A Micro-Metal Inserts Based Microchannel Heat Sink for Thermal Management of Densely Packed Semiconductor Systems

Abstract

The thermal management of high-heat-density devices is essential for reliable operation. In this work, a novel procedure is proposed and investigated for the efficient thermal management of such devices. The proposed procedure introduces different arrangements of metal inserts within a cooling channel heat sink. The objective of those inserts is to form boundary layers to prevent any hot spots from appearing within the flow and increase temperature uniformity. Five different arrangements are introduced and numerically investigated using the commercial software package ANSYS FLUENT 2021R1. The model was validated against previous findings and showed a good agreement with errors of less than 5.5%. The model was then used to study the heat transfer characteristics of the proposed cases compared to traditional straight channels under the same operating conditions. All the proposed arrangements displayed better heat transfer characteristics than the traditional configuration within the studied range. They also exhibited lower temperature nonuniformities, implying better temperature distribution. The temperature contours over the heat source top surface and the flow streamlines are also introduced. Among all the proposed arrangements cases, a microchannel with micro metal insert located at the top wall along with a second row of inserts covering two-thirds of the bottom wall is studied. This case achieved the best heat transfer characteristics and highest temperature uniformity, making it a viable candidate for high power density devices’ thermal management.

1. Introduction

Recently, there has been a considerable increase in compact, high-performance electronic devices in almost every aspect, including, but not limited to, manufacturing, education, communication, transportation, and entertainment. This has led to increasing demand for high-power micro-electronic chips [1,2]. To maintain the reliability and the high performance of said microchips, their operating temperatures should be kept below 85 °C. Therefore, controlling the microchips’ temperatures has become one of the main challenges threatening the widespread electronics industry. This thermal management challenge arises due to two factors. The first one is the high-power density of these chips, which generates high heat flux rates exceeding 1000 W/cm² in some local spots [3,4]. The second factor is the demand for a compact design of these chips, which reduces the available space for heat removal. These two factors eliminated the ability to use conventional thermal management techniques. Therefore, finding novel thermal management techniques that can fulfill the required heat dissipation rates has become an intriguing issue that has concerned many researchers. As part of these devoted efforts, researchers have employed nanofluids [5,6], phase change materials [7,8], and liquid metal [1] as cooling fluids.

Utilizing microchannel heat sinks is considered an efficient tool that can be used to cool down electronic components at a high heat rate. The first microchannel heat sink was presented by Tuckerman and Pease, who presented a simple design comprising several parallel channels [9] capable of dissipating up to 790 W/cm² from the surface of the chip with a relatively low pumping power. Since then, many researchers have tried to enhance the thermal performance of the microchannel heat sink with variable degrees of success.

The effect of using different channel configurations on heat transfer performance was previously investigated [10,11]. It was found that rectangular cross-section microchannels exhibit better heat transfer performance compared to trapezoidal and triangle cross-section microchannels. It was also concluded that the pressure loss is directly proportional to the channel aspect ratio. Hung et al. [12] numerically examined the effect of enlarging the outlet of the microchannel heat sink. The pressure drop was found to be reduced by the increase in the enlargement ratio. On the other hand, Nusselt number, temperature control, and heat transfer efficiency increased.

The impact of adding ribs to the side walls of straight microchannels on the heat transfer performance was also studied. Different cross sections of ribs were tested, including rectangular, semi-circular, and triangular, with different angles [13,14,15]. Using ribs improved the heat transfer performance at lower values of Re. On the other hand, a pressure drop increase was observed. Adding cavities to the straight channel reduced the pressure drop and the heat transfer performance. Thus, a combination between cavities and ribs could enhance heat transfer performance while maintaining an acceptable pressure drop value [16,17,18].

