Experimental and numerical investigations of heat transfer and flow characteristics of cross-cut heat sinks

International Journal of Heat and Mass Transfer 102 (2016) 142–153

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Experimental and numerical investigations of heat transfer and flow characteristics of cross-cut heat sinks Sakkarin Chingulpitak a,b, Nares Chimres a, Kitti Nilpueng c, Somchai Wongwises a,⇑ a Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand b The Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand c Research Centre for Combustion Technology and Alternative Energy (CTAE), Department of Power Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangsue, Bangkok 10800, Thailand

a r t i c l e

i n f o

Article history: Received 27 February 2016 Received in revised form 22 May 2016 Accepted 23 May 2016 Available online 18 June 2016 Keywords: Heat sink Parallel flow Cross cut Plate fin Forced convection

a b s t r a c t This study aims to experimentally and numerically investigate the heat transfer and flow characteristics of plate-fin and cross-cut heat sinks. The accuracy of the measured data is verified by comparing them with the exiting correlations. In the case of the cross-cut heat sink, the effects of cross-cut lengths (Lc) and number of cross-cuts (Nc) are presented. The experimental results show that the cross-cut heat sink with Lc = 1.5 mm gives the lowest thermal resistance. In the case of a numerical study, the numerical results are validated by comparing them with the measured data. The comparison results show that the present model gives reasonable agreement with the measured data. Consequently, the present model is used to find the optimal length and number of cross-cuts. From the numerical results, it is found that the thermal resistance of a cross-cut heat sink with Lc = 1.5 mm and Nc = 6 is 16.2% lower than that of a plate-fin heat sink at the same pumping power. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Over the past several years, the development-related tendency of electronic devices has been to become more compact. Meanwhile, the performance of electronic devices still remains the same or higher than that of older electronic devices. Therefore, the thermal performance improvement of electronic cooling systems is very important. The heat sink is a major part of an electronic cooling system and leads to an increase in the heat transfer area. It is commonly made from aluminum or copper. It can be divided into two main types of fin shapes: the plate fin and pin fin. Many researchers have focused on the optimum design of a plate-fin heat sink based on various fin heights and levels of thickness [1–3]. Li and Chao [1] experimentally investigated the effects of fin height, fin thickness, and Reynolds number on the thermal performance of plate-fin heat sinks. For a given fin thickness, the results showed that the thermal resistance of the plate-fin heat sink decreased with an increase in the fin height. This was due to the fact that the heat transfer area of the higher fin height was larger than that of the lower fin height. For a given fin height, the optimal levels of fin thickness that provided the lowest thermal resistance were ⇑ Corresponding author. Tel.: +662 470 9115; fax: +662 470 9111. E-mail address: [email protected] (S. Wongwises). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.098 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

obtained at different Reynolds numbers. Li et al. [2] presented the effects of fin height, fin thickness, and number of fins on the thermal resistance of plate-fin vapor chamber heat sinks. The experimental study was conducted under various Reynolds numbers from 10,000 to 60,000. Moreover, the surface temperature distribution of heat sinks was also presented by using infrared thermography. For a given fin height and number of fins, the effect of fin thickness on the overall thermal resistance decreased as the Reynolds number increased. In the case of various fin heights, at a given fin thickness and number of fins, the overall thermal resistance decreased with an increase in the fin height because the heat transfer area of the heat sink increased. Notably, the effect of fin height on the decrease of thermal resistance became less significant as the fin height exceeded 20 mm. Wu et al. [3] presented the theoretical model to predict the thermal performance of a plate-fin heat sink. It was developed for a wide range of Reynolds numbers. Finally, they proposed the optimized geometries of the plate-fin heat sink by using their present model. However, some research has been done on heat transfer enhancement through increasing the turbulent flow of the working fluid at the inlet and fin tip clearance of the plate-fin heat sink [4–9]. Recently, Chingulpitak and Wongwises [4] reviewed the literature on the effect of flow directions and behaviors on the thermal performance of heat sinks. They found that only some

