Performance-Enhanced Double Serpentine Minichannel Heat Sink for Phased-Array Radar High-Heat-Flux Chip Cooling

Abstract

Efficient cooling is necessary for the reliability of phased-array radars for a longer life. With the miniaturization and functionalization of microchips, heat flux generated by these chips also rises sharply. Existing liquid cooling techniques are inadequate to meet the ever-increasing cooling requirements. The present paper examines the potential to enhance the convective heat transfer of minichannel heat sinks (MCHSs). Two types of double serpentine minichannel heat sinks are investigated and compared. The first one is a traditional-design MCHS with plate fins, while the second one is a performance-enhanced MCHS design. Three-dimensional conjugate heat transfer models are developed, and the equations governing flow and energy are solved numerically with ANSYS Icepak. The results indicate that the novel MCHS design is found to significantly reduce both the average pressure drop across the minichannels and the total thermal resistance by up to 51% and 8.5%, respectively. Meanwhile, heat transfer enhancement can be obtained for all the rib oblique angles from 13° to 163°, while lowest average pressure drop can be obtained near 90°. The present study provides a new choice for researchers to design more effective MCHSs for the cooling of modern phased-array radar high-heat-flux chips.

1. Introduction

Heat transfer is a vital problem in many engineering fields, and it is also a major challenge in phased-array radar applications. Temperature management of high-heat-flux chips is a crucial aspect for electronics engineers to ensure the safe operation of phased-array radars for a longer duration. Particularly, the inexorable miniaturization of electronic components and increase in electronic packaging density drives the development of more efficient thermal management methods. One of the promising options with the ability to dissipate high heat fluxes over a small area is single-phase micro/minichannel heat sinks. The most appealing feature of micro/minichannels is the incredibly little volume required on the bottom of the devices, typically in compact electronic devices, which allows for integration with as little sacrifice as possible to system compactness [1,2].

The idea of water-cooled microchannel heat sinks with a straight rectangular microchannel came from the pioneering work of Tuckerman and Pease [3] in cooling VLSI applications in 1981. In their experiments, heat fluxes of up to 790 W/cm² could be dissipated with a large pressure drop of 214 kPa across the heat sink for a substrate temperature rise of 71 °C. They also found that the heat transfer coefficient can be increased through decreasing the hydraulic diameter of the channels, but with the expense of increased pressure loss.

The current advanced solution for liquid forced convection cooling using a liquid cold plate heat sink is shown in Figure 1 [4], where there will be two thermal interface material (TIM) layers. Even though TIMs are designed for good conductivity, the contact resistance of the TIM is still a big problem. Also, there exist three main drawbacks for this liquid forced convection cooling solution. Firstly, the presence of the TIMs represents a significant thermal resistance contribution. Secondly, the temperature gradient along the chip surface causes the coolant to be heated up along the cooling channels. Finally, the pressure drop inside the channel scales with the channel length, resulting in a higher pressure drop.

With the goal of enhancing the thermal performance of conventional straight rectangular cross-section micro/minichannel heat sinks, several studies have investigated the fluid flow and heat transfer characteristics after the pioneering work of Tuckerman and Pease. Numerous structures of flow channels for micro/minichannel heat sinks have been proposed, for example, spiraling radial inflow channels, zig-zag channels, multistage channel in-flow, wavy channels with alternating secondary branches, consecutive bifurcating channels, different pin-fin-shaped channels, and different types serpentine channels, as can be seen in the review article of Ghani et al. [5]. For instance, the work of Ahmed et al. [2] examined the potential to decrease the thermal resistance and enhance heat transfer of a serpentine heat exchanger by introducing chevron fins, which create secondary flow paths. This new design was found to significantly reduce both the pressure drop across the heat exchanger and the total thermal resistance, and it enhanced the average Nusselt number compared with a serpentine heat exchanger with plate fins.

