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Comparison of hydrothermal performance between plate fins and plate-pin fins subject to nanofluid-cooled corrugated miniature heat sinks
MR-12275; No of Pages 13 Microelectronics Reliability xxx (2017) xxx–xxx
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Comparison of hydrothermal performance between plate fins and plate-pin fins subject to nanofluid-cooled corrugated miniature heat sinks M. Khoshvaght-Aliabadi a,⁎, S.M. Hassani b, S.H. Mazloumi b a b
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University, Mashhad, Iran
a r t i c l e
i n f o
Article history: Received 15 October 2016 Received in revised form 10 January 2017 Accepted 10 January 2017 Available online xxxx Keywords: Corrugated miniature heat sink Corrugation shape Nanofluid Plate fin Plate-pin fin
a b s t r a c t Thermal and hydraulic performances of two types of fin, namely plate and plate-pin, in water-cooled corrugated miniature heat sinks (MHSs) having triangular, trapezoidal, and sinusoidal shapes are evaluated. In fact, the plate-pin fins are designed and constructed based on the plate fins. Experiments are performed on the fabricated corrugated MHSs in range of Reynolds number between 100 and 900. Temperature contours and velocity vectors are also studied numerically using a CFD approach. The numerical results are validated with recorded experimental data in the present and previous studies. In addition to water, the Al2O3/water nanofluid is also testes in the corrugated MHSs, as nanofluid-cooled corrugated MHSs. The obtained results show that the thermal performance of a corrugated MHS with plate-pin fins is better than that of a corrugated MHS with plate fins. Another obvious advantage of plate-pin fins is that designers can reduce the pressure drop (or pumping power) in the corrugated MHSs for the same heat dissipation. The maximum hydrothermal performance factor of 1.84 is detected for 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Water-cooled miniature heat sinks (MHSs) are efficient equipment in thermal management of electronic or mechanical devices. They are often 4–5 times more efficient compared to air-cooled types. Plate, pin, and plate-pin shapes are three common types of fins which are widely used in the MHSs (Fig. 1). The plate fins are easy to fabricate and have simple structure and low cost while the pin fins provide better hydrothermal performance with higher production cost. In modern electronic or mechanical devices, a powerful thermal management system is required, especially in harsh operating conditions such as high heat fluxes. The technique to improve the thermal performance and solve the hot point is referred to heat transfer enhancement. Generally, the heat transfer enhancement in the MHSs can be carried out either by modifications of surface geometry and fluid property. Some previous studies tried to modify the surface geometry of water-cooled MHSs [1–5]. In addition to water which still has extensive applications, another type of coolant, namely nanofluid, was considered in recent years by researchers [6–10]. However, because of relatively new history of nanofluid-cooled MHSs with modified geometries, the number of researches on this topic is very scarce.
⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (M. Khoshvaght-Aliabadi).
Flow and heat transfer behaviors of CuO/water and Al2O3/water nanofluids inside the pin-fin MHSs were studied numerically [11]. It was reported that the performance of MHSs enhanced as the nanofluids were replaced with the base fluid. Also, decreasing the diameter of Al2O3 nanoparticles in the base fluid increased Nusselt number values while the trend was reverse for CuO nanoparticles. In the other numerical study [12], the performances of Al2O3, CuO, and SiO2 nanoparticles as additives in water flowing in an interrupted MHS were evaluated. It was detected that the interrupted MHS had higher values of Nusselt number compared with the integral MHS. Also, the highest Nusselt number enhancement was predicted for Al2O3, followed by CuO and SiO2. Temperature and flow fields in a trapezoidal grooved MHS were investigated for different nanofluids [13]. The results clarified that the trapezoidal grooved MHS with higher maximum-width and lower minimum-width displayed the maximum thermal performance. It was also reported that Al2O3/water had the highest thermal performance with 4% volume fraction and 25 nm nanoparticle diameter. The performance of a pin-fin MHS with different configurations (square, triangular, and circular) was numerically investigated in the presence of diamond/ water and Al2O3/water nanofluids [14]. The results shown that using of nanofluids instead of the base fluid enhanced the thermal performance with a certain penalty in the pressure drop for all configurations; the diamond/water nanofluid was better than Al2O3/water. A complex structure and Al2O3/water nanofluid were tested in a MHS under constant heat flux [15]. The performance evaluation factor displayed that the higher volume fraction of nanofluids had better comprehensive
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Fig. 1. A schematic of MHSs with plate, pin, and plate-pin fins.
thermal performance. The simultaneous application of wavy channel and nanofluid as a compound technique was examined in the other numerical study [16]. It was reported that nanofluid had higher effect on the performance of MHS with straight channel. Experiments were carried out [17,18] to investigate the performance of a MHS with inline arrangement of circular pin-fins in presence of ZnO/water and SiO2/water nanofluids. The acquired data explained that the thermal performance of nanofluid-cooled MHS was better than that of water-cooled MHS. Comparison between ZnO/water and SiO2/water nanofluids, higher heat transfer performance for ZnO/water nanofluid was observed by about 3–9%. The effects of ribs turbulator with different design parameters on the hydrothermal performance of a nanofluid-cooled MHS were numerically investigated [19]. The results showed that both the heat transfer coefficient and the pressure drop of nanofluid in the ribbed MHS were higher than those of the simple MHS, and this enhancement intensified with increasing the width of ribs. An experimental study on a nanofluid-cooled MHS with inline and staggered arrangements of square pin-fins was also performed [20]. The minimum base temperature of 29.4 °C was reported for the TiO2(Rutile)/water nanofluid flow
in the MHS with staggered arrangement of pin-fins. A new innovative design of MHS with rectangular and triangular double-layered channels working with Al2O3/water and SiO2/water nanofluids was tested [21]. The results showed that the MHS with triangular double-layered channels provided a 27.4% reduction in the wall temperature comparing with the MHS with rectangular double-layered channels. Experimental tests were conducted for Al2O3/water nanofluid through a MHS with corrugated channels [22]. The base temperature and convective thermal resistance were found to drop by decreasing the wave-length and by increasing the wave-amplitude. In the other experimental study [23] the angle effect of pin-fins on the performance of MHS was examined. It was concluded that the MHS with 22.5 degree channel angle had the lowest convective thermal resistance. Recently, the performance of a nanofluid-cooled MHS with offset-strip fins is investigated by Khoshvaght-Aliabadi et al. [24]. Noticeable values for the heat transfer rate to pumping power ratio were obtained for the MHSs with thinner and longer strips and higher transversal and longitudinal pitches. Also, it was reported that the cooling performance of a nanofluid-cooled MHS is greater than a water-cooled MHS. Likewise, several active heat
Fig. 2. (a) Basic configuration of corrugated MHSs with triangular, trapezoidal, and sinusoidal plate fins [4] (b) schematic of plate and plate-pin fins (red dashed lines show considered potion in numerical simulation). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2 (continued).
transfer enhancement techniques were tested. For instance, a novel technology for controlling temperature rise was adopted based on two active heater sources namely 2H-ATC system [25]. It was concluded that this technology can obtain very small temperature rise of the die during the class testing period. In the current study, a compound or hybrid technique is considered to improve the hydrothermal performance of MHSs. The word
“compound or hybrid” used in this paper differs from the literature [26]. In fact, it refers to combination of two passive techniques. The idea of combining plate fins with pin fins is offered as the first passive technique in the water-cooled corrugated MHSs. It is expected that the hydrothermal performance of coolant flowing through the corrugated MHSs with plate-pin fins will be considerably affected. In order to show these effects on the flow and temperature fields, a numerical
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simulation is also carried out using a CFD approach. As the second passive technique, water is replaced with Al2O3/water nanofluid. The Al2O3/water nanofluid is prepared at two weight fractions, i.e. 0.1% and 0.3%. The performance of nanofluid are experimentally tested and compared with water as base fluid. 2. Experimental apparatus and procedures 2.1. Corrugated MHSs and test setup The basic configuration and design parameters of corrugated MHSs in the current study are based on our previous paper [27] and shown in Fig. 2(a). Fig. 2(b) shows schematically the top view of considered geometries for plate and plate-pin fins in the corrugated MHSs. In order to make equal comparison condition, all design parameters, such as number, height, width, and distance of fins, in the corrugated MHSs are set equal. All corrugated MHSs are made of aluminum alloy 6061 with the thermal conductivity of 170 W/m·K using a Bridgeport CNC machine. The general layout and a graphical photo of manufactured experimental setup are shown in Fig. 3(a–b). The coolant (water or Al2O3/ water nanofluid) flows into the loop from a reservoir through a needle value and a micro-filter. The flow rate is measured by a designed system. It consists of a digital timer (ATE-10S, Autonics), two solenoid
valves (UE-25, Nbszc), and a digital balance (TE1502S, Sartorius) with the accuracy of 0.01 g. In order to measure the inlet and outlet temperatures of coolant, two temperature taps are embedded exactly at the top of upstream and downstream plenums in the test module. The applied thermocouples for the bulk temperature measuring are T-type with the accuracy of 0.1 K. Two digital pressure transmitters (PTCHC060BCIA, Sensys) with the accuracy of 10 Pa are used to evaluate the pressure drop across the corrugated MHSs. The distribution of base temperature in the MHSs is detected using nine K-type thermocouples with the accuracy of 0.1 K. They have the axial distance of 10 mm from each other. Note that the base thermocouples are embedded by drilling very small holes in the side surface of base housing. The bottom portion of base housing is heated via eight electrical cartridge heaters at 50 W (25,000 W/m2) using a variac variable transformer (3PN1010B, DAM). The precise adjustment of power is done using a digital multifunction instrument (mfm 3430, Ziegler). Finally, the temperature of coolant after the test module is restored by utilizing a cooling system. 2.2. Working fluids and properties In the present study, water and Al2O3/water nanofluid are used as coolants. In order to prepare nanofluid, water is considered as base fluid and α-Al2O3 nanoparticles are selected as additive. The main
Fig. 3. Experimental setup (a) general layout [4] (b) graphical photo [22].