The use of wavy microchannels to reduce the temperature of the electronic components was also investigated [19,20,21]. It was noticed that a secondary flow was generated when the flow passed through the wavy channels, which resulted in an enhancement in the fluid mixing and an improved heat transfer performance [22]. A numerical investigation led by Mohammed et al. [23] estimated the optimal amplitude of the wavy channel to be between 0.063 and 0.22 µm. However, increasing the amplitude resulted in poor performance compared to conventional straight channels. The pressure drop and the friction factor were found to be increased with the increase of the amplitude. The effect of adding secondary branches to the wavy microchannels was numerically and experimentally studied by Chiam et al. [24]. The advantages of the secondary branches could be found at lower values of Re (<100), while increasing Re over that range resulted in a higher pressure drop compared to conventional wavy channels. This was not the case when secondary branches were added to wavy channels at relatively small amplitudes (<0.075 µm), with high transfer performance and lower pressure drop values.

Chuan et al. [25] and Gong et al. [26] utilized porous media within the walls of the microchannels. It was reported that porous walls reduced the viscous stresses and thus the pressure drop. The pressure drop was reduced by 48% when porous media was used compared to solid walls [25]. Also, the heat transfer performance was enhanced when porous walls were used.

The effect of adding a secondary channel to the flow path on the heat transfer performance of the microchannels was numerically studied [27,28]. Using secondary channels along with ribs reduced the pressure drop by up to 50%. The heat transfer was also enhanced by increasing the flow mixing between the channels [27]. Multi-objective algorithm optimization was used to find the best heat sink geometry with secondary flow channel design [28]. The optimization aimed to minimize the pressure drop and maximize the heat transfer rate. The optimized microchannel reduced the pumping power and the thermal resistance by 23% and 29%, respectively.

As can be seen from the previous research, various efforts were applied to enhance heat transfer within microchannels. However, there is always room for more innovative ideas. The current work investigates the effect of inserting a structured micro-sized metal mesh into the streamline on the heat transfer performance. The proposed concept depends on inducing the formation of a boundary layer by attaching metal inserts with different placements to avoid any hot spots within the device. The design is based on constructal law adopted to modify an actual mini-size straight channels heat sink device. Different cases were studied by dividing the channel length into three zones with the same inlet and outlet conditions.

The main objectives of this work are listed in the following bullet points:

• To describe a promising approach to reduce the high-temperature gradient levels associated with the stream direction, which presents a main downside of the micro channel-based cooling systems;
• To introduce metal inserts to develop a secondary flow that improves the heat transfer and reduces the flow maldistribution;
• To remove any local hotspots which could harm the physical structure of the semiconductor devices, consequently, electronic components’ life span and performance;
• To reduce thermal management systems’ power consumption without compromising cooling performance and reliability.

2. Numerical Modeling and Simulation Analysis

A computational fluid dynamics (CFD) model is established using the commercial package ANSYS Fluent 2021R1 to simulate the thermal management system’s fluid flow and heat transfer. The high-performance computing facility of Maha Cluster at the University of Sharjah was used for simulation. A detailed description of the modeling procedures and case setup is discussed in the following subsections.

2.1. Physical Model and Proposed Configurations

The physical description of the presented model is shown in Figure 1. The heat source is a microelectronic silicon chip with an area of 25 mm × 25 mm, directedly bonded to the main board from the bottom side. Meanwhile, the chip is directly attached to the bottom of a cooling channel. In the current work, the chip is simulated as a constant heat source that acts at the cooling channel bottom wall. The designs used in the current work are shown in Figure 2. The channel dimensions and geometries were designated considering the constraints of 3D metal printing and pumping requirements. The figure shows two schematic graphs to identify the characteristics of the channel geometry of a traditional straight channel and one of the newly introduced cases. An isometric view with a magnification of the internal channel structure sections A-A cross-sectional view of the channel in the middle of the coolant domain is presented. As illustrated in the figure, Case 0 refers to the baseline or the standard straight channel heat sink, whereas cases 1 to 5 present the modified channels. Micro metal inserts are placed in the flow stream at different configurations, as shown in the figure, to improve the heat transfer rate in the cooling channels. As seen from the figure, in Case 1, a single row of metal inserts is introduced in the upper half of the flow path. Case 2 introduces another shorter row of metal at the corner that occupies only about one-third of the area. Case 3 introduces the same second short row as in Case 2 but in the middle. Case 4 presents a longer second row that covers two-thirds of the flow area, whereas Case 5 introduces two complete rows that cover the whole area. The proposed idea is to develop boundary layers to break any hot spots within the device. A parametric study is performed to trade off heat dissipation rates and pumping requirements. As for the coolant, water is used as the working fluid during the numerical study with thermophysical properties carefully defined as polynomial equations in temperature, as described in

Table 1. Thermo-physical properties of cooling fluid as a function of the temperature [29,30].