The uneven bottom surface temperature distribution of micro/minichannel heat sinks will be induced by the limitation of a single inlet and outlet arrangement. Different entrance and exit arrangements have been proposed to upgrade the evenness of the bottom surface temperature and obtain high convective heat transfer coefficient. Liu et al. [6] proposed non-uniform mini baffles to improve the flow distribution, reporting that promotions in flow maldistribution are realized by the non-uniform baffles. Saeed et al. [7] used an analytical model to ensure the uniform distribution of liquid flow within heat sink channels under minimum sizes of the distributor and collector header. Liu et al. [8] proposed a flow into the second flow paths at the last stage and conducted numerical analysis of the impact of the flow path bifurcation structure and dimensions on the uniformity of flow distribution. Ramos Alvarado et al. [9] used the flow region configurations of two modified versions of serpentine microchannels to realize unexceptionable flow uniformity at a remarkably low pressure loss in planar plate heat sinks. Vinodhan et al. [10] proposed a novel MCHS consisting of four components with a scattered coolant entrance and exit plenum for each component. The work of Cao et al. [11] proposed a novel double serpentine MCHS design with through-holes punched in the wall of serpentine microchannels and interleaved in–outlets to decrease the substrate temperature gradient of traditional single serpentine minichannel heat sinks. It can be found that the introduction of interleaved inlet–outlets provides much better uniform substrate temperature; meanwhile, the pressure drop can be reduced.

As included in the study of Fedorov and Viskanta [12], Qu and Mudawar [13], and Li et al. [14], the dependence of the thermo-physical properties of the fluid (i.e., density and viscosity) on temperature must be included in order to accurately capture the linear increase in the channel wall temperature. The rise in surface temperature also limited the efficiency of conventional straight microchannel heat sinks. Additionally, heat transfer performance deteriorated when the flow inside a straight channel became regular and the boundary layer grew. Extensive studies have been conducted on flow channels that inherently provide boundary layer interruption, secondary flows, and chaotic advection that promote heat transfer without a modest change in pumping power. And heat transfer enhancement can be performed via passive means by creating flow disruption, altering the shape of the channel, changing the channel curvature, the introduction of secondary flows, three-dimensional mixing, channel roughness, or attachments to increase surface area and turbulence, altering fluid properties through fluid additives (using nanoparticles) [15,16,17,18,19].

The use of a manifold microchannel is another heat transfer enhancement technology for liquid-cooled microchannel heat sinks [20,21]. Recently, Shen et al. [20] designed and fabricated a silicon-based thermal test chip including staggered pin-fin microchannels and rectangular microchannels with the same area size embedded on each side of the chip, in order to improve the heat dissipation capacity of liquid-cooled manifold microchannel heat sinks. Compared to rectangular microchannel heat sinks, the staggered pin-fin microchannel heat sink could reduce the chip surface temperature by 8 K at the inlet flow rate of 5 mL/s, but the pressure drop increased by 10.46%. The work of Pu et al. [21] proposed a new modified manifold microchannel heat sink (MMCHS) and conducted an extended investigation of the MMCHS for divergent/convergent manifold channels. The findings indicated that the modified MMCHS with baffles reduced average thermal resistance. However, it was observed that the average pressure drop increased in all cases; the average pressure drop even increased by 106.96% in certain configuration compared to typical MMCHSs.

Tao et al. [22] summarized three probable mechanisms for improving single-phase heat transfer: (1) reducing the thermal boundary layer, (2) increasing flow interruptions, and (3) increasing the velocity gradient near the heated surface. Heat transfer enhancement is the outcome of all possible combinations of these three mechanisms. Indeed, the practicality of these methods might be questioned at any time, as the goal is not only to achieve high heat flux but also to achieve greater efficiency and reliability. Pumping power reduction, hot-spot mitigation, production costs, and other special needs emerging from various applications must be considered in the development of heat transfer enhancement methods.

The present study is the first to explore the benefits of using a novel design for single-phase liquid-cooled minichannel heat sinks (MCHSs) where chevron fins and triangular ribs are used together within double serpentine minichannels to control the hydrodynamic and thermal boundary layers. The research findings offer a new choice for the development of more effective cooling solutions and achieve almost fairly good performance improvement compared with the work of Ahmed et al. based on a permutation genetic algorithm, for which the decrement in the pressure drop across the heat exchanger and the total thermal resistance are 60% and 10%, respectively. It should be noted that the design in the present paper has not undergone any structural optimization. Our latest preliminary work combining multi-objective genetic algorithm and topology analysis shows further performance improvement of this novel design. Effects of the novel design on the fluid flow and heat transfer characteristic at different inlet volumetric flow rates and different rib oblique angles are described in detail in the following parts.