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Fig. 3 (continued).
concern during experiments with nanofluid is the agglomeration and sedimentation of nanoparticles. Hence, a two-step method is adopted to prepare a uniform and stable suspension of α-Al2O3 nanoparticles in water. The α-Al2O3 nanoparticles are a commercial production of U.S. Research Nanomaterials, Inc. with average particle size of 20 to 40 nm and purity of 99%. For preparing the Al2O3/water nanofluid with weight concentrations of 0.1% and 0.3%, respectively, 1 g and 3 g of α-Al2O3 nanoparticles are typically added in 1 kg of water and mechanically mixed for nearly 1 h using an electro1magnetic stirrer (MR Hei-End, Heidolph). Then, the mixture is continuously poured into a glass bottle and sonicated by an ultrasonic processor (UP400S, Hielscher GmbH) for 1 h at 400 W and 24 kHz. Using the current preparation procedure, no visible sedimentation or stratification is found after three days while in the present work the time taken to complete an experiment is less than 5 h. In order to verify the non-settling of nanoparticles, the thermal conductivity of prepared nanofluids is measured every 12 h. Likewise, the repeatability of hydrothermal results obtained by nanofluids is also checked after each thermal conductivity measurement. A good repeatability values within ±2% is detected. In order to characterize the prepared nanofluids, primary pictorial and measurement tests are conducted. The shape of nanoparticles is scanned by the TEM, as depicted in Fig. 4(a). It can be seen that the nanoparticles morphology is nearly spherical. The XRD pattern of αAl2O3 nanoparticles is also shown in Fig. 4(b). The XRD pattern depicts the single-phase Al2O3 with a monoclinic structure and no significant peaks of impurities. The required thermo-physical properties of working fluids (density, specific heat, thermal conductivity, and dynamic viscosity) are also evaluated experimentally. The applied measurement apparatus and their accuracy as well as measuring methods are followed from the previous study [22]. It is observed from the results that the values of thermal conductivity, dynamic viscosity, and density increase with the nanoparticles concentration, while the values of specific heat decrease. With the increase in the weight fraction from 0.1% to 0.3%, the thermal conductivity, dynamic viscosity, and density increase from 4.3% to
15.6%, 2.7% to 3.9%, and 2.2 × 10−2% to 5.4 × 10−2%, respectively, but the specific heat capacity decreases from 5.3% to 6.6% than those of the base fluid. 2.3. Data reduction and error analysis The heat produced by the electrical heaters is absorbed with the coolant in the corrugated MHSs. The rate of heat transfer is expressed by the conservation of energy principle, Eq. (1), Q conv ¼ mcp ðT out −T in Þ
ð1Þ
where, m, cp, Tin, and Tout are the mass flow rate, specific heat, inlet and outlet temperature of the fluid, respectively. Eq. (2) is used for the estimation of experimental heat transfer coefficient, h¼
Q conv At ðT w −T m Þ
ð2Þ
where, At is the total surface area in contact with the fluid, Tw is the average wall temperature, and Tm is the mean temperature between the inlet and the outlet. Fourier's law, Eq. (3), is also used to evaluate the local wall temperature on the base surface of MHSs, T wi ¼ T i −
sqcond κs
ð3Þ
where, Ti is the temperature indicated by the base thermocouples (i = 1 to 9), s is the distance between the base thermocouples location and the surface of MHSs, qcond is the heat flux, and κs is the thermal conductively of base housing. To ensure that the corrugated MHSs can absorb as much heat as possible, a suitable thermal paste is used to create a seal between the MHSs and the base housing.
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Fig. 4. (a) TEM of α-Al2O3 nanoparticles (b) XRD of α-Al2O3 nanoparticles [24].
where, κf is the thermal conductively of coolant. Finally, the friction factor is determined from the pressure drop measurements,
The average wall temperature is calculated by Eq. (4), Tw ¼
1 9 ∑ T wi 9 i¼1
ð4Þ
The pressure drop is estimated from the experimental observations and theoretical formula as given in Eq. (5), Δp ¼ pin −pout
ð5Þ
Finally, Reynolds number is considered based on the inlet parameters and calculated by Eq. (6), Re ¼
GDh μ
ð6Þ
where, G is the mass velocity and μ is the dynamic viscosity of coolant, in which, Dh ¼
4Ac L At
hDh κf
2ρΔpDh LG2
ð9Þ
In order to determine the precision of main parameters reported in ‘Results and discussion’ section, such as Reynolds number, Nusselt number, and friction factor, the uncertainties of measuring data must be known. At the studied range, the maximum uncertainties of mass flow rate, temperature, and pressure drop are 0.9% (gps), 0.3% (°C), and 0.06% (Pa), respectively. These values are found from the calibration process and manufactures claim for each instrument. Also, a standard error analysis [28] is employed to quantify the uncertainties of main parameters. Assuming that a, b, c, … are measuring data with the obtained or given uncertainties of ea, eb, ec, …, the uncertainty of a main parameter would be as follows,
ð7Þ
where, Ac is the minimum free flow area and L is the length of MHSs. The hydraulic diameter of MHSs is calculated based on the total surface area and free flow area for each MHS. Also, the average Nusselt number is defined as, Nu ¼
f ¼
ð8Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 ∂E ∂E ∂E δE ¼ ea þ eb þ ec þ … ∂a ∂b ∂c
ð10Þ
The derived results show that the average uncertainties of Reynolds number, Nusselt number, and friction factor due to measurement errors in this study are less than 1.9%, 2.4%, and 2.7%, respectively.
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Fig. 5. Computational domain and boundary conditions.
3. Numerical details and methods 3.1. Problem definition and model development In this study, a numerical simulation is also carried out to capture the flow and temperature fields in the corrugated MHSs with both the plate and the plate-pin fins. Hence, the problem under consideration is the simulation of corrugated MHSs used in the experimental part. Due to the periodical nature of fins in the MHSs, only a part of corrugated MHSs is considered as the computational domain. As shown in Figs. 2 and 5, the computational domain includes only a certain part of fins and coolant domain, and due to the high thermal conductivity of aluminum alloy, the base housing is not considered. The length, width, and height of main part in the computational domain for all cases are 100 mm, 4 mm, and 5 mm. In order to ensure inlet uniformity at the entrance and prevent from reversed flow at the exit, the inlet and outlet of main part are extended 200 mm. The bottom of main part in the computational domain (y = 0) is heated at a constant rate of 50 W, which is the heat generated by electrical heaters inside the base housing in the experimental part. Based on the experiments, the coolant, i.e. water, enters to the computational domain at 27 °C and it exchanges the heat with the fins. The top of main part in the computational domain is
considered thermally insulated, because in the test module, the upper surface of corrugated MHSs is insulated from environment with a plexiglass layer. 3.2. Assumptions, conservation equations, and boundary conditions In the present study, some assumptions are considered before establishing conservation equations for the fluid flow and heat transfer in the computational domain, • • • •
The flow is steady and laminar. The coolant is incompressible and Newtonian. Natural and radiation heat transfer are neglected. Viscous dissipation and body force are not considered.
