultaneously. Firstly, the luminescent intensity distribution Iref was acquired at room temperature, Tref. Then, the heat power and the wind tunnel were turned on. After the establishment of the heat-balance state, the image intensity I captured by the camera and the corresponding temperature value T measured by the thermocouples were collected simultaneously. Experimental data (scatter points) from all of the successful runs were applied to fit the calibration curve fT, shown in Fig. 3, and the deviation between the measurement data and the fitted curve was below 0.2%. The accuracy of the T-type thermocouples was 0.5 K. The uncertainty of the TSP measurement was estimated to be within 0.7 K. Based on the fitted calibration curve and the image intensity distribution, I, measured on the heated plate, the global temperature distribution T was accurately determined. The uncertainty analysis was based on a confidence level of 95% proposed by Moffat [25]. The results, R, of the experiment are assumed to be calculated from a series of variables, Vi, as follows: R ¼ RðV 1 ; V 2 ; V 3 ; . . . ; V N Þ: ð3Þ Then, the comprehensive relative uncertainty was determined as follows: DR ¼ R ( N  X @R i¼1 @V i  DV i R 2 )1=2 ; ð4Þ where DR and DV i denote the uncertainty in R and Vi, respectively. Substituting Eq. (2) into Eq. (4) gave a comprehensive relative uncertainty of the local Nu as 7%. The Nusselt number ratio [8,17,22] Nu* = Nu/Nu0 indicates the magnitude of the enhancement of the heat transfer performance relative to the smooth channel. The Nu0 at the corresponding Reynolds numbers for the smooth channel without a flag were also measured. To further clarify the heat transfer enhancement performance, the results are presented by Nu* below. 3. Results and discussion 3.1. Single flag The flapping dynamics of a single flag next to the wall at three typical gap clearances, Gc/W = 0.19, 0.31, and 0.5, and the resultant heat transfer enhancement were first investigated to establish a benchmark. When Gc/W = 0.19, the clearance was equal to the flag 855 length, i.e., Gc = L; any further reduction in Gc would disturb the flapping motions of the flag because of the latent physical contact between the flag and the wall. When Gc/W = 0.5, the inverted flag was mounted along the centerline of the channel. Gc/W = 0.31 was designed to keep the distance between the channel centerline and the flag at L, such that the two flags would not touch when configured side-by-side, as discussed in Section 3.2. Three distinct dynamic regimes, the biased, flapping, and deflected modes, were recognized with consecutive increases in the Reynolds number, ReW, (indicating that the dimensionless bending stiffness KB decreased), as shown in Fig. 4(a). No obvious wall confinement effect was observed on the flag flapping dynamics, and when Gc/ W varied, the dynamic regimes remained almost unchanged, with a similar ReW range. In biased mode (1), the flag mainly flapped asymmetrically to one side with moderate amplitudes of A/ L = 0.7–1.2 at ReW = 1:64  104 –1:73  104 ; for the following experiments, the flag flapping amplitude A was defined as the maximum tip-to-tip displacement in transverse direction. The instantaneous motions of the inverted flag were recognized by a monitor point located 0.8 L (curvilinear distance along the flag) away from the trailing edge, as shown in Fig. 4(a). Fig. 4(b) gives a typical trajectory of the monitor point in the biased mode for Gc/W = 0.5 and ReW = 1:64  104 , showing a periodical flapping motion of the inverted flag restricted to a single side (x/L > 0) with respect to the free state. In the flapping mode (2), a symmetric oscillation with a significant amplitude of nearly 1.8 L was identified for the ReW range of 1:81  104 to2:34  104 . The trajectory of the monitor point in the flapping mode approximated a sineshaped curve (Fig. 4(c)). In the deflected mode (3), as ReW increased further, the restoring bending force inside the flag was no longer comparable to the aerodynamic force exerted on the flag; therefore, the flag entirely deformed to the channel wall with a diminutive amplitude of less than 0.2 L, as shown in Fig. 4(d). These three dynamic regimes have been observed in previous studies [8,15,17], which also reported bi-stable states with small Reynolds number ranges in both the biased to flapping mode transitions and flapping to deflected mode transitions. In this study, the heat transfer experiments were conducted without the bi-stable states to avoid the effect of mode transition. In Fig. 4(b)–(d), dimensionless time is defined as t* = tU0/L, where t denotes the physical time. The additional turbulence was introduced by the energetic flapping flag, which facilitated the heat transfer enhancement from the heated plate. Yu et al. [15] reported that the channel turbulent kinetic energy can be locally elevated by over 80 times due to the presence of the flapping inverted flag. The performance of a single flag as a cooling mechanism across the three dynamic regimes has been widely investigated, using both numerical [16] and experimental [8,17] methods, and the results have consistently shown that an inverted flag in the flapping mode provides the best cooling performance among the three regimes. Consequently, this study quantified the heat transfer performance in the flapping mode. Fig. 5 depicts the contours of the distribution of the Nusselt number ratio, Nu*, for Gc/W = 0.19 (a and b), 0.31 (c and d), and 0.5 (e) at ReW = 2:08  104 . The relative heat transfer enhancement performance indicated by the dimensionless Nusselt number was confirmed [8,17] to be insensitive to the Reynolds number in the flapping regime, as the flags’ self-oscillating behaviors were simi- Fig. 3. In-situ calibration result for the TSP. lar. Thus, a moderate ReW = 2:08  104 in the flapping mode was chosen as a representative demonstration. In addition, the poor dependency of the heat transfer performance on the Reynolds number is further clarified in Fig. 7. For Gc/W = 0.19 and 0.31, the inverted flag was mounted away from the centerline; in such configurations, the cooling performance of the near side and far side (wall sides 1 and 2, respectively, as shown in Fig. 1) should be measured individually. However, in this study’s original experimental 856 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 Fig. 4. Single flag dynamics: (a) dependency of the flapping amplitude and flapping dynamics on the Reynolds number, ReW, and dimensionless bending stiffness, KB, for various clearances Gc; (b and d) trajectories of the monitor points for biased, flapping, and deflected modes, respectively. set-up (Fig. 2), only wall side 1 with the heated plate was available for heat transfer measurements, while wall side 2 consisted of a transparent Plexiglas plate where the heat transfer was absent. To circumvent this issue, another experiment was conducted, with the inverted flag placed in the symmetric position along the centerline. For instance, the inverted flag mounted at Gc/W = 0.81 was the counterpart for Gc/W = 0.19; the heat transfer measured at side 1 for Gc/W = 0.81 (Fig. 5(b)) could then be regarded as the result measured at side 2 for Gc/W = 0.19. The inverted flags along with their shadows are plotted as grey areas of various sizes in Fig. 5: for Gc/W = 0.19, side 1, (Fig. 5(a)), the inverted flag was far from the camera and LED source; accordingly the size of the blocked grey area is small. In contrast, for Gc/W = 0.81, side 1, (i.e., Gc/W = 0.19, side 2, Fig. 5(b)), the inverted flag was close to the camera and LED source, so the grey area is enlarged. Figs. 5 and 6 demonstrate that as the gap clearance between the inverted flag and the wall decreased, Nu* increased. Fig. 5(a) shows that when Gc/W = 0.19, Nu* increased remarkably to 1.5 for 0.5 < Y* < 1.75 at wall side 1 before gradually decreasing for Y* > 2. In contrast, Fig. 5(b) shows that the best cooling region shifted to 2.5 < Y* < 4, with a Nu* value around 1.2 at side 2 (0.81 W away from the flag). The difference in cooling performance between wall sides 1 and 2 can be explained by the vortex shedding process that takes place behind the inverted flag. PIV measurements [7,15,17] and numerical studies [26] have confirmed that the shedding vortex emits toward the wall and transports downstream. The shedding vortex attached to wall side 1 was immediately behind the flag and swept out the thermal boundary layer, which significantly strengthened the heat transfer performance of the configuration with the small gap clearance Gc/ W = 0.19. The spanwise-averaged Nu* distributions in Fig. 6 (red1 1 For interpretation of color in Figs. 6, 9, 11 and 15, the reader is referred to the web version of this article. Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 857 Fig. 5. Contours of the Nu* distribution for a single flag at ReW = 2:08  104 : (a and b) Gc/W = 0.19, wall sides 1 and 2, respectively; (c and d) Gc/W = 0.31, wall sides 1 and 2, respectively; (e) Gc/W = 0.5. Fig. 6. Spanwise-averaged Nu* distribution of a single flag with various Gc values at ReW = 2:08  104 . solid line) also showed that the maximum Nu* = 1.6 rose at Y* = 1. As the flag was farther from wall side 2 (gap clearance 0.81 W), the vortex dissipated and was transported downstream before attaching to the wall; the weaker peak Nu* = 1.27 then shifted downstream at Y* = 3 (Fig. 6, red dashed line). A similar phenomenon was observed for Gc/W = 0.31 and 0.5; that is, as shown in Fig. 6, the maximum Nu* was attenuated to 1.5 (purple solid line) at Y* = 1 when the inverted flag moved to Gc/W = 0.31. However, compared with the red dashed line (Gc/W = 0.19, side 2), the heat transfer performance for side 2 at Gc/W = 0.31 was substantially augmented with an elevated Nu* value exceeding 1.4 at Y* = 2.5. When the inverted flag was mounted along the centerline for Gc/W = 0.5, the heat transfer performance on sides 1 and 2 should be the same, because the two walls are symmetric; consistent with this prediction, a moderate peak Nu* = 1.46 was obtained at Y* = 1.5. There was a heat transfer performance trade-off between the two walls: a larger Nu* was achieved with a closer gap clearance, Gc, at side 1 due to the vigorous vortex shedding process from the inverted flag; however, Nu* significantly declined because the shedding vortex dissipated before sweeping out the thermal boundary layer on wall side 2. To evaluate the comprehensive heat transfer performance of inverted flags with various Gc values, a thermal enhancement factor g [8,16,27,28] that accounted for both heat transfer benefit, Nu=Nu0 , and pressure drop penalty, F/F0, was defined as follows: g¼ Nu=Nu0 ðF=F 0 Þ1=3 ; ð5Þ where Nu is the global space-averaged Nusselt number for the two wall sides, subscript 0 denotes the smooth channel value at the corresponding Reynolds number, F = 2DpW=Lh qf U 20 is the friction factor, Dp is the pressure drop between two pressure taps located at 858 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 Y* = -3.5 and 6, Lh ¼ 9:5W is the distance between the two pressure taps, and qs is the air density. It is not reasonable to compare only the Nusselt number with that of the clean channel, because the channels modified with vortex generators such as flags and ribs always require more pumping power than a clean channel at the same Reynolds number. The thermal enhancement factor g is defined as the ratio of the Nusselt number of a modified channel to that of a smooth channel at a constant pumping power [27]. Eq. (5) allows a comparison between the clean channel and the modified channel. Table 1 summarizes the heat transfer performance and friction characteristics of the single inverted flag mode. The highest thermal enhancement factor of g = 1 was achieved at Gc/W = 0.19, which is around 4% higher than that of Gc/W = 0.5. Placing the self-oscillating inverted flag in proximity to the channel wall improved the heat transfer performance. The effect of the Reynolds number on heat transfer performance of the inverted flags is demonstrated in Fig. 7. Keeping the inverted flags in the flapping mode for Gc/W = 0.19 in the ReW range of 1:81  104 –2:34  104 resulted in an almost unchanged spanwise-averaged Nu* distribution for side 1, with a similar peak Nu* value around 1.6 at Y* = 1. For side 2, the maximum Nu* slightly Fig. 7. Spanwise-averaged Nu* distribution for a single flag with Gc/W = 0.19 at various ReW values. increased from 1.23 to 1.31 as the ReW rose from 1:81  104 to2:34  104 . It seems that the trends of Nu* distributions are similar in the whole Reynolds number range of flapping regime, which is consistent with previous studies [8,17]. Accordingly, ReW was kept at the fixed value of 2:08  104 for the side-by-side and staggered flags systems, as described in the following sections. 3.2. Side-by-side flags Promoting heat removal in the channel flow by placing a single inverted flag close to the wall had an inevitable disadvantage: the near wall (side 1) received sufficient cooling enhancement, but the far wall (side 2) had poor cooling. Placing two inverted flags sideby-side (Fig. 2(c)) seems to be an effective method for obtaining adequate heat transfer augmentation on both channel walls. Two typical gap clearances were investigated, Gc/W = 0.19 and 0.31, which tested distances between the two flags in the transverse direction of Gx/L = 3.33 and 2, respectively. Fig. 8 demonstrates that the flapping amplitude and dynamics of the side-by-side flags were dependent on KB and ReW. Comparing these with the single flag configurations, the three distinct dynamic regimes were located in similar ReW ranges for the side-by-side configurations at Gc/ W = 0.19 and Gc/W = 0.31, but the transition ReW between the biased, flapping, and deflected modes, declined slightly to 1:73  104 and2:26  104 , respectively. However, the flapping dynamics of the side-by-side inverted flags for Gc/W = 0.19 and 0.31 were totally different. Fig. 9 depicts the snapshots of flag movement and the trajectories of the monitor points at ReW = 2:08  104 . For Gc/W = 0.19 (Fig. 9(a) and (b)), the two flags flapped in phase with periodic and synchronous motions; in contrast, the flapping motions for Gc/W = 0.31 were chaotic (Fig. 9(c) and (d)), as the two flags alternately flapped toward one single side or both. For instance, flag 2 (Fig. 9(d), red line) flapped symmetrically at 20 < t* < 80, whereas it flapped toward a single side at 0 < t* < 230. Fig. 9(c) shows the profiles of the chaotic Table 1 Heat transfer performance and friction characteristics of single inverted flag for various Gc. Gc/W Nu=Nu0 F/F0 g 0.19 0.31 0.5 1.18 1.19 1.17 1.65 1.78 1.80 1.00 0.98 0.96 Fig. 8. Side-by-side flag dynamics. The flapping amplitude and dynamics depend on the Reynolds number, ReW, and the dimensionless bending stiffness, KB, for various gap clearances, Gc. inverted flags at t* = 0–20. Flag 1 flapped symmetrically, whereas flag 2 purely oscillated toward the bottom wall. Such irregular flapping motions were also observed experimentally by HuertasCerdeira et al. [18], and may be the result of strong interactions between the two flags. Fig. 10 compares the Nu* distributions of the side-by-side flags (Fig. 10(b) and (d)) with that of a single flag (Fig. 10(a) and (c)) at ReW = 2:08  104 . Compared with the single inverted flag at Gc/ W = 0.19 (Fig. 10(a)), Fig. 10(b) shows a remarkable rise in Nu* above 1.6 behind the side-by-side flags from Y* = 0.75 to 2, which can be attributed to the additional turbulence caused by the second self-oscillating inverted flag. Furthermore, the peak Nu* rose to 1.8 at Y* = 1 (Fig. 11, green line). As the side-by-side flags were close to the wall (Gc/W = 0.19) and far from each other (Gx = 3.33L), they still flapped with large amplitudes and symmetric motions, and the heat transfer performance, indicated by Nu*, was significantly elevated. However, the results differed when the two side-by-side inverted flags were placed close to each other (Gx = 2L, i.e., Gc/W = 0.31). A diminutive elevation in Nu* was observed in the side-by-side flags (Fig. 10(d)) compared to the single flag (Fig. 10(c)) for Gc/W = 0.31. The peak Nu* slightly increased to 1.54 at Y* = 1.25 for the side-by-side inverted flags (Fig. 11, blue Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 859 Fig. 9. Snapshots of the side-by-side flags and the trajectories of the monitor points: (a and b) Gc/W = 0.19 and (c and d) Gc/W = 0.31. line), a little higher than peak Nu* = 1.49 at Y* = 1 for the single inverted flag (Fig. 11, purple line). In addition, Nu* for the sideby-side case was even smaller than for the single inverted flag at 0.25 < Y* < 1. This small enhancement in heat transfer can be explained by the chaotic motions of the side-by-side flags at Gc/ W = 0.31. At times, the side-by-side flags only flapped toward a single side with smaller amplitudes; therefore, the resulting turbulence of the surrounding fluid may be incomparable to that of symmetrically flapping flags. Table 2 compares the heat transfer performance and friction characteristics of the side-by-side flags with those of the single inverted flag. For Gc/W = 0.19, the global averaged Nusselt number ratio, Nu=Nu0 , was augmented to 1.30 for the side-by-side configuration, and a benefit of around 10% was successfully achieved relative to the single flag ratio of Nu=Nu0 = 1.18. However, the friction ratio, F/F0, increased by 68% because of the additional flag’s blockage, which overall reduced efficiency g by 7%. In contrast to the single inverted flag for Gc/W = 0.31, Nu=Nu0 was enhanced by 3% for the side-by-side flags, and the F/F0 increased by approximately 70%, resulting in an uneconomic thermal enhancement efficiency of g = 0.86. 