2. Problem Descriptions and Data Acquisition Methods

2.1. Design of Minichannel Heat Sink

Two different types double serpentine MCHSs were designed using UG NX 10.0. The first one adopted double serpentine minichannels with plate fins (DSMPFs), while the second one adopted double serpentine minichannels with chevron fins and triangular ribs (DSMTFs). For the sake of facilitating a fair comparison between the two different MCHS configurations, both heat sink models shared the same heat sink size (W × L), channel footprint area (W_fa × L_fa), channel depth (H_ch), channel width (W_ch), fin wall width (W_w), heat sink depth (H), and heat sink base thickness (H_b), as listed in

Table 1. Main dimensions for DSMPF and DSMTF MCHSs (unit: mm).

Characteristics	DSMPF	DSMTF
Heat sink dimensions, W × L × H	40 × 40 × 6
Minichannel footprint area, Wmc × Lmc	30 × 30
Main channel width, Wch	1.5
Fin width, Ww	1
Channel depth, Hch	2
Heat sink base thickness, Hb	2
Hydraulic diameter, Dh,ch	1.714
Outer radius of the curved main channel, R1	2.0
Inner radius of the curved main channel, R2	0.5
Secondary flow channel width, wsc	-	0.5
Secondary flow channel length, lsc	-	1
Leading radius of secondary flow channel, rsc	-	0.5
Chevron fin length, lf	-	1.3
Chevron fin pitch, pf	-	2.3
Chevron oblique angle, θf	-	30°
Triangular rib width, wr	-	0.5
Triangular rib height, hr	-	0.5
Triangular rib pitch, pr		0.8
Triangular rib oblique angle, θr		25°

. Here, the minichannel hydraulic diameter is defined as follows:

$$D_{h,ch}={\displaystyle \frac{2\left(W_{ch}\cdot H_{ch}\right)}{W_{ch}+H_{ch}}}$$

(1)

Figure 2a shows a schematic diagram of the size dimensions of the heat sinks and the double serpentine minichannels with plate fins (DSMPFs) considered in the present paper. During the design of the DSMTF heat sink, the continuous plate fin walls of the serpentine minichannel were firstly broken into small chevron fins to form the chevron secondary microchannels, as shown in Figure 2b. Then, small triangular ribs were placed on the straight walls of the chevron fins, as depicted in Figure 2c. The width and height of the triangular ribs were set as half of the fin wall width, which was 0.5 mm for the present design. The pitch between two adjacent ribs was set to 0.8 mm. The triangular rib oblique angle indicating the angle between the front edge of the rib facing the flow direction and the local main flow velocity vector direction was set to 25° originally.

Thus, secondary flow and turbulence flow would be produced by adding microchannels between the main flow minichannels, thus enhancing the convective heat transfer and obtaining a more homogeneous temperature distribution. Here, a chevron oblique angle of 30°, indicating the angle between the main channel and secondary channel, was adopted in the present design. This value lies in the range suggested by Suga and Aoki [23]. Also, the current design follows the recommendation of Suga and Aoki, whose work recommended that the ratio of the fin pitch in the spanwise direction to the fin length must be 1.5 times the tangent of oblique angle to provide a good balance between heat transfer and pressure drop.

2.2. Data Acquisition Methods

In the following analysis, the Reynolds number (Re) is calculated as follows:

$$\mathrm{Re}={\displaystyle \frac{{\rho }_f\cdot v_{in}\cdot D_h}{{\mu }_f}}$$

(2)

where ρ_f and μ_f are the density and viscosity of water, respectively, and v_in denotes the water inlet velocity to the MCHSs, while D_h is the hydraulic diameter at the inlet section of the MCHSs.

The total volumetric flow rate of the MCHSs is calculated as follows:

$$Q_v=2\cdot v_{in}\cdot \pi \cdot r^2$$

(3)

where r is the radius at the inlet section of the MCHSs, which is 1.5 mm.