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143

Nomenclature ce1, ce1, cl cp Dh H k L _ m P DP Pp Q Re Rth t tf T V V_ U u; v ; w W x, y, z

turbulent model constant specific heat (kJ/kg °C) hydraulic diameter (m), Dh ¼ 2Hf W c =ðHf þ W c Þ height (m) turbulent kinetic energy (m2/s2) length (m) mass flow rate (kg/s) pressure (Pa) pressure drop (Pa) pumping power (W), Pp ¼ V_ DP heat transfer rate (W) Reynolds number thermal resistance (°C/W) time (s) fin thickness (m) temperature (°C) velocity (m/s) volume flow rate (m3/s) velocity vector velocity components (m/s) width (m) Cartesian coordinates

papers discussed the behavior of a fluid flowing into a heat sink. Li et al. [5] studied the effects of a triangular vortex generator, which was installed in front of a test section, on the thermal resistance and pressure drop of a plain-fin heat sink. They conducted a study on the effect of the attack angles of vortex generators, the distance between both of the trailing edges, the distance between a vortex generator and heat sink, and Reynolds numbers. They concluded that the optimal position of a vortex generator occurs when the distance between the trailing edge of the vortex generator and the heat sink is zero. The proper position of the distance between the trailing edges of the vortex generator equals the width of the heat sink. Moreover, the optimized thermal performance of the plain-fin heat sink was achieved at an attack angle of 30°. At a Reynolds number of 10,000, the result indicated that the thermal resistance of the heat sink with the vortex generator was lower than that of the heat sink without vortex generator by about 27%. Zhang et al. [6] studied the effects of a shield on the heat transfer performance of a plate-fin heat sink. The shield was attached to the inner-top surface of the wind duct in order to increase the turbulent flow on the fin tip. The experimental results indicated that the optimized height and position of the shield were equal to half of the fin height and zero, respectively. Suzana et al. [7] numerically obtained the effects of the bypass flow on the thermal performance of a heat sink by using CFD code. They varied the fin density, air flow rate, and clearance area ratio to study the effects on the bypass flow over the heat sink. The results showed that the bypass flow increased with increasing fin density and clearance distance. Prstic and Bar-Cohen [8] experimentally and numerically investigated the effects of fully shrouded, partially shrouded and shielded heat sinks on the thermal performance of a plate-fin heat sink. A shield for the plate-fin heat sink was used to reduce the effect of the bypass flow. The results show that the pressure drop of the shielded heat sink was found to be much lower than that of the fully shrouded heat sink. Furthermore, the thermal resistance of the shielded heat sink was similar to that of the fully shrouded heat sink. Elshafei [9] presented the bypass flow effect of a plate-fin heat sink with various air flow rates, number of fins, and tip-toshroud distances. The experimental results at the high number of

Greek letters D differential e dissipation kinetic energy (m2/s3) l viscosity (kg/ms) lt turbulent viscosity (kg/ms) U dissipation function q density (kg/m3) rk diffusion Prandtl number for k re diffusion Prandtl number for e k thermal conductivity (W/m2°C) Subscripts a avg b c ch f in out plate

air average value base of heat sink cross-cut channel fin inlet outlet plate-fin heat sink