3.3. Staggered flags The flapping dynamics and heat transfer characteristics of the staggered inverted flags were investigated. As the single flag and side-by-side flags configurations gave the best heat transfer performance at Gc/W = 0.19, the gap clearance for the staggered flags was maintained at the same value. The separation distances in the streamwise direction were Gy/W = 2 and 4, as shown in Fig. 1(d). The staggered flags’ flapping dynamics and the resultant heat transfer performances were compared with those of the sideby-side flags, i.e., Gy/W = 0. Fig. 12 shows that the flapping amplitude and flapping dynamics depended on the ReW and KB of the staggered inverted flags. For the staggered configurations Gy/ W = 2 and 4, the flapping amplitude and dynamic regimes were also similar to those of the single flag. The two staggered flags flapped synchronously with nearly the same amplitude throughout the entire ReW range. For brevity, Fig. 12 only depicts the flapping amplitude of the front flag 1. The trajectories of the monitor points revealed the time history of the flag motions for Gy/W = 0 (side-by-side) and 2 and 4 (staggered), as shown in Fig. 13. For the side-by-side system Gy/W = 0, the two flags flapped symmetrically toward both sides with no phase delay. However, their dimensionless flapping period, Dt*, remarkably increased from 10.9 (isolated single flag, Fig. 4(c)) to 16.4, indicating that the side-by-side flags oscillated more slowly than the single flag. As for the staggered systems Gy/W = 2 and 4, Fig. 13(b) and (c), show that the two flags flapped in coupled motions with a constant phase delay and their flapping periods, Dt*, recovered to around 10.4, which is comparable to the single flag value of Dt* = 10.9. We can infer that the interactions between the staggered flags were weaker than those between the side-byside flags. Therefore, placing the dual flags in a staggered configuration might eliminate the chaotic motions observed in the side- 860 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 Fig. 10. Contours of the Nu* distribution for various Gc values at ReW = 2:08  104 : (a) single flag at Gc/W = 0.19, wall side 1; (b) side-by-side flags at Gc/W = 0.19; (c) single flag at Gc/W = 0.31, wall side 1; and (d) side-by-side flags at Gc/W = 0.31. Fig. 11. Spanwise-averaged Nu* distribution of the single flag and side-by-side flags for various Gc values at ReW = 2:08  104 . by-side system with close flag distances, which is a common configuration for narrow channels. Fig. 14 plots the contours of the Nu* distribution for the staggered flags at ReW = 2:08  104 . For Gy/W = 2, Nu* quickly rose to 1.7 behind the front flag at Y* = 0.6 (Fig. 14(b)), with a peak value 1.65 at wall side 1, before the heat transfer performance decayed at Y* > 1.7. Fig. 15 demonstrates that the spanwise-averaged Nu* for the staggered flags was 0.15 higher (purple solid line, Gy/ W = 2, wall side 1) at Y* > 3.5 than the single flag (red solid line). This can be attributed to the rear flag’s vigorous flapping motion. The Nu* distribution was distinct at wall side 2 (Fig. 14(c)), as the cooling augmentation behind the front flag was almost ignorable before Y* = 1.8: the front flag was far from wall side 2 and the shedding vortex did not sweep out the thermal boundary layer at Y* < 1.8. In addition, the rear flag was mounted in proximity to wall side 2, which gave the region 2.2 < Y* < 3.5 favorable heat removal conditions, resulting in a high Nu* value that exceeded 1.7. The peak Nu* was observed at nearly 1.9 (Fig. 15, purple dashed line), which was even higher than that of the side-by-side configurations’ Nu* = 1.8 (Fig. 15, blue solid line), perhaps because for a single inverted flag, the Nu* peak was observed 1 W and 3 W downstream from the flag at wall sides 1 and 2, respectively, as shown in Fig. 6. Similarly, for the staggered system Gy/W = 2, the front flag was mounted at Y* = 0, and the best cooling region was located at around Y* = 3 for wall side 2; the rear flag was mounted in proximity to wall side 2 at Y* = 2, and its best cooling region was at about 1 W behind the rear flag, i.e., Y* = 3. The concerted influence of the dual staggered flags substantially enhanced the heat removal performance, with a maximum Nu* of around 1.9 at Y* = 2.75, wall side 2. When the rear flag moved to Y* = 4 (Fig. 14 (d) and (e)), the heat transfer performance at side 1 was similar to that of Gy/W = 2 (Fig. 14(b)); however, the peak Nu* region for wall side 2 shifted downstream to 4.4 < Y* < 5 (Fig. 14(e)). Table 3 indicates that the most economic cooling performance with a ther- Table 2 Heat transfer performance and friction characteristics of the side-by-side inverted flags for various Gc values. Configuration Gc/W Nu=Nu0 F/F0 g Single Side-by-side Single Side-by-side 0.19 0.19 0.31 0.31 1.18 1.30 1.19 1.22 1.65 2.78 1.78 2.81 1.00 0.93 0.98 0.86 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 861 4. Conclusions Fig. 12. Staggered flag dynamics: flapping amplitude and dynamics depend on the Reynolds number, ReW, and the dimensionless bending stiffness, KB, for various separation distances, Gy, at a fixed gap clearance of Gc/W = 0.19. mal enhancement efficiency of g = 0.94 was achieved at Gy/W = 2. In contrast to our previous study [8], g = 0.87 was obtained by placing inverted flags (C* = 0.25) in tandem along the channel centerline with a similar Reynolds number. Accordingly, placing the shorter inverted flags (C* = 0.19) proximate to the wall in staggered configuration could further improve heat transfer performance. This study investigated the flapping dynamics of dual selfoscillating inverted flags close to the walls within a turbulent channel flow in both side-by-side and staggered configurations. It examined the resultant heat transfer enhancement performance on the channel walls. The time varying curving profiles of the deformed inverted flags were chronologically recorded by a highspeed camera and then identified using a structure boundary detection algorithm. The heat transfer performance indicated by the Nusselt number ratio Nu* was measured quantitatively using the TSP measurement technique. Three distinct dynamic regimes based on the Reynolds number, ReW, and the dimensionless bending stiffness, KB, i.e., the biased, flapping, and deflected modes, were identified for a single inverted flag with gap clearances of Gc/W = 0.19, 0.31, and 0.5. The wall confinement effect of the different gap clearances on the flapping dynamics was ignorable. The best heat transfer enhancement with g = 1.00 was achieved when the flag was placed close to the channel wall with Gc/W = 0.19, and the maximum Nu* of around 1.6 was observed at Y* = 1 for wall side 1 at ReW = 2:08  104 . As the gap clearance increased and the flag was moved farther away from the wall to Gc/W = 0.5, the peak Nu* region shifted downstream at Y* = 1.5 and the Nu* value declined by 1.46. No obvious Reynolds number effect was found on the heat transfer performance in the flapping mode for the ReW range from 1:81  104 to2:34  104 . Two inverted flags arranged in side-by-side configurations were subsequently studied. The same three dynamic regimes were Fig. 13. Trajectories of the monitor points for the fixed gap clearance Gc/W = 0.19 and various separation distances: (a–c) Gy/W = 0, 2, and 4, respectively. 