According to the above assumptions, the differential equations that govern the three-dimensional fluid flow and heat transfer in the corrugated MHSs are expressed as follows. For the coolant (fluid) domain, the continuity, momentum, and energy equations are expressed, respectively, as, ! ∇V ¼ 0
ð11Þ
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• Internal surfaces: conjugate boundary
Table 1 Effects of grids number on numerical results. Grids number
hi
1200000 2107000 3200000 4509000 5800000
– 6.7 4.5 2.3 0.3
+ 1
and hi deviation (%)
Δpi
+ 1
and Δpi deviation (%)
ux ¼ uy ¼ uz ¼ 0;
– 9.7 7.1 4.2 0.7
! ! ! ρ V ∇ V ¼ −∇p þ ∇ μ∇ V
−κ f
∂T f ∂T s ¼ −κ s ∂n ∂n
ð18Þ
• Bottom surface: no slip and constant heat flux condition
ux ¼ uy ¼ uz ¼ 0;
−κ s
∂T ¼q ∂y
ð19Þ
ð12Þ • Outlet surface: all derivatives are zero
! ρcp V ∇T ¼ κ f ∇2 T
ð13Þ ∂ux ∂uy ∂uz ¼ ¼ ¼ 0; ∂x ∂x ∂x
For the fins (solid) region, the energy equation is expressed as, κ s ∇2 T ¼ 0
∂T ¼0 ∂x
ð20Þ
ð14Þ
Based on the considered computational domain as displayed in Fig. 5, the applied boundary conditions are, • Inlet surface: uniform velocity and temperature ux ¼ uin ¼ const; uy ¼ uz ¼ 0; T ¼ T in ¼ const
ð15Þ
• Outside surfaces: no slip and no heat loss for all directions
ux ¼ uy ¼ uz ¼ 0;
T f ¼ Ts;
∂T ∂T ∂T ¼ ¼ ¼0 ∂x ∂y ∂z
ð16Þ
• Lateral surfaces: symmetry condition
∂ux ∂uy ¼ ¼ uz ¼ 0; ∂z ∂z
−κ s
∂T s ¼0 ∂z
ð17Þ
3.3. Solution procedure and grid sensitivity analysis A conjugate heat transfer model based on the finite volume method (FVM) and semi implicit method for pressure linked equation (SIMPLE) algorithm is performed considering the boundary conductions illustrated in Fig. 5. The diffusion terms in the momentum and energy equations are approximated by a second order central difference. The convergence criterion is regarded 10−4 for the continuity, 10−5 for the momentum, and 10−6 for the energy equations. Five sets of grid are evaluated to check the sensitivity of results on grid size by considering the amount of calculated heat transfer coefficient and pressure drop. They consist of 1200000, 2107000, 3200000, 4509000, and 5800000 grids. It should be noted that a structured arrangement of hexahedral grids is selected due to placing in a line with the main flow direction of coolant. Also, the grids are intensified near the fins, where the velocity and temperature gradients are remarkable, to capture the fluid flow and heat transfer features accurately. The effects of grids number on the numerical results are illustrated in Table 1. As depicted, the values of heat transfer coefficient and pressure drop from the last two grid sets
Fig. 6. Considered straight MHS with plate fins in experimental study (top) and numerical simulation (bottom).
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are very close to each other and their differences are less than 1%. Hence, to save the computational time and computer memory, the fourth set of grid, i.e. 4509000, is employed in the final simulations. Finally, the numerical simulations are done based on the commercial CFD package (Fluent V6). 4. Results and discussion 4.1. Validation Before presenting the current experimental and numerical results for the corrugated MHSs, the verification of adopted procedures is done by conducting primary tests for water flow inside a straight MHS with plate fins. In this regard, Nusselt number values obtained from both the experimental and the numerical studies are compared with available experimental data reported by Ho and Chen [29]. Note that, adopting the geometrical structure in the experimental model, Fig. 6 (top), a numerical simulation is separately performed for the straight MHS with plate fins, Fig. 6 (bottom), at Reynolds number ranging from 100 to 900. The results in Fig. 7 show less than 10% deviation between the current experimental results and those of Ho and Chen [29]. Also, the acquired numerical results match well the experimental data, within the maximum error of 5%, thus the presented numerical analysis in the next section can be regarded as reasonable. The deviation between the numerical and the experimental results may be due to the considered simplifying assumptions in the numerical simulation and the measuring uncertainties in the experimental study. After the validation of experimental and numerical results, five Reynolds numbers of 100, 300, 500, 700, and 900 are adopted to analyze the thermal and hydraulic performances of corrugated MHSs. The plate fin and plate-pin fin cases are investigated and the results are compared and analyzed both quantitatively and qualitatively.
Fig. 8. Effect of plate and plate-pin fins on thermal performance of water-cooled corrugated MHSs (a) heat transfer coefficient (b) Nusselt number enhancement.
4.2. Thermal performance Fig. 8(a–b) compares the thermal performance of studied corrugated MHSs versus Reynolds number for water flow as coolant. It can be seen that when Reynolds number goes up, larger values of the heat transfer coefficient are acquired. The corrugated MHSs listed in increasing order of the heat transfer coefficient are the trapezoidal, triangular, and sinusoidal. On the other hand, when the same Reynolds number is adopted, the corrugated MHSs with plate-pin fins have higher heat transfer coefficient values than the corrugated MHSs with plate fins. Fig. 8(b) clarifies that all corrugated MHSs have better thermal performance when they are compared with the straight MHS. Again, the corrugated MHS with trapezoidal plate-pin fins has the highest values of heat transfer coefficient or Nusselt number, followed by the
Fig. 7. Comparison between current experimental and numerical results and Ho and Chen [29] data.
corrugated MHSs with triangular and sinusoidal plate-pin fins. However, the results suggest that the corrugated MHS with sinusoidal shape enjoys more effects from the fins interruption and it has superior variations in the thermal performance compared to the other shapes of fins, i.e. triangular and trapezoidal. Likewise, when the corrugated MHS with triangular shape and the corrugated MHS with trapezoidal shape are compared, the former enjoys a higher effect than the latter. For instance, as the plate-pin fins are employed in the corrugated MHS with sinusoidal shape, Nusselt number enhances averagely about 55%, while for the similar operation, Nusselt number of the corrugated MHS with triangular and trapezoidal shapes increases 33% and 25%, respectively. One notable fact is that the difference of heat transfer coefficient between the plate and the plate-pin cases in the corrugated MHS with trapezoidal shape is not so noticeable; less than 5%. It is also found that higher values of the heat transfer coefficient or Nusselt number due to increased Reynolds number are occurred via the corrugated MHS with trapezoidal shape in comparison with other corrugated MHSs; as Reynolds number increases from 100 to 900, Nusselt number of the corrugated MHS with trapezoidal shape enhances about three times. Temperature contours for water flow at the base plane of simulated MHSs (y = 4 mm), when Reynolds number is 500, are depicted in Fig. 9. It can be seen that both the temperature and the temperature gradient are high near the fins. Obviously, for the corrugated MHSs, the temperature distributions at the exit part are more uniform compared to the straight MHS and they have higher outlet temperature. It can be explained as the corrugated fins are employed in the MHSs, the flow path and total surface area are enlarged, swirl flows are generated, boundary layers are interrupted, hot fluid near the fins and cold fluid in core regime are mixed better, thereby the heat transfer is enhanced. It is noted that for the MHSs with plate fins, the temperature in the core regime is lower, while shows higher values near the fins. After
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Fig. 9. Effect of plate and plate-pin fins on temperature contours of water-cooled corrugated MHSs at Reynolds number of 500.
introducing of plate-pin fins in the corrugated MHSs, the temperature near the plate fins visibly decreases, so the corrugated MHSs with plate-pin fins show a smaller temperature difference between the core regime and the fins wall. It leads to higher temperature values at the exit of corrugated MHSs with plate-pin fins. From experiments, it is recorded that utilizing Al2O3/water nanofluids is associated with heat transfer enhancement in the corrugated MHSs. The variations of heat transfer coefficient for nanofluids compared to the base fluid, i.e. water, are tabulated in Table 2. As shown, the enhancement of heat transfer coefficient is further increased with increment of nanoparticles weight fraction in the base fluid. This is because the increment of nanoparticles concentration brings more enhancements in thermal conductivity of coolant and interaction between nanoparticles and fins. It leads to higher values of the heat transfer coefficient for nanofluid with greater concentration. With respect to the geometry effect, the nanofluid flow in the corrugated MHS with trapezoidal plate fins shows the greatest enhancements as compared to other cases.
differences in the friction factor are not significant. It is apparent from Fig. 10(b) that the corrugated MHSs have higher friction factor than the straight MHS. In other words, the pressure drop is the lowest for the straight MHS. As it can be seen in Fig. 7, it has a smooth flow path without any blocking effects with corrugations or pins.