Property = A + B × T + C × T2 + D × T3 + E × T4, (T in Absolute)
Coefficient	ρ (kg/m3)	Cp (J/kg·K)	K(W/m·K)	µ (Pa·s)
A	−1184.2713	5025.1	−0.785392198460943	0.41260813
B	24.66772581	−4.7536	0.00759075936901133	−0.004756694
C	−0.1032172737	0.0047	−0.00000993306796402867	0.000020683412
D	0.0001919823623	0.000006	-	−0.000000040117972
E	−0.0000001374629319		-	0.000000000029250643

. The detailed heat sink and channel dimensions are listed in

Table 2. Detailed general dimensions of the cooling channel.

Term, Dimension	Value (mm)
Hest sink width	25
Hest sink Length	25
Channel height	2
Channel height	1
Walls thicknesses	0.5
Metal inserts width and height	0.2
Void width and height	0.2–0.3

.

2.2. Model Assumptions

In the current work, mass, momentum, and energy conservation are simultaneously solved to predict the flow characteristics. Some simplifications and assumptions are adopted to simulate the heat transfer and fluid flow characteristics of the current 3-dimensional (3D) model. Concerning the operating conditions:

• The simulations are contacted under 3D steady state steady flow conditions;
• Single-phase, incompressible, and laminar fluid flow prevails across the channel;
• The body forces and the effect of viscous heating are ignored;
• Very smooth walls (No-slip condition at walls). This assumption was based on Knudsen number (Kn) calculations. It is valid when the channel characteristic length is significantly bigger than the mean free path i.e., Kn < 0.001 [31]. In this case, as liquids are incompressible, the mean free path can be considered a constant. A good approach for water is to set the mean free path around 0.31 nm. Therefore, in microfluidic channels with characteristic length scales of more than 300 nm, we can safely assume no-slip boundary conditions;
• The gravity influence is neglected. This assumption is valid for small spaces and tight streams, as confirmed by Dang et al. [32]. As the height of the current cooling (H_HS) channel is only 1 mm, and the calculations are conducted under single-phase and incompressible flow circumstances, the consequence of gravity is ignored in the current simulation. Furthermore, forced convection is assumed to be dominant, with no local density differences.

2.3. Boundary Conditions

The boundary conditions used in the numerical model are depicted in Figure 3 and can be summarized as follows:

• Inlet working fluid velocity with Reynolds number (Re) spanning from 1000 to 2000;
• Inlet working fluid temperature of 293 K;
• Pressure outlet boundary;
• A heat flux of 100 W/cm² at the top wall;
• Symmetric left- and right-hand side walls;
• All other surfaces are considered adiabatic walls.

2.4. Grid Sensitivity Test

A structured mesh was generated using ANSYS Meshing. Figure 4a presents a sample of the structured mesh at different locations. A mesh-independence investigation was carried out before the model was used to study each design case. The grid sensitivity test was performed concerning the average interface temperature, temperature nonuniformity, and pressure drop. A Reynolds number of 2000, an ambient temperature of 293 K, and a heat flux of 100 W/cm² were selected as simulation conditions for the mesh sensitivity study. Different computational structured grid sizes were studied. All the studied grid sizes were physically controlled hexahedral configurations. The coarsest studied element size mesh was 250 μm, and the smallest mesh size was 20 μm. The coarse and extra fine mesh sizes element numbers were between 6000 and 8,000,000 elements, respectively. Figure 4b–d present the effect of changing mech size on the average wall temperature, the nonuniformity, and the pressure drop respectively. The percentage error between each consecutive mesh size was calculated to seek a < 1% error value. Therefore, a mesh of four million elements was chosen to reduce computation time while maintaining acceptable accuracy.