fins showed that the air flows more through the clearance distance between the fin tips and shroud than into the fin passages. This is because the air flow was obstructed due to the increase of fin density. Finally, the proper size of the tip-to-shroud distance was obtained at a Reynolds number above 7000. Furthermore, several research studies have been done on heat transfer improvement with an increase in the turbulent flow of a working fluid in the flow passage of a plate-fin heat sink [10,11]. Yang et al. [10] experimentally studied the pressure drop and heat transfer coefficient of plate-fin heat sinks with eight different fin patterns. The fin patterns of the tested heat sinks were: (1) plain fin; (2) delta vortex generators (delta VG) fin; (3) semi-circular VG fin; (4) delta VG and plain fin; (5) triangular VG fin; (6) triangular-attack VG fin; (7) dimple VG fin; and (8) two-group dimple VG fin. The experimental results show that the triangular-attack VG fin was considered the optimum design of fin patterns. The surface area of the triangular-attack VG fin was 12–15% lower than that of the plain fin at a frontal velocity of about 3–5 m/s and the same heat transfer capacity and pumping power. The experimental results showed that all of the vortex generators were more beneficial than the plain fin pattern was. Kim and Kim [11] experimentally studied the effects of cross-cuts on the thermal performance of heat sinks with various cross-cut lengths, positions, and number of cross-cuts. Among the variable parameters, the results showed that the cross-cut length gave the most significant effect on the thermal performance of a heat sink. The thermal resistance of a cross-cut heat sink was lower than that of plate-fin and square pin-fin heat sinks—about 5–18% and 14–16%, respectively. Moreover, the comparison results were presented in a contour map for selecting the type of heat sink, which was plotted as a function of the dimensionless pumping power and the length of the heat sink. As mentioned above, most of the previous works have studied the effect of the geometry parameters of a plate-fin heat sink, such as thickness and fin height on thermal performance. However, there is still room for improvement in the fin shape of a plate-fin heat sink to increase the thermal performance, which is especially based on reliable manufacturing processes. Thus, this research

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air flow behavior inside the cross-cut heat sink was observed by using smoke and recorded by high-speed photography. Based on the experimental data, the thermal performance of the cross-cut heat sink is calculated in the following procedures: The heat transfer rate from the heat sink to the air can be determined by the following equations:

aims to explore experimental and numerical studies on heat transfer and the flow characteristics of plate-fin heat sinks that are cut transverse (cross-cut heat sink) under the parallel flow condition. The experimental study is conducted to measure the data of plate-fin and cross-cut heat sinks, and in order to verify the numerical results. Moreover, for the numerical study, the lengths of the cross-cut are considered to find the optimum size that gives the maximum heat transfer rate.

_ a cp;a ðT a;av g;out  T a;av g;in Þ Qa ¼ m

ð1Þ

_ a is mass flow rate of air, cp;a is specific heat of air, and where m T a;av g;in and T a;av g;out are average air temperature at the inlet and outlet, respectively. The heat supply (Qheater) is calculated by multiplying the voltage drop and current through the plate heater. The average heat transfer rate between the heat supplied to the test section and the heat absorbed by the air can be determined by the following equation:

2. Experimental apparatus and procedure In order to study the thermal resistance and pressure drop of air flowing through cross-cut heat sinks, the experimental apparatus is set up as shown in Fig. 1. It consists of a wind tunnel, fan with inverter, straightener, and test section. The rectangular wind tunnel is made from an acrylic plate with a 5 mm thickness. The width, height, and length of a wind tunnel are 27 mm, 25 mm, and 800 mm, respectively. Air flow is circulated inside the wind tunnel by using the variable speed fan with an inverter. The straightener is installed to minimize the lateral velocity components caused by the swirling motion in the air flow in the entrance region. Air velocity is controlled at ranges of 1–4 m/s and is measured by the hot wire anemometer with an accuracy of ±1.0% of full scale. T-type thermocouples are used to measure air temperature at the inlet and outlet of the test section. The pressure drop of the air flow across the cross-cut heat sink is measured by the differential pressure transducer with an accuracy of ±0.5% of full scale. The 100watt plate heater is installed at the bottom of the heat sink. To adjust the heat supplied to the heat sink, the plate heater is connected with the variable alternating circuit (AC) transformer. The heat sink base and plate heater are covered with the bakelite plate of 20 mm thickness to reduce heat loss. The thickness of heat sink base is 8 mm. The temperature at the bottom surface of the heat sink is controlled at 70 °C. At a 0.5 mm depth below the top surface of the heat sink base, two thermocouples are installed to measure the wall temperature of the heat sink as shown in Fig. 2. An uncertainty of all temperature measurements is ±0.1 °C. The data acquisition system is used to record the experimental data. For the test section, four aluminum cross-cut heat sinks with different crosscut lengths are used. The width (Wb) and length (Lb) of heat sinks are 27 mm and 75 mm, respectively. It consists of six plate fins with a thickness (tf) of 1 mm and a channel width (Wch) of 3 mm as shown in Fig. 3. The number of cross-cuts (Nc) is two and cross-cut lengths (Lc) are 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm. This paper is a continuation of the authors previous work, some relevant examples of the investigation of flow visualization in rectangular and annular channels are shown in Ref. [12–15]. They conducted experiments to visualize the flow patterns of single- and two-phase flows in small gap channels. In the present study, the