4.3. Hydraulic performance In addition to the thermal performance, the hydraulic characteristic is another important factor for the application of MHSs. Fig. 10(a–b) shows the comparison of corrugated MHSs with straight MHS from the hydraulic performance point of view. Fig. 10(a), which shows the relation between pressure drop and Reynolds number, signifies that with the increase of Reynolds number, the pressure drop augments for all MHSs. It is found that the pressure drop for the corrugated MHSs with plate fins are larger than that of the corrugated MHSs with plate-pin fins. However, the
Table 2 Variations of heat transfer coefficient for nanofluids compared to base fluid (%). Corrugated MHS
0.1% nanofluid
0.3% nanofluid
1. Triangular & plate 2. Triangular & plate-pin 3. Trapezoidal & plate 4. Trapezoidal & plate-pin 5. Sinusoidal & plate 6. Sinusoidal & plate-pin
12.9 12.4 14.1 11.2 11.8 13.3
21.2 19.6 22.8 18.3 19.1 20.7
Fig. 10. Effect of plate and plate-pin fins on hydraulic performance of water-cooled corrugated MHSs (a) pressure drop (b) friction factor augmentation.
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Fig. 11. Effect of plate and plate-pin fins on velocity vectors and temperature contours of water-cooled corrugated MHSs at Reynolds number of 900.
In order to have a better understand from the fluid flow and heat transfer characteristics, the velocity vectors and temperature contours at zoom views in the corrugated MHSs are demonstrated in Fig. 11. Note that in the convection heat transfer, the temperature and velocity fields are coupled. It is clear that there are remarkable differences in the velocity vectors and temperature contours of the corrugated MHSs. By comparing the velocity vectors of the plate and the plate-pin fins, it can be seen that at the same conditions, the plate-pin structure of fins intensifies the number and size of swirl flows in the corrugated MHSs. Higher and larger swirl flows in the corrugated MHS with plate-pin fins could lead to chaotic advection which dramatically enhances the convective fluid mixing and heat transfer. Note that in addition to the number and size, the potential of heat transfer enhancement in the corrugated MHSs depends on the location and strength of generated swirl flows relative to the fins which have higher temperature. As depicted in Fig. 11, in the corrugated MHSs with plate-pin fins, the expansion and strength of main longitudinal swirl flows in corrugations is considerable in comparison with the corrugated MHSs with plate fins. This causes a significant exchange between the core and the fin fluids. It is also
shown that as a plate fin is interrupted into the plate-pin fins, a corner longitudinal swirl flow starts to generate behind each fin. Due to the high temperature gradient in the location of generated swirl flow, a local heat transfer enhancement occurs in this area and the temperature of coolant increases. Similar to the thermal performance, the hydraulic performance of corrugated MHSs can be affected when water as coolant is replaced with a nanofluid. For instance, the variations of pressure drop for nanofluids compared to water are presented in Table 3. It can be seen Table 3 Variations of pressure drop for nanofluids compared to base fluid (%). Corrugated MHS
0.1% nanofluid
0.3% nanofluid
1. Triangular & plate 2. Triangular & plate-pin 3. Trapezoidal & plate 4. Trapezoidal & plate-pin 5. sinusoidal & plate 6. Sinusoidal & plate-pin
5.6 3.8 7.2 4.6 6.5 4.3
17.9 10.1 19.5 12.8 19.2 10.6
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that the nanofluids show larger pressure drop values compared to water and the pressure drop increases with nanoparticles concentration. 4.4. Overall thermal-hydraulic performance From the results presented in Sections 4.2 and 4.3, it is found that the fin shape, fin structure, Reynolds number, and nanoparticles weight fraction have significant influences on both the thermal and the hydraulic performances of corrugated MHSs. Hence, the overall performance of corrugated MHSs should be evaluated using an appropriate hydrothermal performance factor. In this regard, the hydrothermal performance factor defined in Eq. (15) is considered to appraise the overall effectiveness of corrugated MHSs compared with that of the straight MHS [30]. NuCorrugated MHS =NuStraight MHS η¼ 1 =3 f Corrugated MHS =f Straight MHS
ð21Þ
The relationship between the hydrothermal performance factor and Reynolds number for water flow inside the corrugated MHSs is depicted in Fig. 12. It is evident from the figure that the performance factor values of corrugated MHSs with plate-pin fins are higher than those of corrugated MHSs with plate fins. In whole range of Reynolds number, the performance factor of all corrugated MHSs with plate-pin fins is larger than unity and it increases with increasing of Reynolds number. This means that the overall performance of corrugated MHSs improves at higher Reynolds numbers. As an example, the hydrothermal performance factor can reach 1.72 at Reynolds number of 900 for water flow inside the corrugated MHS having sinusoidal plate-pin fins. It is noticeable to state that at lower Reynolds numbers, the maximum values of performance factor are obtained for the corrugated MHS with trapezoidal plate-pin fins, while at higher Reynolds numbers, the maximum values are observed for the corrugated MHS with sinusoidal plate-pin fins. The effects of tested nanofluids on the hydrothermal performance factor of corrugated MHS are illustrated in Fig. 13. Comparing between Figs. 12 and 13, the nanofluids do not affect the performance factor of corrugated MHSs in low Reynolds numbers and there is no noticeable increase in comparison to water. Likewise, as Reynolds number goes up, the performance factor enhances further, and this is more evident at higher Reynolds numbers. In other words, using nanofluids in the corrugated MHSs causes a better hydrothermal performance in high Reynolds numbers in comparison to lower Reynolds numbers. At the studied range, the maximum performance factor of 1.84 is recorded for the 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins.
Fig. 13. Effect of plate and plate-pin fins on thermal-hydraulic performance of nanofluidcooled corrugated MHSs.
5. Conclusion In the present study, we compare the thermal and hydraulic performances of plate and plate-pin fins in corrugated miniature heat sinks (MHSs). This analyses is performed for different configurations of corrugated fins, namely triangular, trapezoidal, and sinusoidal. In the second part, the performance of Al2O3/water nanofluid in the corrugated MHSs with both the plate and the plate-pin fins is examined compared to water as base fluid. According to the obtained results, concluding remarks are drawn as follow, ➢ The use of corrugated fins in the MHSs leads to considerable enhancement in heat transfer with a certain pressure drop penalty in comparison with the straight MHS. Highest values of the heat transfer coefficient and pressure drop are recorded for the corrugated MHS with trapezoidal fins. ➢ It is shown that the plate-pin fins poses higher heat transfer coefficient and lower pressure drop values than the plate fins in the corrugated MHSs. For instance, the heat transfer coefficient is increased about 22.9% and the pressure drop is decreased about 49.3% in the corrugated MHS with sinusoidal fins, when the plate fins are changed with the plate-pin fins. ➢ For all corrugated MHSs, the Al2O3/water nanofluid can enhance the heat transfer coefficient effectively albeit with a penalty in the pressure drop. However, the results express that it has higher effects on the heat transfer coefficient than the pressure drop. ➢ Likewise, we can also see that the hydrothermal performance factor of corrugated MHSs enhances as Reynolds number goes up. The values of corrugated MHSs with plate-pin fins are higher than those of corrugated MHSs with plate fins. ➢ At the studied range, the maximum performance factor of 1.84 is recorded for the 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins. Finally, the current work will help designers to select a corrugated MHS with better hydrothermal performance in microelectronic systems.
Fig. 12. Effect of plate and plate-pin fins on thermal-hydraulic performance of watercooled corrugated MHSs.
Nomenclature Ac minimum free flow area, m2 At active heat transfer area, m2 a corrugation amplitude, m cp specific heat, J·kg−1·K−1 Dh hydraulic diameter, m E dependent variable e independent variable
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f G h L l m Nu Q q Re Δp s T V w
friction factor mass velocity, kg·m−2·s−1 heat transfer coefficient, W·m−2·K−1 MHS length, m corrugation length, m mass flow rate, kg·s−1 Nusselt number heat transfer rate, W heat flux, W·m−2 Reynolds number pressure drop, Pa distance between thermocouples location and MHS, m temperature, K velocity, m/s minichannel width, m
Greek symbols
density, kg·m−3 dynamic viscosity, Pa·s thermal conductivity, W·m−1·K−1 nanoparticles fraction hydrothermal performance factor
ρ μ κ φ η
Subscripts
cond conv f in m out w s
conduction convection fluid inlet mean outlet wall solid
Acronyms
MHS TEM XRD
miniature heat sink transmission electron microscopy X-ray diffraction
Acknowledgements The corresponding author would like to thank Mr. O. Sartipzadeh for his kind help in the experimental setup fabrication at Islamic Azad University (IAU) of Shahrood Branch. References [1] Y.T. Yang, H.S. Peng, Investigation of planted pin fins for heat transfer enhancement in plate fin heat sink, Microelectron. Reliab. 49 (2) (2009) 163–169. [2] P. Cova, N. Delmonte, F. Giuliani, M. Citterio, S. Latorre, M. Lazzaroni, A. Lanza, Thermal optimization of water heat sink for power converters with tight thermal constraints, Microelectron. Reliab. 53 (2013) 1760–1765. [3] M. Conrad, A. Diatlov, R.W. De Doncker, Purpose, potential and realization of chipattached micro-pin fin heat sinks, Microelectron. Reliab. 55 (2015) 1992–1996.