862 Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 Fig. 14. Contours of the Nu* distribution for staggered flags at ReW = 2:08  104 and Gc/W = 0.19: (a) Gy/W = 0; (b and c) Gy/W = 2, wall sides 1 and 2, respectively; (d and e) Gy/ W = 4, wall sides 1 and 2, respectively. Table 3 Heat transfer performance and friction characteristics of the staggered inverted flags for various Gy at Gc/W = 0.19. Fig. 15. Spanwise-averaged Nu* distribution of staggered flags for various Gy values at ReW = 2:08  104 . examined. The two flags periodically and synchronously flapped with the same phase for Gc/W = 0.19 at ReW = 2:08  104 ; however, the dimensionless flapping period increased to Dt* = 16.4, much longer than for the isolated single flag Dt* = 10.9. In contrast to the single flag with Gc/W = 0.19, an elevated maximum Nu* = 1.8 was recognized at Y* = 1 for the side-by-side flags with Gy/W Nu=Nu0 F/F0 g 0 2 4 1.30 1.29 1.24 2.78 2.61 2.47 0.93 0.94 0.91 Gc/W = 0.19. Although the global averaged Nusselt number ratio, Nu=Nu0 , rose to 1.30, the friction factor ratio, F/F0, simultaneously increased by 68%, which led to an overall downward trend in thermal enhancement efficiency of g = 0.93. As for Gc/W = 0.31, the two side-by-side flags were closer to each other, resulting in chaotic flapping motions: the two inverted flags alternated between a symmetric flapping motion toward both wall sides and an asymmetric flapping motion toward a single side.Nu=Nu0 = 1.22 was slightly augmented by 3% for the side-by-side flags with Gc/ W = 0.31; however, F/F0 was augmented by 70% due to the large blockage of the two flags, which eventually led to a significant decrease in thermal enhancement efficiency of g = 0.86. The two staggered flags’ coupling flapping behaviors were determined at ReW = 2:08  104 for Gy/W = 2 and 4. Unlike the side-by-side system, the oscillating dynamics of the staggered flags was similar to that of the single flag, i.e., with a comparable flapping period Dt* = 10.4 and amplitude A/L = 1.8. The maximum heat transfer enhancement Nu* = 1.9 was achieved at Y* = 2.75, which could be attributed to the concerted influence of two staggered Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863 flags for Gy/W = 2. The resultant thermal enhancement efficiency g = 0.94 was superior to g = 0.87, which was obtained by mounting tandem flags along the channel centerline [8]. This shows that placing flags close to the wall in a staggered configuration is more economical than the single flag and side-by-side double flag configurations. Conflict of interest The authors declare that they have no conflict of interest in relation to this study. Acknowledgments The authors gratefully acknowledge financial support for this study from the National Natural Science Foundation of China (11725209). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.048. References [1] J. Han, J.S. Park, Developing heat transfer in rectangular channels with rib turbulators, Int. J. Heat Mass Transf. 31 (1) (1988) 183–195. [2] G.J. VanFossen, Heat transfer coefficients for staggered arrays of short pin fins, ASME 1981 International Gas Turbine Conference and Products Show, American Society of Mechanical Engineers, 1981. [3] P. Ligrani, N. Burgess, S. Won, Nusselt numbers and flow structure on and above a shallow dimpled surface within a channel including effects of inlet turbulence intensity level, J. Turbomach. 127 (2) (2005) 321–330. [4] G.I. Mahmood, M.Z. Sabbagh, P.M. Ligrani, Heat transfer in a channel with dimples and protrusions on opposite walls, J. Thermophys. Heat Transf. 15 (3) (2001) 275–283. [5] H.-Y. Li, Y.-X. Wu, Heat transfer characteristics of pin-fin heat sinks cooled by dual piezoelectric fans, Int. J. Therm. Sci. 110 (2016) 26–35. [6] H. Ma, L. Tan, Y. Li, Investigation of a multiple piezoelectric–magnetic fan system embedded in a heat sink, Int. Commun. Heat Mass Transf. 59 (2014) 166–173. [7] D. Kim et al., Flapping dynamics of an inverted flag, J. Fluid Mech. 736 (2013). 863 [8] Y. Chen et al., Heat transfer enhancement of turbulent channel flow using tandem self-oscillating inverted flags, Phys. Fluids 30 (7) (2018) 075108. [9] J.B. Lee, S.G. Park, H.J. Sung, Heat transfer enhancement by asymmetrically clamped flexible flags in a channel flow, Int. J. Heat Mass Transf. 116 (2018) 1003–1015. [10] J.B. Lee et al., Heat transfer enhancement by flexible flags clamped vertically in a Poiseuille channel flow, Int. J. Heat Mass Transf. 107 (2017) 391–402. [11] Y. Jin et al., On the couple dynamics of wall-mounted flexible plates in tandem, J. Fluid Mech. 852 (2018). [12] K. Shoele, R. Mittal, Computational study of flow-induced vibration of a reed in a channel and effect on convective heat transfer, Phys. Fluids 26 (12) (2014) 127103. [13] Y. Yu, Y. Liu, Flapping dynamics of a piezoelectric membrane behind a circular cylinder, J. Fluids Struct. 55 (2015) 347–363. [14] M. Shelley, N. Vandenberghe, J. Zhang, Heavy flags undergo spontaneous oscillations in flowing water, Phys. Rev. Lett. 94 (9) (2005) 094302. [15] Y. Yu, Y. Liu, Y. Chen, Vortex dynamics behind a self-oscillating inverted flag placed in a channel flow: time-resolved particle image velocimetry measurements, Phys. Fluids 29 (12) (2017) 125104. [16] S.G. Park et al., Enhancement of heat transfer by a self-oscillating inverted flag in a Poiseuille channel flow, Int. J. Heat Mass Transf. 96 (2016) 362–370. [17] Y. Yu, Y. Liu, Y. Chen, Vortex dynamics and heat transfer behind self-oscillating inverted flags of various lengths in channel flow, Phys. Fluids 30 (4) (2018) 045104. [18] C. Huertas-Cerdeira, B. Fan, M. Gharib, Coupled motion of two side-by-side inverted flags, J. Fluids Struct. 76 (2018) 527–535. [19] J. Ryu, S.G. Park, H.J. Sung, Flapping dynamics of inverted flags in a side-by-side arrangement, Int. J. Heat Fluid Flow 70 (2018) 131–140. [20] H. Huang, H. Wei, X.-Y. Lu, Coupling performance of tandem flexible inverted flags in a uniform flow, J. Fluid Mech. 837 (2018) 461–476. [21] T. Liu, Pressure-and Temperature-Sensitive Paints, Wiley Online Library, 2005. [22] C. He et al., Measurement of flow structures and heat transfer behind a wallproximity square rib using TSP, PIV and split-fiber film, Exp. Fluids 57 (11) (2016) 165. [23] D. Peng et al., Simultaneous PSP and TSP measurements of transient flow in a long-duration hypersonic tunnel, Exp. Fluids 57 (12) (2016) 188. [24] Z. Ghorbani-Tari, Y. Chen, Y. Liu, End-wall heat transfer of a rectangular bluff body at different heights: temperature-sensitive paint measurement and computational fluid dynamics, Appl. Therm. Eng. 122 (2017) 697–705. [25] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1) (1988) 3–17. [26] J. Ryu et al., Flapping dynamics of an inverted flag in a uniform flow, J. Fluids Struct. 57 (2015) 159–169. [27] P. Promvonge, C. Thianpong, Thermal performance assessment of turbulent channel flows over different shaped ribs, Int. Commun. Heat Mass Transf. 35 (10) (2008) 1327–1334. [28] R.K.B. Gallegos, R.N. Sharma, Flags as vortex generators for heat transfer enhancement: gaps and challenges, Renew. Sustain. Energy Rev. 76 (2017) 950–962. International Journal of Heat and Mass Transfer 136 (2019) 597–609 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Heat transfer enhancement in microchannel heat sink with bidirectional rib Guilian Wang a,⇑, Nan Qian a, Guifu Ding b a b School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai 201620, People’s Republic of China National Key Laboratory of Science and Technology on Micro/Nano Fabrication, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China a r t i c l e i n f o Article history: Received 10 September 2018 Received in revised form 25 January 2019 Accepted 9 February 2019 Keywords: Bidirectional rib Microchannel Heat transfer Pressure drop a b s t r a c t The heat transfer and flow characteristics of the microchannel heat sink (MCHS) with bidirectional ribs (BRs) are experimentally and numerically studied in the present paper. The BR, composed of vertical rib (VR) and spanwise rib (SR), can interrupt the thermal boundary layer and induce recirculation in both vertical and spanwise directions. Its cooling effectiveness is compared with that of the widely-used VR and SR for the Reynolds number ranged from 100 to 1000. The results show that the Nussalt number of the microchannel with BRs (BR-MC) is up to 1.4–2 and 1.2–1.42 times those of microchannels with VRs (VR-MC) and SRs (SR-MC), respectively. This implies that the BR can strengthen the heat transfer more sufficiently. Meanwhile, the utilizing of BR gives rise to the larger pressure drop penalty due to its broader obstruction areas. In addition, the higher relative rib height of VR (eVR) and relative rib width of SR (eSR) are revealed to enhance the heat transfer but induce pressure drop in the BR-MC. The thermal enhancement factor can keep larger than 1 when eVR < 0.316 and 0.026 < eSR < 0.357. Ó 2019 Published by Elsevier Ltd. 1. Introduction The inexorable miniaturization and high speed operation of electronic devices have resulted in a tremendous increase in power density, which will cause huge amount of heat in electronic devices. To avoid heat accumulation and preserve their component lifespan and reliability, many powerful heat dissipation methods have been developed till now which include microchannel heat sink (MCHS), jet impingement, sprays, heat pipes, piezoelectrically driven droplets, etc. [1–5]. Among these techniques, MCHS is the most practical choice due to its favorable and attractive features such as light weight, compactness and high heat transfer area to volume ratio [6–11]. The water-cooled microchannel technology was proposed initiatively by Tuckerman and Pease [12]. They demonstrated that a heat flux as high as 790 W/cm2 can be removed with a maximum substrate temperature rise of 71 °C. Although high thermal performance can be achieved by using MCHS, several techniques, such as nanofluid, surface area increase and thermal boundary layer redeveloping, have been proposed to promote the heat transfer with the escalating thermal demands of electronic devices. Arani et al. [13] numerically investigated water/single-wall carbon nanotubes nanofluid in a double layered MCHS. They concluded that the increase of nanoparticle volume ⇑ Corresponding author. E-mail address: wglwrc2016@126.com (G. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.018 0017-9310/Ó 2019 Published by Elsevier Ltd. fraction causes an increment of the Nusselt number but pressure drop augmentation. Hung et al. [14] investigated the hydraulic and thermal performances of the porous-MCHSs with different configuration designs. They found that porous microchannels can improve the cooling performance due to the surface area increase. Xu et al. [15] studied experimentally and numerically the hydrothermal characteristics of silicon MCHS which consists of ten parallel triangular microchannels separated by five transverse trapezoidal microchannels. They found that the proposed MCHS can decrease the temperature by 14 °C compared with the conventional MCHS. The results demonstrated that the redeveloping of thermal boundary layer has a significant effect on improving the heat transfer in the MCHS. Based on the thermal boundary layer redeveloping mechanism, some researchers proposed the MCHS with variable cross-sections, fins, grooves or ribs. Chai et al. [16] numerically and experimentally investigated the fluid flow and heat transfer in MCHS with periodic expansion–constriction cross-sections. The results show that the expansion–constriction cross-sections provide a significant influence on the heat transfer. Shafeie et al. [17] performed detailed numerical study of the MCHS with different height of micro pin fins. It was shown that the finned microchannels have better heat transfer performance than the smooth microchannels at the same pumping power. Moreover, the finned case with highest fin depth (500 mm) had the highest heat removal among studied finned heat sinks. Ahmed et al. [18] investigated numerically 598 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 Nomenclature A Cp Dh f h l _ m N Nu P p Q q DT T t u area, m2 specific heat, J kg1 K1 hydrodynamic diameter, m frictional factor heat transfer coefficient, W m2 K1 length, m mass flow rate, kg s1 the number of microchannels in heat sink Nusselt number pitch of the rib, m pressure, Pa total heat transfer, W heat flux, W m2 temperature difference, K temperature, K thickness, m velocity, m s1 the MCHS with triangular, trapezoidal and rectangular grooves. They found that there was a significant enhancement in heat transfer using grooved microchannels, and the ones with trapezoidal groove can provide the highest Nusselt number enhancement of 51.59%. The ribs, also called roughness elements or turbulators, have been extensively studied and widely used due to their marked effect on the heat transfer enhancement. Chai et al. [19] investigated the pressure drop and heat transfer characteristics of the interrupted MCHS with rectangular ribs. Compared with interrupted microchannel without rectangular ribs and smooth microchannel, the interrupted one with rectangular ribs can provide the higher heat transfer enhancement factor. Desrues er al. [20] conducted numerical simulations to study the thermal performance of the microchannels with alternated vertical ribs and found that the proposed microchannels with VRs can provide a higher Nusselt number than the smooth ones. Jiang et al. [21] carried out experimental and numerical studies to investigate the flow and heat transfer characteristics of mist/steam two-phase flow in the channel with 60 deg spanwise ribs. They showed that ribs mounted on the sidewalls could lead to secondary flows and then improved the heat transfer characteristics. Xie et al. [22] performed an experimental study for heat transfer enhancement in a MCHS with various vertical crescent ribs protruded from the bottom wall. It was found that the ribs can improve the heat transfer performance by generating vortices. Xia et al. [23] computationally investigated the hydrothermal performance of MCHS with spanwise cavities and ribs. The results showed that Nusselt number for the MCHS with spanwise cavities and ribs increased about 1.3–3 times more than the rectangular microchannel, while the apparent friction factor increased about 6.5 times more. Although thermal performance enhancement in MCHS can be achieved by using ribs, high pressure drop is also induced due to high-flow disturbances and blocking-flow effect. Therefore, the geometry and arrangement of ribs should be optimized to tradeoff between the enhanced heat transfer and the pressure drop penalty. Ghani et al. [24] proposed a new configuration of MCSH with sinusoidal cavities and ribs, and investigated numerically its geometric parameters on hydrothermal performance. The results showed that the microchannel with relative cavity amplitude of 0.15, relative rib width of 0.3 and relative rib length of 0.5 yielded the best overall performance with Pf = 1.85 at Re = 800. Akbari et al.  u w mean flow velocity, m s1 width, m Greek symbols l dynamic viscosity, Pa s q density, kg m3 k thermal conductivity, W m1 K1 Subscripts c microchannel f fluid in inlet out outlet r rib s smooth microchannel w wall [25] performed a numerical analysis of heat transfer and flow characteristics of MCHS with different rib height. They found that the heat transfer rate can be enhanced by increasing the rib height, volumetric percentage of nanoparticles and Reynolds number. However, the existence of ribs causes an increase in the average friction factor. Wang et al. [26] also conducted parameters optimization of the slant rectangular ribs in the MCHS by comprehensive consideration of heat transfer and pressure drop. The optimization results showed that the MCHS with the slant rectangular ribs have the best thermal performance with the attack angles of 52.5°, the relative height of 0.3, the relative length of 1 and the relative width of 0.1, respectively. Many other researches are focused on the effect of rib’s cross sectional shape on hydrothermal performance of MCHS. Chai et al. [27] studied numerically the heat transfer of the MCHS with rectangular, backward triangular, isosceles triangular, forward triangular and semicircular ribs. The results revealed that the forward triangular ribs can induce the largest Nusselt number in the microchannel. Meanwhile, the one with semicircular offset ribs brings about the best overall thermal performance. Moon et al. [28] also conducted a numerical investigation to analyze the effect of cross-sectional rib shapes on the heat transfer and friction loss performances. Among the considered sixteen rib shapes, the boot-shaped rib gave the best heat transfer performance with an average friction loss performance. Gholami et al. [29] investigated the effect of rectangular, oval, parabolic, triangular and trapezoidal ribs on the forced flow and heat transfer of the MCHS. The results indicated that the parabolic rib had the best proportion of Nusselt number enhancement comparing to the augmentation of the friction factor. From the review of the available literature on thermal performance in the microchannel roughened with VRs and SRs, it is clear that VRs and SRs both can improve the heat transfer characteristic by disturbing the thermal boundary layers and inducing the recirculation for the mixing of hot and cold fluids. However, the disturbed thermal boundary layers and induced recirculation are only in the vertical or spanwise direction. Therefore, the heat transfer enhancement by the VRs and SRs is restricted in single direction, which is insufficient for improving the heat transfer ability of MCHS. In this paper, a new type of rib called ‘‘bidirectional rib (BR)”, composed of VR and SR, is proposed to interrupt the thermal boundary layers and induce the recirculation in both vertical and 599 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 spanwise directions, and further intensify thermal transfer enhancement. 