Q av g ¼ ðQ a þ Q heater Þ=2

ð2Þ

The thermal resistance (Rth) of the air flowing through the crosscut heat sink can be calculated from

Rth ¼

ðT b;av g  T a;av g Þ Q av g

ð3Þ

where T b;av g is the average heat sink base temperature, and T a;av g is the average air temperature. The Reynolds number (Re), based on hydraulic diameter, is calculated by

Re ¼

qVDh l

ð4Þ

where V is the average frontal velocity of the air at a flow passage between fins, and Dh is the hydraulic diameter of the flow passage between fins. To drive the air through the heat sink, the pumping power (Pp) requirement is defined by

Pp ¼ V_ DP

ð5Þ

where V_ is the volume flow rate of the air, and DP is the total pressure drop between the inlet and outlet of the test section. 3. Theory 3.1. Mathematical model and numerical method The 3D turbulent flow of the air and the heat transfer of the plate-fin and cross-cut heat sinks are proposed. The air flow is assumed to be incompressible, to be 3D, and to flow steadily. The effects of buoyancy and radiation heat transfer are neglected. The governing equations of mass, momentum, and energy for steady turbulent flow [16,17] are as follows:

1030 800 288

230

60 Insu lator

100

98

T

Fan with in ver ter

Straigh tener

T

216.5

A

Test section

27 Wind tunnel d uct

200

40

35

45

35

A 25

40

T

45

Acrylic p late

200

ΔP

+ -

Var iac (Con trol H eat Flux) Sect ion A-A

Fig. 1. Schematic diagram of the experimental apparatus.

Unit: mm

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Fig. 2. Detail of the test section.

Energy equation:

Wch tf

Lf

Hf Lb Wb Fig. 3. The configuration of cross-cut heat sink.

Continuity equation:

ð6Þ

ð7aÞ

Dv @P þ div ðl grand v Þ y-momentum q ¼ @y @t

ð7bÞ

Dw @P ¼ þ div ðl grand wÞ @t @z

ð7cÞ

z-momentum q

@ðqkÞ þ div ðqkUÞ ¼ div @t





lt grad k rk

Transport equation for e:

Momentum equation:

Du @P ¼ þ div ðl grand uÞ x-momentum q @t @x

Di ¼ p div U þ div ðk grand TÞ þ U Dt

ð8Þ

For the primary checking of the present model, the laminar and k–e turbulence models are taken into account for calculation purposes. Based on the experimental conditions of this study, the air velocity is considered in the range of a Reynolds number from 700 to 1800. The comparison results show that the present model with the k–e turbulence model gives a better prediction when compared to considering laminar flow. This is because the turbulent flow may occur at a low Reynolds number due to the air flow’s disturbance in the cross-cut region, which is consistent with the study of Sahiti et al. [18]. They found that, because Re P 500, the laminar model cannot predict the flow characteristic of air flowing through the pin-fin heat sink. They concluded that the flow is already in the transition region. Thus, in this present model, the air flowing through the cross-cut heat sink is considered to be a turbulent flow. The standard k–e turbulence model [16,19] is used to predict the air flow characteristic as follows: Transport equation for k:

Lc

@u @ v @w þ ¼0 þ @x @y @z

q





lt grad e rk e2  C 2e q

@ðqeÞ þ div ðqeUÞ ¼ div @t

þ 2lt Eij  Eij  qe

ð9Þ

e

þ C 1e 2lt Eij  Eij k

k

ð10Þ

The turbulent viscosity can be represented as:

lt ¼ qcl

2

k

e

ð11Þ

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The empirical constants appear in the turbulence model and are given by the following values:

cl ¼ 0:09;

ce1 ¼ 1:44;

ce2 ¼ 1:92;

rk ¼ 1:0;

re ¼ 1:3:

3.2. Computational domain and simulation settings

no-slip and adiabatic conditions. The interface area between the air and heat sink is set to be a no-slip wall and no thermal contact resistance. The relative pressure at the outlet of the air domain is set as 0.0 Pa. 3.4. Validation and optimization

In this study, the commercial program ANSYS CFX 16.0 is used to solve the numerical problems of the mathematical model. The high resolution transient scheme is used to discretize the main governing equations. Fig. 4 shows the computation domains of the air and heat sink, which are considered to be in the steady state. To save the computer resource, the thickness of the heat sink base is 0.5 mm according to the position of the thermocouples, which is described in the experimental apparatus. The heat sink is made from aluminum with a thermal conductivity of 237 W/ mK. The thermal conductivity of the air is 0.0261 W/mK. The density, viscosity, and specific heat of the air is 1.185 kg/m3, 1.831  105 kg/ms, and 1.005 kJ/kg °C, respectively. The convergence of the iterative solution is achieved when the residual root mean square (RMS) errors are less than 104. In the case of mesh generation, the air and heat sink domains are investigated with unstructured non-uniform grid system. The meshes are mainly generated in tetrahedral, prismatic, and pyramid elements. Moreover, the grid independency is investigated carefully to ensure the validity and accuracy of the simulation results. For this purpose, the number of elements, 748,729, 1,608,544, 3,167,598, 5,550,018 and 8,659,710, are employed. The simulation results show that the variation of pressure drop and heat transfer rate is smaller than 0.5% for the number of element of 5,550,018. It can be concluded that the numerical predictions can be considered as the grid independency. However, the same number of elements cannot be generated for all geometries of the heat sink. Thus, in this study, the element number varies between 3,800,000 and 5,880,000 elements.

The numerical results are validated by comparing them with the measured data under the same conditions. The tendency of the comparison results, including the cross-cut length and number of cross-cut effects, are considered to verify the present model. Moreover, in this study, the optimum design parameters of the cross-cut heat sink are presented. In terms of the optimum design parameter, the effect of the cross-cut lengths of 0.5, 1.5, 2.0, 3.5 and 4.0 mm on the heat transfer rate is considered. The other parameters are the same as the dimensions of the tested heat sink as shown in Table 1. 4. Result and discussion In order to verify the accuracy of the experimental data, the thermal resistance and pressure drop for the plate-fin heat sink is compared with exiting correlations from the previous researchers [20,21]. The pressure drop of the air flowing across the crosscut heat sink is measured directly by the differential pressure transducer. The average uncertainty of pressure drop is the accuracy of differential pressure transducer which is ±0.5%. Based on the root mean sum square method, the average uncertainty of thermal resistance is ±3.0%. The experimental results show that the tendency of the experimental data is consistent with that of the exiting correlations. That is, the thermal resistance of the plate-fin heat sink decreases and the pressure drop increases with an increasing Reynolds number as shown in Fig. 5a and b. The mean absolute deviation (MAD) between the measured data and correlations are 5.03% and 8.03% for thermal resistance and

3.3. Boundary conditions The heat sink is assumed to be continuity material. This means that the effect of thermal contact resistance on the heat transfer between the base and fin is neglected. The temperatures at the bottom surface of the heat sink are in the range of 40–60 °C. The air flow is set to be uniform flow at the inlet boundary condition, with the velocities of 2, 3, and 4 m/s. The flow is fully developed at the front of heat sink. The air temperatures are given as 33 °C at ambient pressure. All of the side walls are characterized as featuring

Table 1 Design parameters of cross-cut heat sink for numerical investigation. Unit: mm. Base

Cross-cut fin

Width, Wb

27

Height, Hf

25

Length, Lc

Length, Lb Thickness, tb

75 0.5

Thickness, tf Channel width, Wch

1 3

Number of fin, Nf Number of cross cut, Nc

Outlet

Lf

Heated

Inlet (Uniform flow)

Fig. 4. Computational domain.