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Comparison of hydrothermal performance between plate fins and plate-pin fins subject to nanofluid-cooled corrugated miniature heat sinks M. Khoshvaght-Aliabadi a,⁎, S.M. Hassani b, S.H. Mazloumi b a b
Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University, Mashhad, Iran
a r t i c l e
i n f o
Article history: Received 15 October 2016 Received in revised form 10 January 2017 Accepted 10 January 2017 Available online xxxx Keywords: Corrugated miniature heat sink Corrugation shape Nanofluid Plate fin Plate-pin fin
a b s t r a c t Thermal and hydraulic performances of two types of fin, namely plate and plate-pin, in water-cooled corrugated miniature heat sinks (MHSs) having triangular, trapezoidal, and sinusoidal shapes are evaluated. In fact, the plate-pin fins are designed and constructed based on the plate fins. Experiments are performed on the fabricated corrugated MHSs in range of Reynolds number between 100 and 900. Temperature contours and velocity vectors are also studied numerically using a CFD approach. The numerical results are validated with recorded experimental data in the present and previous studies. In addition to water, the Al2O3/water nanofluid is also testes in the corrugated MHSs, as nanofluid-cooled corrugated MHSs. The obtained results show that the thermal performance of a corrugated MHS with plate-pin fins is better than that of a corrugated MHS with plate fins. Another obvious advantage of plate-pin fins is that designers can reduce the pressure drop (or pumping power) in the corrugated MHSs for the same heat dissipation. The maximum hydrothermal performance factor of 1.84 is detected for 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Water-cooled miniature heat sinks (MHSs) are efficient equipment in thermal management of electronic or mechanical devices. They are often 4–5 times more efficient compared to air-cooled types. Plate, pin, and plate-pin shapes are three common types of fins which are widely used in the MHSs (Fig. 1). The plate fins are easy to fabricate and have simple structure and low cost while the pin fins provide better hydrothermal performance with higher production cost. In modern electronic or mechanical devices, a powerful thermal management system is required, especially in harsh operating conditions such as high heat fluxes. The technique to improve the thermal performance and solve the hot point is referred to heat transfer enhancement. Generally, the heat transfer enhancement in the MHSs can be carried out either by modifications of surface geometry and fluid property. Some previous studies tried to modify the surface geometry of water-cooled MHSs [1–5]. In addition to water which still has extensive applications, another type of coolant, namely nanofluid, was considered in recent years by researchers [6–10]. However, because of relatively new history of nanofluid-cooled MHSs with modified geometries, the number of researches on this topic is very scarce.
⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (M. Khoshvaght-Aliabadi).
Flow and heat transfer behaviors of CuO/water and Al2O3/water nanofluids inside the pin-fin MHSs were studied numerically [11]. It was reported that the performance of MHSs enhanced as the nanofluids were replaced with the base fluid. Also, decreasing the diameter of Al2O3 nanoparticles in the base fluid increased Nusselt number values while the trend was reverse for CuO nanoparticles. In the other numerical study [12], the performances of Al2O3, CuO, and SiO2 nanoparticles as additives in water flowing in an interrupted MHS were evaluated. It was detected that the interrupted MHS had higher values of Nusselt number compared with the integral MHS. Also, the highest Nusselt number enhancement was predicted for Al2O3, followed by CuO and SiO2. Temperature and flow fields in a trapezoidal grooved MHS were investigated for different nanofluids [13]. The results clarified that the trapezoidal grooved MHS with higher maximum-width and lower minimum-width displayed the maximum thermal performance. It was also reported that Al2O3/water had the highest thermal performance with 4% volume fraction and 25 nm nanoparticle diameter. The performance of a pin-fin MHS with different configurations (square, triangular, and circular) was numerically investigated in the presence of diamond/ water and Al2O3/water nanofluids [14]. The results shown that using of nanofluids instead of the base fluid enhanced the thermal performance with a certain penalty in the pressure drop for all configurations; the diamond/water nanofluid was better than Al2O3/water. A complex structure and Al2O3/water nanofluid were tested in a MHS under constant heat flux [15]. The performance evaluation factor displayed that the higher volume fraction of nanofluids had better comprehensive
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Fig. 1. A schematic of MHSs with plate, pin, and plate-pin fins.
thermal performance. The simultaneous application of wavy channel and nanofluid as a compound technique was examined in the other numerical study [16]. It was reported that nanofluid had higher effect on the performance of MHS with straight channel. Experiments were carried out [17,18] to investigate the performance of a MHS with inline arrangement of circular pin-fins in presence of ZnO/water and SiO2/water nanofluids. The acquired data explained that the thermal performance of nanofluid-cooled MHS was better than that of water-cooled MHS. Comparison between ZnO/water and SiO2/water nanofluids, higher heat transfer performance for ZnO/water nanofluid was observed by about 3–9%. The effects of ribs turbulator with different design parameters on the hydrothermal performance of a nanofluid-cooled MHS were numerically investigated [19]. The results showed that both the heat transfer coefficient and the pressure drop of nanofluid in the ribbed MHS were higher than those of the simple MHS, and this enhancement intensified with increasing the width of ribs. An experimental study on a nanofluid-cooled MHS with inline and staggered arrangements of square pin-fins was also performed [20]. The minimum base temperature of 29.4 °C was reported for the TiO2(Rutile)/water nanofluid flow
in the MHS with staggered arrangement of pin-fins. A new innovative design of MHS with rectangular and triangular double-layered channels working with Al2O3/water and SiO2/water nanofluids was tested [21]. The results showed that the MHS with triangular double-layered channels provided a 27.4% reduction in the wall temperature comparing with the MHS with rectangular double-layered channels. Experimental tests were conducted for Al2O3/water nanofluid through a MHS with corrugated channels [22]. The base temperature and convective thermal resistance were found to drop by decreasing the wave-length and by increasing the wave-amplitude. In the other experimental study [23] the angle effect of pin-fins on the performance of MHS was examined. It was concluded that the MHS with 22.5 degree channel angle had the lowest convective thermal resistance. Recently, the performance of a nanofluid-cooled MHS with offset-strip fins is investigated by Khoshvaght-Aliabadi et al. [24]. Noticeable values for the heat transfer rate to pumping power ratio were obtained for the MHSs with thinner and longer strips and higher transversal and longitudinal pitches. Also, it was reported that the cooling performance of a nanofluid-cooled MHS is greater than a water-cooled MHS. Likewise, several active heat
Fig. 2. (a) Basic configuration of corrugated MHSs with triangular, trapezoidal, and sinusoidal plate fins [4] (b) schematic of plate and plate-pin fins (red dashed lines show considered potion in numerical simulation). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2 (continued).
transfer enhancement techniques were tested. For instance, a novel technology for controlling temperature rise was adopted based on two active heater sources namely 2H-ATC system [25]. It was concluded that this technology can obtain very small temperature rise of the die during the class testing period. In the current study, a compound or hybrid technique is considered to improve the hydrothermal performance of MHSs. The word
“compound or hybrid” used in this paper differs from the literature [26]. In fact, it refers to combination of two passive techniques. The idea of combining plate fins with pin fins is offered as the first passive technique in the water-cooled corrugated MHSs. It is expected that the hydrothermal performance of coolant flowing through the corrugated MHSs with plate-pin fins will be considerably affected. In order to show these effects on the flow and temperature fields, a numerical
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simulation is also carried out using a CFD approach. As the second passive technique, water is replaced with Al2O3/water nanofluid. The Al2O3/water nanofluid is prepared at two weight fractions, i.e. 0.1% and 0.3%. The performance of nanofluid are experimentally tested and compared with water as base fluid. 2. Experimental apparatus and procedures 2.1. Corrugated MHSs and test setup The basic configuration and design parameters of corrugated MHSs in the current study are based on our previous paper [27] and shown in Fig. 2(a). Fig. 2(b) shows schematically the top view of considered geometries for plate and plate-pin fins in the corrugated MHSs. In order to make equal comparison condition, all design parameters, such as number, height, width, and distance of fins, in the corrugated MHSs are set equal. All corrugated MHSs are made of aluminum alloy 6061 with the thermal conductivity of 170 W/m·K using a Bridgeport CNC machine. The general layout and a graphical photo of manufactured experimental setup are shown in Fig. 3(a–b). The coolant (water or Al2O3/ water nanofluid) flows into the loop from a reservoir through a needle value and a micro-filter. The flow rate is measured by a designed system. It consists of a digital timer (ATE-10S, Autonics), two solenoid
valves (UE-25, Nbszc), and a digital balance (TE1502S, Sartorius) with the accuracy of 0.01 g. In order to measure the inlet and outlet temperatures of coolant, two temperature taps are embedded exactly at the top of upstream and downstream plenums in the test module. The applied thermocouples for the bulk temperature measuring are T-type with the accuracy of 0.1 K. Two digital pressure transmitters (PTCHC060BCIA, Sensys) with the accuracy of 10 Pa are used to evaluate the pressure drop across the corrugated MHSs. The distribution of base temperature in the MHSs is detected using nine K-type thermocouples with the accuracy of 0.1 K. They have the axial distance of 10 mm from each other. Note that the base thermocouples are embedded by drilling very small holes in the side surface of base housing. The bottom portion of base housing is heated via eight electrical cartridge heaters at 50 W (25,000 W/m2) using a variac variable transformer (3PN1010B, DAM). The precise adjustment of power is done using a digital multifunction instrument (mfm 3430, Ziegler). Finally, the temperature of coolant after the test module is restored by utilizing a cooling system. 2.2. Working fluids and properties In the present study, water and Al2O3/water nanofluid are used as coolants. In order to prepare nanofluid, water is considered as base fluid and α-Al2O3 nanoparticles are selected as additive. The main
Fig. 3. Experimental setup (a) general layout [4] (b) graphical photo [22].