2.5. Model Validation

The CFD model is validated using previous literature investigations utilizing water as a single-phase coolant. The validation was conducted for multi-bifurcation cooling channel at different coolant flow rates, as shown in Figure 5. The numerical results are consistent with Xie et al. [33] data for the same conditions. Nusselt number and pressure drop values were compared. As can be seen from Figure 2a,b, the average variation between any two numerical values was found to be less than 5.5% for the Nusselt number and less than 2.8% for the pressure drop in all investigated cases. Also, the generated Nu values for case 0 were compared to the Sieder–Tate correlation [29] and were found to be in good agreement, as can be seen from Figure 2c. Hence, the mathematical model’s dependability was confirmed and established.

The error analysis was estimated using the root mean square percent deviation (RMSD) and the mean absolute percent error (MAE) [34] techniques as follows:

$$MAE\left(\%\right)=\frac{100}{n}{\displaystyle \sum }_1^n\left|\frac{X_{sim,i}-X_{exp,i}}{X_{exp,i}}\right|$$

(1)

$$RMSD\left(\%\right)=100\times \sqrt{\frac{{{\displaystyle \sum }}_1^n{\left(\frac{X_{sim,i}-X_{exp,i}}{X_{exp,i}}\right)}^2}{n}}$$

(2)

where $X_{sim,i}$, $X_{exp,i}$ are the predicted and experimental values. The range of errors using MAE and RMSD were 0.56% and 0.7% for Nusselt number. As for the pressure drop, the error was very small (less than 0.1% for both techniques). The Nusselt number error analysis for case 0 had error of 1.85% and 1.89%, respectively.

The data obtained from the model was reduced using the equations mentioned in Appendix A.

3. Results and Discussion

Numerical studies of the heat transfer performance were carried out for all the considered cases with various metal mesh insert locations and lengths. The inlet Re was specified in the range of 1000 to 2000, and the corresponding ranges of the volumetric flow rate and inlet velocity were calculated. The convective heat transfer coefficient was evaluated in each case (Case 1 to Case 5) and compared with the reference case (Case 0). Figure 6 introduces the heat transfer coefficient and Nu change with the inlet Re for all investigated cases. Over the Re range, the heat transfer performance of Case 0 (a cooling channel without any metal insert) showed the lowest heat transfer performance.

As shown in Figure 6, the impact of the metal inserts on the heat transfer coefficient and Nu is significant compared to the reference case in all the proposed configurations. At the lowest inlet Re < 1000, cases 4 and 5 with a longer length of the second row of the metal insert attained a slightly higher heat transfer coefficient than that with a short length (Cases 2 and 3) and Case 1 with a single row. Although Case 5 exhibited comparable heat transfer coefficient values to those of Case 4, the Nu number values are relatively low due to the decrease in the hydraulic diameter. At the studied range, Case 4 had the highest values among all the cases. This means that Case 4 has the best thermal performance in heat transfer.

Figure 7 compares solid, fluid, and total thermal resistances between the conventional Case 0 and the enhanced Cases 1 to 5. All the thermal resistances’ fluid thermal resistance decreased significantly with any increase in Re. As can be seen from the figure, the thermal resistance initially dramatically decreased with the increases of the Re, then the reduction rate diminishes for higher Re values.

Figure 8 shows the variations of the Nusselt number ratio (Nu/Nu₀) and the fanning friction factor ratio (f/f₀) with Re, where the denominators present the values for Case 0. From Figure 8a, increasing Re had no significant effect on the Nu/Nu₀, or the f/f₀ values within the studied range. Case 1 exhibited the lowest Nu/Nu₀ and f/f₀ values, whereas Case 4 attained the highest values of about Nu/Nu₀ = 5, and f/f₀ of about 15.

The efficiency evaluation criterion (EEC) is used to evaluate the enhanced performance at identical Re. From Figure 9, Re had a negligible effect on the thermal performance of all the investigated cases. Again, Case 4 exhibited the best performance within the studied range. The performance factor (PF), which measures the EEC to the power of 1/3, is used to gauge the overall effectiveness of the proposed design. The value of describes how successful the thermal system is in reducing pressure drop. If the value is more than 1, it means that thermal performance is better than pressure drop, and if it is less than 1, it means the opposite.