2. Problem statement and numerical methods 2.1. Physical models A novel MCHS with BRs consists of two parts as shown in Fig. 1 (a): a cover with VR-roughened microchannels; a substrate with the SR-roughened microchannels. The VRs part contained in BRs are in-line distributed on the bottom surface of the cover and the SRs part are in staggered arrangement on the sidewalls. When the fluid flows through the BRs, the VRs part can improve the uniformity of the temperature and flow fields in the vertical direction. At the same time, the temperature and flow fields in the spanwise direction can be improved by the SRs part. The geometry dimension of the proposed MCHS with BRs is 21 mm  11.9 mm  1.5 mm (L  W  H). The main structural parameters of the designed structure are shown in Table 1. Considering that the designed MCHS is a periodic structure, only single-branch microchannel is selected as the computational domain to reflect the flow and heat transfer characteristics, as shown in Fig. 2(a). In order to study the effect of rib geometry on the fluid flow and heat transfer, other two relevant geometries, the microchannel only with VRs (VR-MC) and the microchannel only with SRs (SR-MC), are also considered in the present study, as shown in Fig. 2(b–c). 2.2. Governing equations and boundary conditions The commercial FluentTM software is used to simulate the solidfluid conjugate heat transfer process for different ribbed cases, which can provide us a convenient and precise method for evaluating the heat transfer and flow characteristics. Meanwhile, the following assumptions are made to simplify the analysis: (1) Radiation, gravitational force, viscous dissipation and thermal contact resistance between components are neglected; (2) The solid and fluid properties are constant; (3) The fluid flow is steady and incompressible, and laminar flow prevails across the microchannels. According to the aforesaid assumptions, the basic governing equations can be written as follows: Continuity equation: r  ðquÞ ¼ 0 ð1Þ Momentum equation: ðu  rÞqu ¼ rp þ lr2 u ð2Þ Energy equation: u  rT ¼ k qC p r2 T ð3Þ Energy equation in the solid domain is given by: kr2 T ¼ 0 ð4Þ where q is water density, u is the velocity at the inlet of the microchannel, p is pressure, Cp is the specific heat of the water, l is the dynamic viscosity, and k is the thermal conductivity of water. The symmetric boundary conditions are applied onto the symmetric surface of model. Uniform velocity with different values and constant temperature (Tin = 293 K) is applied in the inlet of the microchannel. At the exit, a pressure outlet boundary condition is specified with a fixed pressure of 1.013  105 Pa. A uniform constant heat flux of q = 100 W/cm2 is applied on the top surface. The bottom surface has the assumed natural convection heat transfer Fig. 1. Schematic of (a) the MCHS with BRs and (b) BR geometry. Table 1 Microchannel geometry details. Parameter hc lc wc hVR wVR lVR hSR wSR lSR P tw Values (lm) 500 10,000 450 150 450 100 350 150 100 1000 175 600 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 Fig.3. The structured grid of ribbed passage in BR. The Reynolds number (Re) is defined as:  Re ¼ q u Dh =l ð5Þ  is mean velocity, Dh is the hydraulic diameter of the where u microchannel and it is calculated as: Dh ¼ 2wc hc =ðwc þ hc Þ Fig. 2. Schematic of single-branch microchannels with (a) BRs, (b) VRs, and (c) SRs. coefficient of 10 W/m2 K since it is exposed in the air environment [30]. The aforesaid mass, momentum and energy governing equations are solved using the standard pressure and second-order upwind discretization scheme. The SIMPLE algorithm is employed for pressure velocity coupling to achieve the stability of solution convergence, and the convergence criteria of 10-6 for continuity and 10-8 for the energy equation are used in the numerical solution. 2.3. Grid independence study To ensure the high accuracy of simulation results, every model adopts hexahedral elements generated by ANSYS ICEM CFD 14.5. As shown in the Fig. 3, fine mesh is concentrated near the wall region to resolve the large velocity gradient and thermal boundary layer, while the grid in the other parts is relatively sparse. To this end, the height of the first layer elements adjacent to the solid walls is set to be small enough to ensure a dimensionless wall distance (y+) less than 1.0. To verify the mesh independence, four grid systems separately with 340,210 elements, 633,714 elements 1,206,609 and 2,301,476 elements are generated in the BR-MC case and then the Nusselt number and friction factor are compared with different grid systems. The test results of the Nusselt number, friction factor and their relative error between the finest grids and other grids are shown in Table 2. It is found that the Nusselt number and friction factor with the third grid system differ from those with the fourth one by 300, the rate of decreasing in the apparent friction factor is not distinct due to the prominent blocking effect of ribs. Fig. 7. The Nusselt number as a function of Reynolds number for all ribbed microchannels. Fig. 8. The normalized Nusselt number as a function of Reynolds number for all ribbed microchannels. Table 3 Uncertainties for different parameters involved in the experimental tests. Parameters Uncertainty (%) Parameters Uncertainty (%) Dh A L Tout- Tin Twall _ m 0.69 0.1 0.2 2 2 0.98 4p Re 0.98 1.79 2.1 4.89 5.93 6.75 s Nu f g 3.3. Uncertainty analysis An uncertainty analysis was carried out to give some quantitative description of the validity of test data. The uncertainties asso_ were ciated with direct measured parameters (W, H, L, T, P and m) obtained from the manufacturers’ specification sheets. While the uncertainties of the calculated values (Dh, A, Tout, Tin, 4p, Re, Nu, f, s and h) were determined using standard error analysis [32]. Their maximum uncertainties are all listed in Table 3. 4. Results and discussions In this section, the average Nusselt numbers and apparent friction factor for all ribbed cases are measured and predicted with the Reynolds number varying from 100 to 1000. Detailed discussion has been provided for the mechanisms of different ribs on modification of heat transfer and flow characteristics. Thereafter, the effects of relative rib height of VR (eVR) and relative rib width of SR (eSR) on hydrothermal performance are elucidated. 4.1. Overall heat transfer and pressure drop characteristics 604 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 Fig. 9. The apparent friction factor as a function of Reynolds number for all ribbed microchannels. 4.2. Flow field and heat transfer mechanisms In order to deeply understand the underlying mechanisms of the heat transfer and pressure drop characteristics among the three considered configurations, streamlines in the 3D microchannel model are presented and discussed in this section, as shown in Fig. 10. When the fluid passes over the VRs in the microchannel, partial fluid is deflected to the vertical wall and then a large recirculation is created behind the VR, as shown in the Fig. 10(a). With the existence of the recirculation, the cold fluid at the center of microchannel is mixed with the hotter fluid closed to the vertical walls, which can produce a larger thermal difference between wall and coolant. At the same time, the thermal boundary layer closed to the vertical wall is disturbed and then redeveloped between the two adjacent VRs. However, the flow streamlines in the spanwise direction, except for the ones closing to the VR, are approximately paralleled with the streamwise. For SR-MC, the flow streamlines are forcing to deflect in the spanwise direction and recirculation is generated behind the SRs. Therefore, the interruption of thermal boundary layer and fluid mixing occur near the spanwise walls. In comparison with the VR and SR, the BR provides a larger recirculation flow occupying most flow region in the microchannel, which indicates more cool fluid in the mainstream region is mixed with hotter fluid. As shown in the Fig. 10(c), it firstly flows towards the heating cover due to the VR part and then turns to the ribbed sidewall as result of SR part. The two deflections make the thermal boundary layers near the vertical and spanwise walls redevelop. Due to the successive distribution of the BRs, the thermal boundary layers will be interrupted again before they are fully developed. Thus, most thermal boundary layers in the BR-MC are in the developing state. This is main reason that the heat transfer efficiency of Fig. 10. Streamlines for microchannels with (a) VRs, (b) SRs and (c) BRs between the fifth and