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5
Fig. 3 (continued).
concern during experiments with nanofluid is the agglomeration and sedimentation of nanoparticles. Hence, a two-step method is adopted to prepare a uniform and stable suspension of α-Al2O3 nanoparticles in water. The α-Al2O3 nanoparticles are a commercial production of U.S. Research Nanomaterials, Inc. with average particle size of 20 to 40 nm and purity of 99%. For preparing the Al2O3/water nanofluid with weight concentrations of 0.1% and 0.3%, respectively, 1 g and 3 g of α-Al2O3 nanoparticles are typically added in 1 kg of water and mechanically mixed for nearly 1 h using an electro1magnetic stirrer (MR Hei-End, Heidolph). Then, the mixture is continuously poured into a glass bottle and sonicated by an ultrasonic processor (UP400S, Hielscher GmbH) for 1 h at 400 W and 24 kHz. Using the current preparation procedure, no visible sedimentation or stratification is found after three days while in the present work the time taken to complete an experiment is less than 5 h. In order to verify the non-settling of nanoparticles, the thermal conductivity of prepared nanofluids is measured every 12 h. Likewise, the repeatability of hydrothermal results obtained by nanofluids is also checked after each thermal conductivity measurement. A good repeatability values within ±2% is detected. In order to characterize the prepared nanofluids, primary pictorial and measurement tests are conducted. The shape of nanoparticles is scanned by the TEM, as depicted in Fig. 4(a). It can be seen that the nanoparticles morphology is nearly spherical. The XRD pattern of αAl2O3 nanoparticles is also shown in Fig. 4(b). The XRD pattern depicts the single-phase Al2O3 with a monoclinic structure and no significant peaks of impurities. The required thermo-physical properties of working fluids (density, specific heat, thermal conductivity, and dynamic viscosity) are also evaluated experimentally. The applied measurement apparatus and their accuracy as well as measuring methods are followed from the previous study [22]. It is observed from the results that the values of thermal conductivity, dynamic viscosity, and density increase with the nanoparticles concentration, while the values of specific heat decrease. With the increase in the weight fraction from 0.1% to 0.3%, the thermal conductivity, dynamic viscosity, and density increase from 4.3% to
15.6%, 2.7% to 3.9%, and 2.2 × 10−2% to 5.4 × 10−2%, respectively, but the specific heat capacity decreases from 5.3% to 6.6% than those of the base fluid. 2.3. Data reduction and error analysis The heat produced by the electrical heaters is absorbed with the coolant in the corrugated MHSs. The rate of heat transfer is expressed by the conservation of energy principle, Eq. (1), Q conv ¼ mcp ðT out −T in Þ
ð1Þ
where, m, cp, Tin, and Tout are the mass flow rate, specific heat, inlet and outlet temperature of the fluid, respectively. Eq. (2) is used for the estimation of experimental heat transfer coefficient, h¼
Q conv At ðT w −T m Þ
ð2Þ
where, At is the total surface area in contact with the fluid, Tw is the average wall temperature, and Tm is the mean temperature between the inlet and the outlet. Fourier's law, Eq. (3), is also used to evaluate the local wall temperature on the base surface of MHSs, T wi ¼ T i −
sqcond κs
ð3Þ
where, Ti is the temperature indicated by the base thermocouples (i = 1 to 9), s is the distance between the base thermocouples location and the surface of MHSs, qcond is the heat flux, and κs is the thermal conductively of base housing. To ensure that the corrugated MHSs can absorb as much heat as possible, a suitable thermal paste is used to create a seal between the MHSs and the base housing.
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Fig. 4. (a) TEM of α-Al2O3 nanoparticles (b) XRD of α-Al2O3 nanoparticles [24].
where, κf is the thermal conductively of coolant. Finally, the friction factor is determined from the pressure drop measurements,
The average wall temperature is calculated by Eq. (4), Tw ¼
1 9 ∑ T wi 9 i¼1
ð4Þ
The pressure drop is estimated from the experimental observations and theoretical formula as given in Eq. (5), Δp ¼ pin −pout
ð5Þ
Finally, Reynolds number is considered based on the inlet parameters and calculated by Eq. (6), Re ¼
GDh μ
ð6Þ
where, G is the mass velocity and μ is the dynamic viscosity of coolant, in which, Dh ¼
4Ac L At
hDh κf
2ρΔpDh LG2
ð9Þ
In order to determine the precision of main parameters reported in ‘Results and discussion’ section, such as Reynolds number, Nusselt number, and friction factor, the uncertainties of measuring data must be known. At the studied range, the maximum uncertainties of mass flow rate, temperature, and pressure drop are 0.9% (gps), 0.3% (°C), and 0.06% (Pa), respectively. These values are found from the calibration process and manufactures claim for each instrument. Also, a standard error analysis [28] is employed to quantify the uncertainties of main parameters. Assuming that a, b, c, … are measuring data with the obtained or given uncertainties of ea, eb, ec, …, the uncertainty of a main parameter would be as follows,
ð7Þ
where, Ac is the minimum free flow area and L is the length of MHSs. The hydraulic diameter of MHSs is calculated based on the total surface area and free flow area for each MHS. Also, the average Nusselt number is defined as, Nu ¼
f ¼
ð8Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 ∂E ∂E ∂E δE ¼ ea þ eb þ ec þ … ∂a ∂b ∂c
ð10Þ
The derived results show that the average uncertainties of Reynolds number, Nusselt number, and friction factor due to measurement errors in this study are less than 1.9%, 2.4%, and 2.7%, respectively.
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Fig. 5. Computational domain and boundary conditions.
3. Numerical details and methods 3.1. Problem definition and model development In this study, a numerical simulation is also carried out to capture the flow and temperature fields in the corrugated MHSs with both the plate and the plate-pin fins. Hence, the problem under consideration is the simulation of corrugated MHSs used in the experimental part. Due to the periodical nature of fins in the MHSs, only a part of corrugated MHSs is considered as the computational domain. As shown in Figs. 2 and 5, the computational domain includes only a certain part of fins and coolant domain, and due to the high thermal conductivity of aluminum alloy, the base housing is not considered. The length, width, and height of main part in the computational domain for all cases are 100 mm, 4 mm, and 5 mm. In order to ensure inlet uniformity at the entrance and prevent from reversed flow at the exit, the inlet and outlet of main part are extended 200 mm. The bottom of main part in the computational domain (y = 0) is heated at a constant rate of 50 W, which is the heat generated by electrical heaters inside the base housing in the experimental part. Based on the experiments, the coolant, i.e. water, enters to the computational domain at 27 °C and it exchanges the heat with the fins. The top of main part in the computational domain is
considered thermally insulated, because in the test module, the upper surface of corrugated MHSs is insulated from environment with a plexiglass layer. 3.2. Assumptions, conservation equations, and boundary conditions In the present study, some assumptions are considered before establishing conservation equations for the fluid flow and heat transfer in the computational domain, • • • •
The flow is steady and laminar. The coolant is incompressible and Newtonian. Natural and radiation heat transfer are neglected. Viscous dissipation and body force are not considered.