0.5, 1.0, 1.5, 2.0, 3.5, 4.0 6 2, 4, 6

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Experimental data Correlation of Teertstra et al. [20] 3

Plate-fin heat sink Lf = 75 mm Wch = 3 mm

o

Thermal resistance, Rth,plate ( C/W)

4

tf = 1 mm 2

1

0 700

800

900

1000

1100

1200

1300

1400

1500

1600

1400

1500

1600

Reynolds number, Re

(a) 50 Experimental data Correlation of Muzychza and Yovanovich [21]

Pressure drop, ΔP (Pa)

40

Plate-fin heat sink Lf = 75 mm Wch = 3 mm tf = 1 mm

30

20

10

0 700

800

900

1000

1100

1200

1300

Reynolds number, Re

(b) Fig. 5. Comparison between experimental data obtained from plate-fin heat sink with existing correlations. (a) Thermal resistance (b) Pressure drop.

pressure drop, respectively. Therefore, it can be concluded that the experimental apparatus is reasonably accurate for measuring the pressure and temperature of the test section. 4.1. Flow behavior In this section, the flow behavior of the air along the cross-cut heat sink as well as the effects of air velocity and cross-cut length on thermal resistance and pressure drop are investigated both experimentally and numerically. Based on the numerical results, the relationship between the thermal resistance ratio and pumping power for different cross-cut lengths and numbers of cross-cuts is presented. To observe the air flow behavior inside the cross-cut

heat sink, the flow visualization by using smoke and velocity vectors from the simulation are presented in Fig. 6. Based on the experimental and numerical results, the air flow inside the crosscut heat sink can be separated into two parts. The first part is that air flows along the core of the channel. The second part is that air flows at the cross-cut region. It is found that some parts of the air flow into the cross-cut region before striking the next plate fin and returning to the channel. This flow mechanism leads to the mixing of the air flow inside the channel. In addition, it can be clearly seen that the recirculation zone possibly occurred at the trailing edges of the fins as shown in Fig. 6c. Based on the simulation result, it is found that the air flow disturbance at the cross-cut regions increases with increasing in the air velocity and cross-cut length.

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Flow direction

(a)

Main flow Mixed zone Section A

Main flow Mixed zone

(b)

Recirculation zone

Mixed zone

(c) Fig. 6. Flow behaviour of air inside the cross-cut heat sink. (a) Experiment (b) Simulation (c) Simulation (Section A).

4.2. Effect of air velocity The relationships between the thermal resistance, pressure drop, and Reynolds number are shown in Figs. 7 and 8, respec-

tively. As expected, an increase of air velocity leads to a decrease of thermal resistance and increase of pressure drop. It can be explained that the turbulence of air flow inside the channel increases with increasing air velocity. Moreover, it is evident that

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4

Lc = 0.5 mm Lc = 1.0 mm 3

o

Thermal resistance, Rth,c ( C/W)

Experimental data

Cross-cut heat sink tf = 1 mm Wch = 3 mm

Numerical results Lc = 0.5 mm Lc = 1.0 mm

Nc = 2

2

1

0 700

800

900

1000

1100

1200

1300

1400

1500

1600

Reynolds number, Re Fig. 7. The relationship between Reynolds number and thermal resistance.

60

Pressure drop, ∆P (Pa)

50

40

Experimental data Lc = 0.5 mm

Cross-cut heat sink tf = 1 mm

Lc = 1.0 mm Numerical results Lc = 0.5 mm Lc = 1.0 mm

Wch = 3 mm Nc = 2

30

20

10

0 700

800

900

1000

1100

1200

1300

1400

1500

1600

Reynolds number, Re Fig. 8. The relationship between Reynolds number and pressure drop.