Thermal resistance is defined by the ratio of the temperature difference of the substrate and the inlet of the minichannel to the heating power received by water in the minichannel region. Thus, the total thermal resistance of the MCHSs in the present study can be calculated as follows:

$$R_{th}={\displaystyle \frac{T_{w,\max }-T_{f,in}}{q}}$$

(4)

where T_{w, max} is the surface maximum temperature of the heat sink, while T_{f, in} is the water inlet temperature, and q is the total heat supplied into the MCHSs.

The average pressure drop (ΔP_avg) in the MCHSs is defined as the average pressure difference of the two serpentine minichannels:

$$\Delta P_{avg}={\displaystyle \frac{\left(p_{1,out}-p_{1,in}\right)+\left(p_{2,out}-p_{2,in}\right)}{2}}$$

(5)

where p_1/2,out and p_1/2,in are the average pressures at the outlet or inlet of the two separate minichannels, respectively.

3. Numerical Methods and Validations

3.1. Numerical Methods

The characteristic size of the minichannels in this paper lies in the range of several millimeters to a few tenths of a millimeter. Under this scale, N-S equations, non-slip wall condition, and Fourier’s law are all valid. Thus, numerical models of the three-dimensional flow and heat transfer in the MCHSs were developed in the FEM software ANSYS/Icepak under the assumptions listed below: (1) flow and heat transfer are steady with uniform flow velocity at the inlet; (2) the volume force and the impact of surface tension are neglected; (3) the effects of radiation and buoyancy are negligible; (4) the thermo-physical properties of water are supposed to be unchanged; (5) the axial conduction and viscous dissipation are not under consideration; (6) the contact thermal resistance between the MCHSs and the heat source is ignored.

Flow was modeled using the following general governing equations comprising continuity, momentum, and energy equations.

Continuity equation:

$$\nabla \cdot \overrightarrow{v}=0$$

(6)

Momentum equation:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \overrightarrow{v}\right)+\nabla \cdot \left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \cdot \left(\overline{\overline{\tau }}\right)+\rho \overrightarrow{g}+\overrightarrow{F}$$

(7)

$$\overline{\overline{\tau }}=\mu \left[\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)-{\displaystyle \frac{2}{3}}\nabla \cdot \overrightarrow{v}I\right]$$

(8)

Energy equation:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho h\right)+\nabla \cdot \left(\rho h\overrightarrow{v}\right)=\nabla \cdot \left[\left(\kappa +{\kappa }_t\right)\nabla T\right]+S_h$$

(9)

The control volume-based CFD methodology was used in the present study, and the above governing equations were solved simultaneously, which integrated the governing equations in each control volume. Discrete equations conserving each quantity on a control volume basis were obtained. The outputs included the temperature profile, pressure contour, velocity vectors, and the like. The convergence criteria for all the numerical computations were carried out using 1 × e⁻³ for the flow and 1 × e⁻⁷ for the energy equations.

3.2. Boundary Conditions and Thermo-Physical Properties

Inlet boundary conditions:

$$\overrightarrow{v}=v_{in},T=T_{f,in}=20°\text{C}$$

(10)

Outlet boundary conditions:

$$p=p_{out}=1atm$$

(11)

Interface between solid and coolant:

$${\overrightarrow{u}}_{s,wall}=0,T_{s,wall}=T_{f,wall}$$

(12)

While the conductive and convective heat transfer to the fluid were coupled by imposing heat flux continuity at the interface between the fluid and the solid walls, heat fluxes were applied underneath the heat sink for all the MCHS models. All the outer surface boundaries were considered to be adiabatic, except at the bottom of the MCHSs. Copper was chosen as the material of MCHSs, while the coolant was water. The thermo-physical properties of water and copper are shown in

Table 2. Thermo-physical properties of water and copper.

	μ, Pa*s	ρ, kg/m3	κ, W/(m*K)	Cp, J/(kg*K)
Water	0.001	998.2	0.6	4128
Copper	-	8933	387.6	390

.