According to the above assumptions, the differential equations that govern the three-dimensional fluid flow and heat transfer in the corrugated MHSs are expressed as follows. For the coolant (fluid) domain, the continuity, momentum, and energy equations are expressed, respectively, as, ! ∇V ¼ 0
ð11Þ
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• Internal surfaces: conjugate boundary
Table 1 Effects of grids number on numerical results. Grids number
hi
1200000 2107000 3200000 4509000 5800000
– 6.7 4.5 2.3 0.3
+ 1
and hi deviation (%)
Δpi
+ 1
and Δpi deviation (%)
ux ¼ uy ¼ uz ¼ 0;
– 9.7 7.1 4.2 0.7
! ! ! ρ V ∇ V ¼ −∇p þ ∇ μ∇ V
−κ f
∂T f ∂T s ¼ −κ s ∂n ∂n
ð18Þ
• Bottom surface: no slip and constant heat flux condition
ux ¼ uy ¼ uz ¼ 0;
−κ s
∂T ¼q ∂y
ð19Þ
ð12Þ • Outlet surface: all derivatives are zero
! ρcp V ∇T ¼ κ f ∇2 T
ð13Þ ∂ux ∂uy ∂uz ¼ ¼ ¼ 0; ∂x ∂x ∂x
For the fins (solid) region, the energy equation is expressed as, κ s ∇2 T ¼ 0
∂T ¼0 ∂x
ð20Þ
ð14Þ
Based on the considered computational domain as displayed in Fig. 5, the applied boundary conditions are, • Inlet surface: uniform velocity and temperature ux ¼ uin ¼ const; uy ¼ uz ¼ 0; T ¼ T in ¼ const
ð15Þ
• Outside surfaces: no slip and no heat loss for all directions
ux ¼ uy ¼ uz ¼ 0;
T f ¼ Ts;
∂T ∂T ∂T ¼ ¼ ¼0 ∂x ∂y ∂z
ð16Þ
• Lateral surfaces: symmetry condition
∂ux ∂uy ¼ ¼ uz ¼ 0; ∂z ∂z
−κ s
∂T s ¼0 ∂z
ð17Þ
3.3. Solution procedure and grid sensitivity analysis A conjugate heat transfer model based on the finite volume method (FVM) and semi implicit method for pressure linked equation (SIMPLE) algorithm is performed considering the boundary conductions illustrated in Fig. 5. The diffusion terms in the momentum and energy equations are approximated by a second order central difference. The convergence criterion is regarded 10−4 for the continuity, 10−5 for the momentum, and 10−6 for the energy equations. Five sets of grid are evaluated to check the sensitivity of results on grid size by considering the amount of calculated heat transfer coefficient and pressure drop. They consist of 1200000, 2107000, 3200000, 4509000, and 5800000 grids. It should be noted that a structured arrangement of hexahedral grids is selected due to placing in a line with the main flow direction of coolant. Also, the grids are intensified near the fins, where the velocity and temperature gradients are remarkable, to capture the fluid flow and heat transfer features accurately. The effects of grids number on the numerical results are illustrated in Table 1. As depicted, the values of heat transfer coefficient and pressure drop from the last two grid sets
Fig. 6. Considered straight MHS with plate fins in experimental study (top) and numerical simulation (bottom).
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are very close to each other and their differences are less than 1%. Hence, to save the computational time and computer memory, the fourth set of grid, i.e. 4509000, is employed in the final simulations. Finally, the numerical simulations are done based on the commercial CFD package (Fluent V6). 4. Results and discussion 4.1. Validation Before presenting the current experimental and numerical results for the corrugated MHSs, the verification of adopted procedures is done by conducting primary tests for water flow inside a straight MHS with plate fins. In this regard, Nusselt number values obtained from both the experimental and the numerical studies are compared with available experimental data reported by Ho and Chen [29]. Note that, adopting the geometrical structure in the experimental model, Fig. 6 (top), a numerical simulation is separately performed for the straight MHS with plate fins, Fig. 6 (bottom), at Reynolds number ranging from 100 to 900. The results in Fig. 7 show less than 10% deviation between the current experimental results and those of Ho and Chen [29]. Also, the acquired numerical results match well the experimental data, within the maximum error of 5%, thus the presented numerical analysis in the next section can be regarded as reasonable. The deviation between the numerical and the experimental results may be due to the considered simplifying assumptions in the numerical simulation and the measuring uncertainties in the experimental study. After the validation of experimental and numerical results, five Reynolds numbers of 100, 300, 500, 700, and 900 are adopted to analyze the thermal and hydraulic performances of corrugated MHSs. The plate fin and plate-pin fin cases are investigated and the results are compared and analyzed both quantitatively and qualitatively.
Fig. 8. Effect of plate and plate-pin fins on thermal performance of water-cooled corrugated MHSs (a) heat transfer coefficient (b) Nusselt number enhancement.
4.2. Thermal performance Fig. 8(a–b) compares the thermal performance of studied corrugated MHSs versus Reynolds number for water flow as coolant. It can be seen that when Reynolds number goes up, larger values of the heat transfer coefficient are acquired. The corrugated MHSs listed in increasing order of the heat transfer coefficient are the trapezoidal, triangular, and sinusoidal. On the other hand, when the same Reynolds number is adopted, the corrugated MHSs with plate-pin fins have higher heat transfer coefficient values than the corrugated MHSs with plate fins. Fig. 8(b) clarifies that all corrugated MHSs have better thermal performance when they are compared with the straight MHS. Again, the corrugated MHS with trapezoidal plate-pin fins has the highest values of heat transfer coefficient or Nusselt number, followed by the
Fig. 7. Comparison between current experimental and numerical results and Ho and Chen [29] data.
corrugated MHSs with triangular and sinusoidal plate-pin fins. However, the results suggest that the corrugated MHS with sinusoidal shape enjoys more effects from the fins interruption and it has superior variations in the thermal performance compared to the other shapes of fins, i.e. triangular and trapezoidal. Likewise, when the corrugated MHS with triangular shape and the corrugated MHS with trapezoidal shape are compared, the former enjoys a higher effect than the latter. For instance, as the plate-pin fins are employed in the corrugated MHS with sinusoidal shape, Nusselt number enhances averagely about 55%, while for the similar operation, Nusselt number of the corrugated MHS with triangular and trapezoidal shapes increases 33% and 25%, respectively. One notable fact is that the difference of heat transfer coefficient between the plate and the plate-pin cases in the corrugated MHS with trapezoidal shape is not so noticeable; less than 5%. It is also found that higher values of the heat transfer coefficient or Nusselt number due to increased Reynolds number are occurred via the corrugated MHS with trapezoidal shape in comparison with other corrugated MHSs; as Reynolds number increases from 100 to 900, Nusselt number of the corrugated MHS with trapezoidal shape enhances about three times. Temperature contours for water flow at the base plane of simulated MHSs (y = 4 mm), when Reynolds number is 500, are depicted in Fig. 9. It can be seen that both the temperature and the temperature gradient are high near the fins. Obviously, for the corrugated MHSs, the temperature distributions at the exit part are more uniform compared to the straight MHS and they have higher outlet temperature. It can be explained as the corrugated fins are employed in the MHSs, the flow path and total surface area are enlarged, swirl flows are generated, boundary layers are interrupted, hot fluid near the fins and cold fluid in core regime are mixed better, thereby the heat transfer is enhanced. It is noted that for the MHSs with plate fins, the temperature in the core regime is lower, while shows higher values near the fins. After
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Fig. 9. Effect of plate and plate-pin fins on temperature contours of water-cooled corrugated MHSs at Reynolds number of 500.
introducing of plate-pin fins in the corrugated MHSs, the temperature near the plate fins visibly decreases, so the corrugated MHSs with plate-pin fins show a smaller temperature difference between the core regime and the fins wall. It leads to higher temperature values at the exit of corrugated MHSs with plate-pin fins. From experiments, it is recorded that utilizing Al2O3/water nanofluids is associated with heat transfer enhancement in the corrugated MHSs. The variations of heat transfer coefficient for nanofluids compared to the base fluid, i.e. water, are tabulated in Table 2. As shown, the enhancement of heat transfer coefficient is further increased with increment of nanoparticles weight fraction in the base fluid. This is because the increment of nanoparticles concentration brings more enhancements in thermal conductivity of coolant and interaction between nanoparticles and fins. It leads to higher values of the heat transfer coefficient for nanofluid with greater concentration. With respect to the geometry effect, the nanofluid flow in the corrugated MHS with trapezoidal plate fins shows the greatest enhancements as compared to other cases.
differences in the friction factor are not significant. It is apparent from Fig. 10(b) that the corrugated MHSs have higher friction factor than the straight MHS. In other words, the pressure drop is the lowest for the straight MHS. As it can be seen in Fig. 7, it has a smooth flow path without any blocking effects with corrugations or pins.
4.3. Hydraulic performance In addition to the thermal performance, the hydraulic characteristic is another important factor for the application of MHSs. Fig. 10(a–b) shows the comparison of corrugated MHSs with straight MHS from the hydraulic performance point of view. Fig. 10(a), which shows the relation between pressure drop and Reynolds number, signifies that with the increase of Reynolds number, the pressure drop augments for all MHSs. It is found that the pressure drop for the corrugated MHSs with plate fins are larger than that of the corrugated MHSs with plate-pin fins. However, the
Table 2 Variations of heat transfer coefficient for nanofluids compared to base fluid (%). Corrugated MHS
0.1% nanofluid
0.3% nanofluid
1. Triangular & plate 2. Triangular & plate-pin 3. Trapezoidal & plate 4. Trapezoidal & plate-pin 5. Sinusoidal & plate 6. Sinusoidal & plate-pin
12.9 12.4 14.1 11.2 11.8 13.3
21.2 19.6 22.8 18.3 19.1 20.7
Fig. 10. Effect of plate and plate-pin fins on hydraulic performance of water-cooled corrugated MHSs (a) pressure drop (b) friction factor augmentation.