the disturbance in the main flow due to the cross-cut effect is also higher. These are the causes of the decrease of thermal resistance in the cross-cut heat sink. In Fig. 8, the results show that pressure drop increases with increasing air velocity as a result of the higher friction between the air and fin surface, and the flow disturbance at the cross-cut regions. By considering the comparison results in Figs. 7 and 8, it is clearly seen that the numerical results agree well with the measured data, with MADs of 5.72% and 12.7% for thermal resistance and pressure drop, respectively. 4.3. Effect of cross-cut length Fig. 9 shows the effect of cross-cut length (Lc) on the thermal resistance. It is evident that thermal resistance decreases when

the cross-cut length increases from 0.5 mm to 1.5 mm. However, it slightly increases when the cross-cut length is greater than 1.5 mm. Based on the presented data, it is indicated that the optimum thermal resistance occurs at a cross-cut length around 1.5 mm. The reason for this result can be explained by the turbulent flow and heat transfer area, due to varying cross-cut lengths. That is, the increase of the cross-cut length results in the increase of turbulent flow and decrease of thermal resistance. Meanwhile, it leads to the decrease of the heat transfer area and the increase of thermal resistance. This indicates that the effect of turbulent flow is higher than that of the heat transfer area when the cross-cut length is smaller than 1.5 mm. Conversely, the effect of turbulent flow is dominated by the effect of the heat transfer area as cross-cut length is higher than 1.5 mm, resulting in a higher thermal resistance.

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1.8

1.4

o

Thermal resistance, Rth,c ( C/W)

1.6

1.2 1.0 0.8 0.6 0.4

Experimental data Re = 1337 Re = 1783 Numerical results Re = 1337 Re = 1783

Cross-cut heat sink tf = 1 mm Wch = 3 mm Nc = 2

0.2 0.0 0.0

0.5

1.0

1.5

2.0

2.5

Cross cut length, Lc (mm) Fig. 9. Effect of cross-cut length on thermal resistance.

By considering the effect of cross-cut length on the total pressure drop as shown in Fig. 10, it can be seen that the total pressure drop increases with increasing cross-cut length. It is clearly seen that the total pressure drop greatly increases when the cross-cut length is lower than 1.0 mm. However, as the cross-cut length is greater than 1.0 mm, it is slightly changed. This is due to the fact that the total pressure drop inside the channel consists of a frictional pressure drop and a pressure drop due to the cross-cut effect. This means that, at a narrow cross-cut length (Lc 6 1.0 mm), the total pressure drop mainly depends on the pressure drop due to the cross-cut effect, resulting in a large change in the total pressure drop. On the contrary, at a larger cross-cut length (Lc > 1.0 mm), the influence of the decrease of frictional pressure drop due to the reduction of the surface area is higher. Therefore,

it leads to a slight change of the total pressure drop. The effect of cross-cut length on the thermal resistance and pressure drop is also calculated as shown in Figs. 9 and 10. The numerical results show good agreement with measured data for thermal resistance and pressure drop. The MADs are around 2.82% and 10.28%, respectively. Based on the comparison results, it is evident that the present numerical model is reliable for predicting the air flow behavior inside the cross-cut heat sink. Thus, the present model is used to find the proper dimension of the cross-cut heat sink by comparing it with the plate-fin heat sink. The relationships between the thermal resistance ratio and pumping power at different cross-cut lengths, along with the number of cross-cuts, are presented in Figs. 11–13. The thermal resistance ratio is defined as the ratio of the thermal resistance of the cross-cut heat

40 Experimental data Re = 1337 Re = 1783 Numerical results Re = 1337 Re = 1783

Pressure drop, ΔP (Pa)

30

Cross-cut heat sink tf = 1 mm Wch = 3 mm Nc = 2

20

10

0 0.0

0.5

1.0

1.5

2.0

Cross cut length, Lc (mm) Fig. 10. Effect of cross-cut length on pressure drop at different Reynolds numbers.

2.5

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1.4

Thermal resistance ratio, Rth,c/Rth,plate

Numerical results

Lc = 0.5 mm Lc = 1.5 mm

tf = 1.0 mm 1.2

Wch = 3.0 mm

Lc = 3.5 mm Lc = 4.0 mm

Nc= 2 700 < Re < 1800

1.0

0.8

0.6 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Pumping power, Pp (W) Fig. 11. Effect of cross-cut length on thermal resistance ratio.