3.3. Validations of Grid Sensitivity

Once the model (Figure 3a) had been finished being designed, a computational grid (Figure 3b) was generated as the basis of the solution procedure. Firstly, in order to test the influence of the grid number on the simulation accuracy, the grid-dependence of the numerical solutions was tested for the two different MCHS models. For the five sets of grids listed in

Table 3. Validations of grid independence.

	DSMPF
	Grid1	E%	Grid2	E%	Grid3	E%	Grid4	E%	Grid5
Grids	1.484 × 106		2.213 × 106		3.927 × 106		5.716 × 106		8.807 × 106
Tw,max (°C)	71.704	12.014	68.755	7.406	66.443	3.794	65.005	1.548	64.014
ΔP (Pa)	5274.60	15.194	5580.11	10.283	5754.37	7.481	5932.16	4.622	6219.64
	DSMTF
	Grid1	E%	Grid2	E%	Grid3	E%	Grid4	E%	Grid5
Grids	1.560 × 106		2.364 × 106		4.453 × 106		6.689 × 106		1.066 × 107
Tw,max (°C)	65.883	7.615	64.366	5.138	62.761	2.516	61.881	1.078	61.221
ΔP (Pa)	3054.83	11.598	3142.69	8.786	3261.89	5.327	3348.28	2.819	3445.42

, the max element sizes at each direction were equal to about 1/20, 1/30, 1/40, 1/50, and 1/60 of the computational domain dimensions, respectively. The mesh type was selected as hex-dominant. So, the mesh consisted mostly of hexahedral elements but included triangular or pyramidal cells. The numerical simulations were carried out at a water inlet velocity of 1 m/s and inlet temperature of 20 °C. A heat flux of 40 W/cm² (462.4 W) was supplied underneath the MCHSs.

The effects of the grid density on the predicted values of the maximum temperature on the heat sink wall (T_{w, max}) and the average pressure drop (ΔP_avg) are listed in Table 3. The deviation percentage (E%) of T_{w, max} and ΔP_avg were calculated with respect to the solutions on grid 5 in each case (absolute value). Finally, grid 4 was employed for all MCHS computations reported as a suitable compromise between efficiency and accuracy. The meshes for all the configurations mentioned below have proper resolution, smoothness, and low skewness, with additional refinement around the triangular ribs and chevron fins.

3.4. Validations Against Previous Studies

Numerical methods and the CFD software tool were also validated through comparison of the simulation results with the experimental results of Ahmed et al. for the serpentine minichannel heat sink with chevron fin structure. The heat sink used for numerical simulations had the same parameters as the one used in the experimental work of Ahmed et al. [2]. Water was used as the coolant, with flow rates varying from 0.180 to 0.318 L/min, which was in consistent with the experiments of Ahmed et al., corresponding to a Reynolds number (Re) of about 2545~4487. The water inlet temperature was set at 20 °C.

Two blocks equal to the size of the heaters were placed underneath the copper heat sink to represent the heaters used in the experiment, and each block gave a power of 50 W (31 W/cm²). A thin layer with a thickness of 200 μm and thermal conductivity of 2.2 W/(m*K) was placed between the blocks and the heat sink, representing the ethoxy material layer used in the experiment. Results were obtained in terms of the thermal resistance versus Re, as can be seen in Figure 4. In consideration of the accuracy of the numerical models and the inherent numerical calculation errors, the simulation results agreed reasonably well with the experimental results of Ahmed et al., with a maximum discrepancy of less than 6%.

4. Results and Discussions

4.1. Effects of Volumetric Flow Rates

In this section, volumetric flow rates from 0.063 L/min to 0.318 L/min are studied, which correspond to a Reynolds number range of 449~2246, depending on the hydraulic diameter of the water inlet tube. Thus, single-phase laminar flow regimes were considered in the flow channel, and heat fluxes of 40 W/cm² were supplied underneath the MCHSs for the DSMPF and DSMTF designs to simulate the heat generation of the electronic components. As we all know, the design of an MCHS must achieve lower thermal resistance with the least pressure losses. Thus, the effects of volumetric flow rate are studied in terms of average pressure drop (ΔP_avg) in the two separate channels and total thermal resistance (R_th) numerically.