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Fig. 11. Effect of plate and plate-pin fins on velocity vectors and temperature contours of water-cooled corrugated MHSs at Reynolds number of 900.
In order to have a better understand from the fluid flow and heat transfer characteristics, the velocity vectors and temperature contours at zoom views in the corrugated MHSs are demonstrated in Fig. 11. Note that in the convection heat transfer, the temperature and velocity fields are coupled. It is clear that there are remarkable differences in the velocity vectors and temperature contours of the corrugated MHSs. By comparing the velocity vectors of the plate and the plate-pin fins, it can be seen that at the same conditions, the plate-pin structure of fins intensifies the number and size of swirl flows in the corrugated MHSs. Higher and larger swirl flows in the corrugated MHS with plate-pin fins could lead to chaotic advection which dramatically enhances the convective fluid mixing and heat transfer. Note that in addition to the number and size, the potential of heat transfer enhancement in the corrugated MHSs depends on the location and strength of generated swirl flows relative to the fins which have higher temperature. As depicted in Fig. 11, in the corrugated MHSs with plate-pin fins, the expansion and strength of main longitudinal swirl flows in corrugations is considerable in comparison with the corrugated MHSs with plate fins. This causes a significant exchange between the core and the fin fluids. It is also
shown that as a plate fin is interrupted into the plate-pin fins, a corner longitudinal swirl flow starts to generate behind each fin. Due to the high temperature gradient in the location of generated swirl flow, a local heat transfer enhancement occurs in this area and the temperature of coolant increases. Similar to the thermal performance, the hydraulic performance of corrugated MHSs can be affected when water as coolant is replaced with a nanofluid. For instance, the variations of pressure drop for nanofluids compared to water are presented in Table 3. It can be seen Table 3 Variations of pressure drop for nanofluids compared to base fluid (%). Corrugated MHS
0.1% nanofluid
0.3% nanofluid
1. Triangular & plate 2. Triangular & plate-pin 3. Trapezoidal & plate 4. Trapezoidal & plate-pin 5. sinusoidal & plate 6. Sinusoidal & plate-pin
5.6 3.8 7.2 4.6 6.5 4.3
17.9 10.1 19.5 12.8 19.2 10.6
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that the nanofluids show larger pressure drop values compared to water and the pressure drop increases with nanoparticles concentration. 4.4. Overall thermal-hydraulic performance From the results presented in Sections 4.2 and 4.3, it is found that the fin shape, fin structure, Reynolds number, and nanoparticles weight fraction have significant influences on both the thermal and the hydraulic performances of corrugated MHSs. Hence, the overall performance of corrugated MHSs should be evaluated using an appropriate hydrothermal performance factor. In this regard, the hydrothermal performance factor defined in Eq. (15) is considered to appraise the overall effectiveness of corrugated MHSs compared with that of the straight MHS [30]. NuCorrugated MHS =NuStraight MHS η¼ 1 =3 f Corrugated MHS =f Straight MHS
ð21Þ
The relationship between the hydrothermal performance factor and Reynolds number for water flow inside the corrugated MHSs is depicted in Fig. 12. It is evident from the figure that the performance factor values of corrugated MHSs with plate-pin fins are higher than those of corrugated MHSs with plate fins. In whole range of Reynolds number, the performance factor of all corrugated MHSs with plate-pin fins is larger than unity and it increases with increasing of Reynolds number. This means that the overall performance of corrugated MHSs improves at higher Reynolds numbers. As an example, the hydrothermal performance factor can reach 1.72 at Reynolds number of 900 for water flow inside the corrugated MHS having sinusoidal plate-pin fins. It is noticeable to state that at lower Reynolds numbers, the maximum values of performance factor are obtained for the corrugated MHS with trapezoidal plate-pin fins, while at higher Reynolds numbers, the maximum values are observed for the corrugated MHS with sinusoidal plate-pin fins. The effects of tested nanofluids on the hydrothermal performance factor of corrugated MHS are illustrated in Fig. 13. Comparing between Figs. 12 and 13, the nanofluids do not affect the performance factor of corrugated MHSs in low Reynolds numbers and there is no noticeable increase in comparison to water. Likewise, as Reynolds number goes up, the performance factor enhances further, and this is more evident at higher Reynolds numbers. In other words, using nanofluids in the corrugated MHSs causes a better hydrothermal performance in high Reynolds numbers in comparison to lower Reynolds numbers. At the studied range, the maximum performance factor of 1.84 is recorded for the 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins.
Fig. 13. Effect of plate and plate-pin fins on thermal-hydraulic performance of nanofluidcooled corrugated MHSs.
5. Conclusion In the present study, we compare the thermal and hydraulic performances of plate and plate-pin fins in corrugated miniature heat sinks (MHSs). This analyses is performed for different configurations of corrugated fins, namely triangular, trapezoidal, and sinusoidal. In the second part, the performance of Al2O3/water nanofluid in the corrugated MHSs with both the plate and the plate-pin fins is examined compared to water as base fluid. According to the obtained results, concluding remarks are drawn as follow, ➢ The use of corrugated fins in the MHSs leads to considerable enhancement in heat transfer with a certain pressure drop penalty in comparison with the straight MHS. Highest values of the heat transfer coefficient and pressure drop are recorded for the corrugated MHS with trapezoidal fins. ➢ It is shown that the plate-pin fins poses higher heat transfer coefficient and lower pressure drop values than the plate fins in the corrugated MHSs. For instance, the heat transfer coefficient is increased about 22.9% and the pressure drop is decreased about 49.3% in the corrugated MHS with sinusoidal fins, when the plate fins are changed with the plate-pin fins. ➢ For all corrugated MHSs, the Al2O3/water nanofluid can enhance the heat transfer coefficient effectively albeit with a penalty in the pressure drop. However, the results express that it has higher effects on the heat transfer coefficient than the pressure drop. ➢ Likewise, we can also see that the hydrothermal performance factor of corrugated MHSs enhances as Reynolds number goes up. The values of corrugated MHSs with plate-pin fins are higher than those of corrugated MHSs with plate fins. ➢ At the studied range, the maximum performance factor of 1.84 is recorded for the 0.3% nanofluid flow in the corrugated MHS with sinusoidal plate-pin fins. Finally, the current work will help designers to select a corrugated MHS with better hydrothermal performance in microelectronic systems.
Fig. 12. Effect of plate and plate-pin fins on thermal-hydraulic performance of watercooled corrugated MHSs.
Nomenclature Ac minimum free flow area, m2 At active heat transfer area, m2 a corrugation amplitude, m cp specific heat, J·kg−1·K−1 Dh hydraulic diameter, m E dependent variable e independent variable
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f G h L l m Nu Q q Re Δp s T V w
friction factor mass velocity, kg·m−2·s−1 heat transfer coefficient, W·m−2·K−1 MHS length, m corrugation length, m mass flow rate, kg·s−1 Nusselt number heat transfer rate, W heat flux, W·m−2 Reynolds number pressure drop, Pa distance between thermocouples location and MHS, m temperature, K velocity, m/s minichannel width, m
Greek symbols
density, kg·m−3 dynamic viscosity, Pa·s thermal conductivity, W·m−1·K−1 nanoparticles fraction hydrothermal performance factor
ρ μ κ φ η
Subscripts
cond conv f in m out w s
conduction convection fluid inlet mean outlet wall solid
Acronyms
MHS TEM XRD
miniature heat sink transmission electron microscopy X-ray diffraction
Acknowledgements The corresponding author would like to thank Mr. O. Sartipzadeh for his kind help in the experimental setup fabrication at Islamic Azad University (IAU) of Shahrood Branch. References [1] Y.T. Yang, H.S. Peng, Investigation of planted pin fins for heat transfer enhancement in plate fin heat sink, Microelectron. Reliab. 49 (2) (2009) 163–169. [2] P. Cova, N. Delmonte, F. Giuliani, M. Citterio, S. Latorre, M. Lazzaroni, A. Lanza, Thermal optimization of water heat sink for power converters with tight thermal constraints, Microelectron. Reliab. 53 (2013) 1760–1765. [3] M. Conrad, A. Diatlov, R.W. De Doncker, Purpose, potential and realization of chipattached micro-pin fin heat sinks, Microelectron. Reliab. 55 (2015) 1992–1996.
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Please cite this article as: M. Khoshvaght-Aliabadi, et al., Comparison of hydrothermal performance between plate fins and plate-pin fins subject to nanofluid-cooled corrugated miniature heat..., Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.01.005