Thermal resistance ratio, Rth,c/Rth,plate

1.00

0.95

0.90

0.85

0.80

Cross-cut heat sink tf = 1 mm

Pp = 0.011 W, Pp = 0.031 W,

Wch = 3 mm 0.75

0.70 0.0

Nc = 4

1.0

2.0

3.0

4.0

Cross-cut length, Lc (mm) Fig. 12. Variation of thermal resistance ratio with cross-cut length.

sink to the thermal resistance of the plate-fin heat sink (Rth,c/Rth,plate). Pumping power (Pp) is calculated by multiplying the between-volume flow rate and pressure drop. Fig. 11 shows the relationship between the thermal resistance ratios and pumping power at different cross-cut lengths. It is found that the thermal resistance ratio is higher when the pumping power is increased. At the same pumping power as shown in Fig. 12, the thermal resistance ratio decreases as the cross-cut length increases from 0.5 mm to 1.5 mm. It is nearly constant when the cross-cut length is changed between 1.5 mm and 2.0 mm. However, the thermal resistance ratio increases when the cross-cut length is higher. This indicates that the range of optimum crosscut length is between 1.5 mm and 2.0 mm. As shown in Fig. 13a, under the same pumping power, it is clearly seen that the thermal

resistance ratio decreases with an increasing number of cross-cuts at Lc = 2.0 mm (Lc 6 2.0). On the contrary, at Lc = 4.0 mm (Lc > 2.0), the thermal resistance ratio increases with an increasing number of cross-cuts as shown in Fig. 13b. From the numerical results in Fig. 13a and b, it can be concluded that the thermal resistance ratio depends on both the cross-cut length and number of crosscuts together. To specify the proper dimension of the cross-cut length and number of cross-cuts for the cross-cut heat sink, the dimensionless parameter is presented in terms of Lc/tf. Based on the data in this study, it can be concluded that the changing of the cross-cut length leads to the optimum condition of the thermal resistance ratio when 1.5 6 Lc/tf 6 2.0. Under this conditions, it is also found that the increase of the number of cross-cuts results in the decrease of the thermal resistance ratio.

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Thermal resistance ratio, Rth,c/Rth,plate

1.4

1.2

Numerical results tf = 1.0 mm

Nc = 2 Nc = 4

Wch = 3.0 mm

Nc = 6

Lc = 2.0 mm 700 < Re < 1800 1.0

0.8

0.6 0.00

0.02

0.04

0.06

0.08

Pumping power, Pp (W)

(a) 1.4

Thermal resistance ratio, Rth,c/Rth,plate

Numerical results

1.2

tf = 1.0 mm

Nc = 2 Nc = 4

Wch = 3.0 mm

Nc = 6

Lc = 4.0 mm 700 < Re < 1800

1.0

0.8

0.6 0.00

0.02

0.04

0.06

0.08

0.10

Pumping power, Pp (W)

(b) Fig. 13. Effect of number of cross-cut on thermal resistance ratio. Lc = 2.0 mm (b) Lc = 4.0 mm.

5. Conclusion This paper presents the thermal-fluid characteristics of air flowing inside cross-cut heat sinks. The effect of Reynolds number, cross-cut length, and number of cross-cuts on thermal resistance and pressure drop are investigated experimentally and numerically. Based on the numerical simulation, the thermal resistance ratio of the cross-cut heat sink to the thermal resistance of the plate fin heat sink (Rth/Rth,plate) under the same pumping power (Pp) is also investigated. The experimental results show that, at the cross-cut regions, some parts of air turned to the gap before striking the next plate fin and returning to the channel. This flow mechanism leads to the turbulence of air flow inside the channel. Under the same Reynolds number, the lowest thermal resistance

appears at a cross-cut length of 1.5 mm. The numerical results indicate that, under the same pumping power, the optimum thermal resistance ratio occurs when the cross-cut length range is between 1.5 mm and 2.0 mm. In addition, an increase of the number of cross-cuts results in the decrease of the thermal resistance ratio as the cross-cut length is lower than 2.0 mm.

Acknowledgements The authors would like to thank the ‘‘Research Chair Grant” National Science and Technology Development Agency (NSTDA), the Thailand Research Fund (RGJ PhD. Program) and the National Research University Project (NRU) for the support.

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