seventh ribs at Re = 500 in 3D microchannel structure. G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 BR-MC is better than those of VR-MC and SR-MC, shown in the Figs. 7 and 8. Meanwhile, the 2D cross-sectional streamlines are also displayed to explore the flow field and heat transfer mechanisms. Fig. 11 displays the streamlines on the y-z cross section of x = 0.3125 mm (left) and x-y cross section of z = 0.9 mm (right) at Re = 500, selected between the fifth and sixth ribs of the test section. Apparently, the introduction of VR, SR and BR all induces recirculation flow in the microchannels. In Fig. 11(a), the VR can induce a large recirculation flow between two adjacent VRs on the y-z cross section, which disturbs the thermal boundary layer in vertical direction and causes the fluid under the cover exchanges with the mainstream. On the other x-y cross section, the streamlines are flat, which indicates no distinct secondary flow structure in the spanwise. On the contrary, the SRs can induce two recirculation flow on the x-y cross section, while there is no recirculation flow on the y-z cross section. As shown in Fig. 11(b), one small recirculation flow occurs at the leading bottom corner of the rib and the other large recirculation flow is located between the two adjacent ribs. Therefore, the VRs and SRs only generate recirculation flow and disturb the thermal boundary in the vertical and spanwise direction, respectively. However, no obvious flow structure change emerges in the other direction. For BR-MC, recirculation flow can be observed on both y-z and x-y cross sections, as shown in Fig. 11(c). On the y-z cross section, two small recirculations are located on the trailing of VR and one relatively larger recirculation happens between two ribs. At the same time, a large scale recirculation flow and a small recirculation flow can be observed on the x-y cross section, and their positions and shapes are similar to those in the SR-MC. With the generated 605 recirculations in multi direction, the temperature field is more uniform and the temperature difference between the wall and coolant is smaller, which can improve convective heat transfer in the microchannel. However, owing to the bidirectional distribution of the BR, the cross-section area is larger than those of the SR-MC and VR-MC, which leads to a decrease in the flow area and thus a higher pressure drop. Fig. 12 shows the detailed temperature field distribution between the fifth and sixth ribs on central cross sections (x = 0.3125 mm, y = 5.55 mm, z = 0.9 mm) for three ribbed microchannels at Re = 500. The temperature field distributions for all cases possess the same temperature level number. For VR-MC, as shown in Fig. 12(a), there exists obvious boundary between recirculation region and main stream. In the recirculation region, the temperature field presents uniform temperature and small gradient toward the heated cover due to the recirculation flow shown in Figs. 10(a) and 11(a). However, the thermal contour lines near the other walls are still dense. These imply that the VRs destroy the thermal boundary layer near the top wall and improve the temperature uniformity in the vertical direction. For SR-MC, in terms of temperature contour as revealed in Fig. 12(b), the temperature contour lines near the ribbed sidewalls are sparser compared with those close to the other walls. Therefore, the VRs and SRs only reduce the thermal boundary layer thickness in the corresponding ribbed direction. Compared with the VR-MC and SR-MC, the temperature contour lines in the BR-MC are sparse in the whole flow field and the temperature distribution is more uniform, as shown in Fig. 12(c). This indicates that the BRs can make the thermal boundary layer thinner in both vertical and spanwise direction and induce the greater temperature difference between walls and Fig. 11. Cross-sectional streamlines at x = 0.3125 mm (left) and z = 0.9 mm (right) between the fifth and sixth ribs for (a) VR-MC, (b)SR-MC and (c) BR-MC at Re = 500. 606 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 Fig. 12. Temperature field distribution between the fifth rib and sixth rib on center cross sections (x = 0.3125 mm, y = 5.55 mm, z = 0.9 mm) for (a) VR-MC, (b) SR-MC and (c) BR-MC at Re = 500. coolant, which is advantageous to transport heat away from the wall and will bring about more heat transfer enhancement. Heat transfer on the four walls of three ribbed microchannels has been demonstrated in terms of local Nusselt number (Nux), as shown in Fig. 13. Apparently, the local Nusselt numbers on four walls of three ribbed microchannels all display the cycle behavior between two adjacent ribs. Moreover, the local Nusselt numbers of BR-MC are all larger than those of the VR-MC and SR-MC. This indicates that the BRs provide the higher convective heat transfer enhancement as a result of the thinner thermal boundary layers, as observed in Fig. 12. For VR-MC and SR-MC, the periodic higher heat transfer appears at the leading of the ribs due to the impingement of coolant, while the deceleration downstream of the rib due to sudden expansion leads to a lower heat transfer on the trailing of ribs. This trend is also observed for the BR-MC. In addition, a higher heat transfer in the BR-MC is observed on the non-ribbed sidewalls near the VR part, which is aroused by the impingement and acceleration of the flow, respectively. 4.3. Effects of relative rib height of VR (eVR) and relative rib width of SR (eSR) on hydrothermal performance According to the prior results, it can be concluded that the BRMC significantly outperforms VR-MC and SR-MC with respect to heat transfer performance. The next step of the present study is aimed at analyzing the effects of rib geometry on the thermalhydraulic performance of BR-MC. The selected main geometry parameters, relative rib height of VR (eVR) and relative rib width G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 607 Fig. 13. Contours of local Nusselt number on (a) top wall, (b) left wall, (c) right wall and (d) bottom wall of the considered cases at Re = 500. of SR (eSR), are defined as the ratio of the VR height to the microchannel height (eVR = hVR/hc) and the SR width to the microchannel width (eSR = wSR/wc), respectively. The hVR and wSR are in the range of 0–200 lm, whereas the other geometric parameters of BR are kept constant as listed in Table 1. Fig. 14 depicts the variation of Nusselt number with eSR and eVR for BR-MC at Re = 500. The figure shows that the Nusselt number both continuously increases with the increment of eSR and eVR. When eSR = 0.45 and eVR = 0.4, the Nusselt numbers can reach 12.05 and 11.88, respectively. With the larger eSR and eVR, the more volume of cooling fluid is involved in mixing in each redeveloping zone. Besides, the enlargement in eSR and eVR promotes jet impingement and enlarges the surface area. All these factors are contributing to the heat transfer enhancement. In addition, the results with eSR = 0 and eVR = 0 once again confirm that the BR can provide more sufficient heat transfer enhancement in comparison with SR and VR. The effects of eSR and eVR on the apparent friction factor are seen from Fig. 15. It is obvious that the apparent friction factor both increases continuously with the increasing of eSR and eVR for the Fig. 14. Variation of average Nusselt number with eSR and eVR for BR-MC at Re = 500. (Correlation with eSR: Nu = 5.06648 + 19.29044eSR  9.25658eSR2, error < 3.28%; correlation with eVR , Nu = 7.00058 + 13.83435eSR 5.96057eSR2, error < 5.94%.) 