The nonuniformity degree within the heat source for all the proposed configurations was compared with the base case to determine the impact of the metal inserts on the wall temperature uniformity at all Re ranges and the same operating conditions. It was observed that the temperature variation was decreased for all cases with the increase in Re, thereby enhancing the temperature distribution uniformity. It is also clear from the figure that the introduction of the metal inserts considerably enhanced the wall temperature uniformity and reduced the temperature gradient with the length of the device. Cases 3 and 4 showed the lowest nonuniformity levels over the Re range. For Cases 3 and 4, the average uniformity enhancement compared to Case 0 was about 85.4% and 86.6%, respectively. For instance, when Re = 2000, nonuniformity in Case 0 was 48 K, whereas it was 5.84 K and 4.7 K in Cases 3 and 4, respectively. For Cases 1, 2, and 5, the average enhancement of wall temperature uniformity was 67.1%, 82%, and 78.3%, respectively. The metal inserts improved the heat transfer generally and deduced flow and heat maldistribution, which can be interpreted as the metal inserts regenerating the boundary conditions, which kept the heat transfer capability of the working fluid along the flow stream (Figure 10).

Figure 11 shows the temperature contours of the heat source when the structured metal inserts are involved under the same heat flux of 100 W/cm² and Re = 2000. All the subfigures used different legends scales due to the significant difference in the obtained results. The figure shows the typical wall temperature distribution contours, which match the literature [33,35,36]. The contours show that the metal inserts considerably reduced the average wall temperature and nonuniformity. It is evident that the metal inserts’ length and petition control the flow field and hotspot location. For more details, Cases 1 and 5 are comparable with Case 0 as the metal inserts were placed along the flow stream. However, in Case 5, the cooling channel is wholly packed with metal inserts, which is not the case in Case 1, where the metal inserts were placed in the top half of the channel. The difference between the two designs (Cases 1 and 5) is reflected in the pressure drop value, nonuniformity (even though the contours distribution is almost the same), and average wall temperature. For Case 2, the metal inserts had a negative effect where the hot spot occurred near the heat source center, a critical position in which any hotspots must be avoided. In the last two, Cases 3 and 4, the lowest nonuniformity levels were achieved, as depicted in the figure. However, Case 4 is preferable as the metal inserts were packed after 1/3 of the channel length from the inlet. In the regions near the inlet, the cooling fluid temperature is typically low, so boundary regeneration is not as important.

For more clarification, the streamlines of each case at Re = 2000 are shown in Figure 12. An automatically generated legend is used to show areas of high and low-velocity values. The enhancement in the average wall temperature, uniformity, and Nu mentioned earlier can be justified more with the flowing velocity streamlines. It can be noted that the flow inside the flow channel was distributed differently due to the packing of the metal inserts. Hence, higher interaction between the solid surface and the incoming flow. The effect of distributed flow channels generated by the metal inserts is reflected in the enhancement of heat transfer and heat dissipation. As shown in Figure 12a for Case 0, the large flow channels show low resistance to the incoming flow, simplifying its stream along the channel without any distributed manner.in contrast, in Cases 1 to 5, the complex micro inserts’ inner structure forces the flow to change trajectory as it flows past the flow channel, inducing vortices that enhance turbulence and heat transfer.

4. Conclusions

Thermal management of high heat flux surfaces is essential with the recent progress in the high computing devices. In this study, a new technique is proposed to improve the thermal management of high-power of these devices. The proposed technique introduces metal inserts within the flow path of a cooling channel. These inserts can be monolithically fabricated within the flow channel during the fabrication with the use of 3D metal printing technology. The intent of using the inserts is to break the flow and generate boundary layers that decrease the formation of hot spots within the flow. Five different configurations were introduced and numerically compared. The fluid flow and heat transfer characteristics of these configurations are compared. The results showed that using micro inserts in the microchannel enhances the heat transfer compared to the conventional channel without micro-metal inserts. For instance, using micro inserts on part of the bottom wall of the heated wall of the microchannel attained an average uniformity enhancement of 86.6% compared to the conventional smooth case. Further, at Re = 2000, the temperature non-uniformity decreased from 48 °C for the smooth case to 4.7 °C for the case with using metal inserts covering two-thirds of the bottom heated wall.