The forced convection cooling system uses a pump to aid with fluid flow. The cross-sectional area for flow, volumetric flow rate, and pressure drop are all system limitations. The selected MCHS should have lower pressure losses than the pump delivery pressure to ensure the normal operation of the cooling system. It can be seen from Figure 5a that ΔP_avg increases as Re increases for both MCHSs. The DSMTF heat sink has a lower ΔP_avg compared to DSMPF, which is beneficial for system integration. The decline rate of ΔP_avg can be up to 51% in the present study. This significant reduction for the DSMTF design can be attributed to the flow of water between the chevron fins that form the secondary flow channels. Also, the disturbance of the triangular ribs to the fluid flow causes redevelopment of the flow boundary layer.

Thermal resistance (R_th) measures the resistance of the MCHS to dissipating the input power and is a commonly used parameter within the field of electronic cooling [24,25]. As can be seen from Figure 5b, R_th decreases monotonically with Re as a result of the decrease in the surface temperature of the MCHSs. The results indicate that using the DSMTF design typically leads to up to 8.5% reduction in the total thermal resistance compared with the DSMPF heat sink, from 0.076 to 0.068 K/W at Re = 2246 (0.318 L/min). This decrease in the total thermal resistance is probably due to the re-initialization of both the hydrodynamic and the thermal boundary layers at the leading edge of each triangular rib, which in turn lead to reductions in the thickness of the boundary layers. In addition, the effective heat transfer area for the DSMTF design is larger than the DSMPF one.

Figure 6 shows the pressure contours along the flow channel at the mid-depth plane of the channel at Re = 2246 for both the DSMPF and DSMTF designs. For both configurations, the entrances and exits of the coolant were located on the top side surface of the heat sinks, and both of the models had an interleaved inlet–outlet arrangement. That is, in the upper part of the flow channel, the coolant flows in from the left and leaves from the right, while in the lower part of the flow channel, the direction of the coolant flow is opposite. It can be seen that the average pressure drop across the DSMTF heat sink is about 60% of that for the DSMPF heat sink. This significant decrease in the pressure drop can be attributed to the secondary microchannels, which draw the coolant from the main minichannel into them and thus reduce the velocity in the main channel. It can also be seen in the figures that the pressure in the DSMTF design appears more uniform along the flow channel compared with the DSMPF design.

Figure 7 shows the temperature contours along the flow channel at the mid-depth plane of the channel at Re = 2246 for both the DSMPF and DSMTF designs. The temperature distributions of the two MCHSs are clearly different from each other. And the wall temperature increases with the flow length due to the sensible heat gain by the coolant. For the DSMTF MCHS, it can be seen that breaking the continuous serpentine fins into chevron shaped fins and the existence of triangular ribs have a significant influence on the temperature field. The formation of vortices leads to better fluid mixing between the main flow and secondary flow channels, which can cause a high temperature gradient over the heating microchannel wall. In addition, the DSMTF MCHS possesses a larger convective heat transfer area, thereby enhancing the heat transfer.

Figure 8 shows the predicted velocity vectors in the flow channel colored by velocity magnitude for the DSMTF MCHS design at Re = 2246 with a uniform heat flux of 40 W/cm². The chevron secondary microchannel and triangular ribs located near the main curved minichannel are enlarged at the 7.5%-depth, mid-depth, and 92.5%-depth planes of the minichannel to show the flow structures more clearly in Figure 8a–c. It can be seen that vortexes are generated near the corner sections of the chevron secondary microchannel and between the adjacent triangular ribs. The position and strength of the vortexes nearly remain unchanged from the bottom of the flow channel to the top.

Attributed to the existence of the chevron secondary microchannel, an increase in the momentum of the secondary flow will be induced in the minichannel. Also, the triangular ribs disrupt the recirculation region, which induces the redevelopment of the boundary layers and provides chaotic advection that promotes heat transfer. Thus, by creating flow disruption and altering the shape of the channel, fluid mixing and heat transfer in the minichannel are enhanced.