608 G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 5. Conclusion The hydrothermal performance of MCHS with BRs has been studied experimentally and numerically, and compared with those with relevant rib geometries such as VRs and SRs. Mechanisms underlying the heat transfer enhancement by BRs are clarified in detail. Furthermore, the effects of eVR and eSR on heat transfer and flow performance are discussed. The main conclusions can be made as follows: Fig. 15. Variation of average friction factor with eSR and eVR for BR-MC at Re = 500. (Correlation with eSR: f = 0.11544–0.67269eSR + 6.92454eSR2, error < 10.1%; correlation with eVR: f ¼ 0:12525eeSR =0:18815 þ 0:02525, error < 5.2%.) entire Reynolds numbers. When eSR = 0.45 and eVR = 0.4, the apparent friction factor are 13.6 and 6.6 times of the ones at eSR = 0 and eVR = 0, respectively. According to the Fig. 9, the reduction of crosssection area of fluid flow leads to an increment of apparent friction factor. Similarly, the increasing of eSR and eVR also make the crosssection area shrink and then block the fluid flow. This is the reason that the pressure drop significantly increases with the increment of the eSR and eVR. Therefore, the eSR and eVR cannot be too large because they will induce much more pressure drop and weaken the thermal performance. According to the results with eSR = 0 and eVR = 0, it is proved that the apparent friction factor in the BR-MC is higher than SR-MC and VR-MC as result of the combined barrier effect of SR and VR in the microchannel. Fig. 16 shows the thermal enhancement factor as a function of eSR and eVR for BR-MC at Re = 500. The thermal enhancement factor firstly increases dramatically and then decreases as eSR and eVR increase. The eVR = 0.15 and eSR = 0.17 introduce the maximal thermal enhancement factor of 1.19 and 1.16, respectively. When eVR < 0.316 and 0.026 < eSR < 0.357, the thermal enhancement factor is all larger than unity. This implies that the BR-MC possess high heat transfer enhancement which can offset the pressure drop penalties caused by the BRs. While the thermal enhancement factor is smaller than unity when eVR > 0.316 and eSR > 0.357. This is because the increase of eVR and eSR causes a more significant increment in the pressure drop penalty than the heat transfer enhancement. Owing to the serious pressure drop, the BR-MC loses its advantages as an effective heat transfer enhancement method. Fig. 16. The thermal enhancement factor as a function of eSR and eVR at Re = 500. (1) With the same mass flow rate, the Nusselt number of the BRMC is nearly 1.2–1.42 times and1.4–2 times those of VR-MC and SR-MC, which means that the heat transfer enhancement ability of BR is better than VR and SR. (2) For all ribbed microchannels, the apparent friction factor all increases with the rise of Reynolds number. The utilizing of the BRs in the microchannel causes the highest apparent friction factor which attributes to the more prominent blocking effect. (3) The BRs provide the higher heat transfer by interrupting thermal boundary layer and inducing the recirculation in both vertical and spanwise directions. Therefore, the local Nusselt number of four walls in BR-MC is kept to be highest. (4) For BR-MC, the rises of eVR and eSR both can improve the heat transfer but increase the apparent friction factor. Taking the heat transfer and pressure drop into account concurrently, the BRs with eVR < 0.316 and 0.026 < eSR < 0.035 can provide the thermal enhancement factor values above than 1. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgements This research has been sponsored by the Young Foundation of shanghai, China (ZZGCD16004), the National Natural Science Foundation of China (No. 51605277, No. 61803254 and No. 61601296). References [1] G. Wang, D. Niu, F. Xie, Y. Wang, X. Zhao, G. Ding, Experimental and numerical investigation of a microchannel heat sink (MCHS) with micro-scale ribs and grooves for chip cooling, Appl. Therm. Eng. 85 (2015) 61–70. [2] C. Mira-Hernandez, M.D. Clark, J.A. Weibel, S.V. Garimella, Development and validation of a semi-empirical model for two-phase heat transfer from arrays of impinging jets, Int. J. Heat Mass Transf. 124 (2018) 782–793. [3] D.Y. Yeo, H.C. No, Modeling film boiling within chimney-structured porous media and heat pipes, Int. J. Heat Mass Transf. 124 (2018) 576–585. [4] S.P. Aly, A.F.M. Arif, K.S. Al-Athel, J. Mostaghimi, S.M. Zubair, Performance of open pore metal foam heat sinks fabricated with thermally sprayed interface, Appl. Therm. Eng. 105 (2016) 411–424. [5] Y.M. Yu, T.W. Simon, M. Zhang, T. Yeom, M.T. North, T.H. Cui, Enhancing heat transfer in air-cooled heat sinks using piezoelectrically-driven agitators and synthetic jets, Int. J. Heat Mass Transf. 68 (2014) 184–193. [6] A. Ghahremannezhad, K. Vafai, Thermal and hydraulic performance enhancement of microchannel heat sinks utilizing porous substrates, Int. J. Heat Mass Transf. 122 (2018) 1313–1326. [7] T.M. Harms, M.J. Kazmierczak, F.M. Gerner, Developing convective heat transfer in deep rectangular microchannels, Int. J. Heat Fluid Flow 20 (2) (1999) 149–157. [8] S. Lu, A comparative analysis of innovative microchannel heat sinks for electronic cooling, Int. Commun. Heat Mass Transf. 76 (2016) 271–284. [9] J. Ryu, D.H. Choi, S.J. Kim, Numerical optimization of the thermal performance of a microchannel heat sink, Int. J. Heat Mass Transf. 45 (13) (2002) 2823– 2827. [10] C.J. Ho, P.-C. Chang, W.-M. Yan, P. Amani, Thermal and hydrodynamic characteristics of divergent rectangular minichannel heat sinks, Int. J. Heat Mass Transf. 122 (2018) 264–274. [11] Z. Yang, J. Shi, J. Yao, X. Zhang, G. Ding, X. Zhao, A laterally driven MEMS inertial switch with double-layer suspended springs for improving single-axis sensitivity, IEEE Trans. Compo. Packag. Manuf. Technol. 8 (10) (2018) 1845– 1854. G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609 [12] D.B. Tuckerman, R.F. Pease, High-performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (5) (1981) 126–129. [13] A.A.A. Arani, O.A. Akbari, M.R. Safaei, A. Marzban, A.A.A.A. Alrashed, G.R. Ahmadi, T.K. Nguyen, Heat transfer improvement of water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double-layered microchannel heat sink, Int. J. Heat Mass Transf. 113 (2017) 780–795. [14] T.-C. Hung, Y.-X. Huang, W.-M. Yan, Thermal performance analysis of porousmicrochannel heat sinks with different configuration designs, Int. J. Heat Mass Transf. 66 (2013) 235–243. [15] J.L. Xu, Y.H. Gan, D.C. Zhang, X.H. Li, Microscale heat transfer enhancement using thermal boundary layer redeveloping concept, Int. J. Heat Mass Transf. 48 (9) (2005) 1662–1674. [16] L. Chai, G. Xia, L. Wang, M. Zhou, Z. Cui, Heat transfer enhancement in microchannel heat sinks with periodic expansion–constriction cross-sections, Int. J. Heat Mass Transf. 62 (2013) 741–751. [17] H. Shafeie, O. Abouali, K. Jafarpur, G. Ahmadi, Numerical study of heat transfer performance of single-phase heat sinks with micro pin-fin structures, Appl. Therm. Eng. 58 (1–2) (2013) 68–76. [18] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, Int. Commun. Heat Mass Transf. 66 (2015) 47–57. [19] L. Chai, G. Xia, M. Zhou, J. Li, J. Qi, Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers, Appl. Therm. Eng. 51 (1–2) (2013) 880–889. [20] T. Desrues, P. Marty, J.F. Fourmigué, Numerical prediction of heat transfer and pressure drop in three-dimensional channels with alternated opposed ribs, Appl. Therm. Eng. 45–46 (2012) 52–63. [21] G. Jiang, X. Shi, G. Chen, J. Gao, Study on flow and heat transfer characteristics of the mist/steam two-phase flow in rectangular channels with 60 deg. ribs, Int. J. Heat Mass Transf. 120 (2018) 1101–1117. [22] G. Xie, X. Liu, H. Yan, J. Qin, Turbulent flow characteristics and heat transfer enhancement in a square channel with various crescent ribs on one wall, Int. J. Heat Mass Transf. 115 (2017) 283–295. 609 [23] G. Xia, Y. Zhai, Z. Cui, Numerical investigation of thermal enhancement in a micro heat sink with fan-shaped reentrant cavities and internal ribs, Appl. Therm. Eng. 58 (1–2) (2013) 52–60. [24] I.A. Ghani, N. Kamaruzaman, N.A.C. Sidik, Heat transfer augmentation in a microchannel heat sink with sinusoidal cavities and rectangular ribs, Int. J. Heat Mass Transf. 108 (2017) 1969–1981. [25] O.A. Akbari, D. Toghraie, A. Karimipour, M.R. Safaei, M. Goodarzi, H. Alipour, M. Dahari, Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al2O3 nanofluid in a rib-microchannel, Appl. Math. Comput. 290 (2016) 135–153. [26] R.-J. Wang, J.-W. Wang, B.-Q. Lijin...
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RESEARCH INNOVATIONS ENERGY AND MASS TRANSPORT

RESEARCH INNOVATIONS AND APPLICATIONS IN ENERGY AND MASS
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Heat transfer enhancement in Microchannel heat sink
The use of electronic devices hits new highs with every dawn with almost every activity
on our planet incorporating electronic technology to not only improve output efficiency but also
reduce operating costs. Due to their high speed of operation, electronic devices result in a
tremendous increase in power density which causes huge amounts of heat (Wang, Qian and Ding
2019). While the previous version of technologies like Microchannel heat sinks (MCHS) has
been efficient there is a need to improve their operation to meet the high cooling demand of
extremely fast electronic devices.
In light of this, Microchannel heat sinks have attractive features like the lightweight,
compactness and high heat transfer area to volume ratio whereby it employs water-cooling
technology where a heat flux as high as 790w/cm2 can be re...


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