4.2. Effects of Rib Oblique Angle

The triangular rib oblique angle was set as 25° originally. Rib oblique angles ranging from 13° to 163° will be discussed in terms of the flow and heat transfer performance of the DSMTF MCHS in the following part. The DSMTF MCHS parameters in Table 1 are constant for all the configurations with different oblique angles, yielding sixteen parallel minichannel configurations. Numerical solutions are obtained for different oblique angles at a volumetric flow rate of 0.210 L/min (Re = 1497) with constant heat flux of 40 W/cm² (462.4 W) supplied underneath the MCHSs.

Figure 9 shows the CFD results and B-spline fitting curves of the variations in total thermal resistance and average pressure drop versus rib oblique angles of the DSMTF MCHSs. All the cases with different oblique angles have lower total thermal resistance compared with the DSMPF design. The total thermal resistance increases with the increment in the oblique angle at the beginning, then it remains nearly constant with minor fluctuation, and then it decreases with the increment of the oblique angle. Meanwhile, the variation in the average pressure drop possesses a contrary tendency with the total thermal resistance. Additionally, as shown by the dashed lines in Figure 9, when the oblique angle reaches a certain value, the average pressure drop will increase sharply as the oblique angle further decreases or increases. The reason will be analyzed and discussed in the following part from the perspective of minichannel structures.

As can be seen in Figure 10a, when the oblique angle decreases or increases to a certain value, the tip of the first triangular rib near the curved minichannel has already approached the flow channel midline. For the dimension parameters listed in Table 1, the corresponding oblique angle values are 22° or 146°. The disturbance of the triangular ribs to the fluid flow may be increased as the further decrement or increment in the oblique angle. This will cause a sharp increase in the pressure loss, as indicated by the dashed lines in Figure 9.

As can be seen in Figure 10b, when the oblique angle further decreases or increases to a certain value, the tip of the first triangular rib near the curved minichannel may contact the wall surface of the curved minichannel, and the fluid will be blocked by the triangular rib. For the dimension parameters listed in Table 1, the corresponding oblique angle values are 13° or 164°. Thus, the rib oblique angles ranging from 13° to 163° are discussed in this section and the rib oblique angle needs to be carefully evaluated to balance the enhancement of convective heat transfer and increment in pressure loss in the design of the heat sink.

5. Conclusions

As a means of dissipating high heat fluxes encountered in electronics cooling, liquid-cooled micro/minichannel heat sinks are of great interest. The present study demonstrated that employing chevron secondary microchannels and triangular ribs to disrupt the hydrodynamic and thermal boundary layers and transferring fluid between main flow and secondary flow channels can lead to reductions in thermal resistance compared with traditional straight-wall minichannel heat sinks (DSMPF) with a substantial decrement in pressure loss.

This new design is found to significantly reduce both the average pressure drop across the minichannels and the total thermal resistance by up to 51% and 8.5%, respectively. In addition, all the cases with different rib oblique angles studied in the present paper have lower total thermal resistance compared with the DSMPF design. However, a sharp increase in the pressure loss will be found when the oblique angle is below or above a certain value. The novel structure of the minichannel proposed in the present paper and the related research conclusions may contribute to the design of the enhanced heat transfer structures in the MCHS, which enables designers to explore appropriate compromises between designs with a low pressure drop and those with low thermal resistance.

In this study, although the performance of the MCHS was effectively improved through structural improvement, there is still room for further enhancement. Firstly, this study applied a uniform heat flux of 40 W/cm² underneath the MCHSs but did not account for the presence of local hotspots. Subsequent research will consider this aspect to better adapt to practical applications. Secondly, a topology optimization method may be adopted to automatically design the flow channel to obtain the maximal heat exchange and minimum pumping power under certain conditions, limitations, and specific metrics. Also, a multi-objective genetic algorithm will be adopted to optimize different structural parameters of the MCHS derived by the topology optimization method. Thirdly, the performance enhancement of this novel design needs to be experimentally verified, and experimental tests on DSMTF and DSMPF heat sinks need to be conducted.

6. Patents

The DSMTF MCHS proposed in this article has been applied for a Chinese patent (Patent No.: 202311195823.X).