Simulation Study on Nanofluid Heat Transfer in Immersion Liquid-Cooled Server

Abstract

In order to study the application of nanofluids for enhancing heat transfer in the field of liquid-cooled data centers, a mathematical and physical model of liquid-cooled servers was established in this paper. FC–40 was used as the server cooling liquid base, and simulation studies were conducted on the flow and heat transfer of five types of nanofluid: Cu–FC40, CuO–FC40, Al–FC40, Al₂O₃–FC40, and TiO₂–FC40. The results showed that using Al–FC40 nanofluids as the cooling medium had the best heat transfer effect. Under the same operating conditions, the average Nusselt number Nu and friction resistance coefficient f of five types of nanofluid were analyzed, and the heat transfer state of Al–FC40 nanofluid had the smallest f. Further analysis was conducted on the influence of ‘nanoparticle volume fraction’ α and ‘server inlet flow rate’ u on fluid flow and heat transfer. Our research found that an increase in α and the acceleration of u can effectively reduce the surface temperature of server components. As u increases, Nu gradually increases and f generally decreases, but the amplitude of the increase and decrease becomes smoother.

1. Introduction

With the rapid development of the Chinese digital economy and the continuous advancement of the informationization process, data centers have become an essential “computing base” to support the digital transformation of the economy and society, and are an important engine to fuel the vigorous development of the digital economy. High-throughput computing business makes the heat dissipation of server chips a serious challenge, with chip thermal package shell temperatures increasing, even reaching the limit of air-cooled heat dissipation. The specific heat capacity of liquid is 1000~3500 times that of air, and its thermal conductivity is 15~25 times that of air, so for higher-thermal-density heat dissipation, liquid cooling with greater heat capacity and faster heat transfer becomes the obvious choice. Among them, the single-phase submerged liquid cooling method is favored because of its high heat dissipation capacity and its advantages of safety and energy savings. Single-phase submerged liquid cooling immerses the electronic components of the server in a liquid-cooled cabinet, which is filled with a special cooling medium, and the heat is transferred out through the circulating flow of the coolant [1].

In 1995, Choi and Eastman introduced a brand new concept—nanofluidics [2]. In 2002, Qiang Li and Yimin Xuan [3] measured the in-tube convective heat transfer coefficient of copper–water nanofluid under turbulent flow, and the experimental results showed that the addition of nanoparticles to the liquid significantly increased the in-tube convective heat transfer coefficient of the liquid. The flow and convective heat transfer characteristics of deionized water, Cu-water nanofluid and Al-water nanofluid, in a parallel semicircular microchannel heat sink were experimentally investigated by Bin Sun et al. [4]. It was found that the heat transfer effect of Cu-water nanofluid was better than that of Al-water nanofluid. In 2018, Saeed et al. [5] prepared three heat sinks with different channel structures using two different volume concentrations of nanofluid and distilled water, and tested their heat transfer characteristics. The results showed that the nanofluid significantly improved the thermal performance of the microchannel heat sink compared to distilled water. In 2022, Liang Zhang et al. [6] conducted a numerical simulation study of the heat transfer characteristics of Cu-ethanol, Cu-ethylene glycol, and Cu-propylene glycol-based nanofluids in a wave-walled tube, and analyzed the effect of nanoparticle volume fraction φ on the heat transfer characteristics of the nanofluids. The results show that the thermal conductivity of the nanofluids was larger than that of the base fluid under the same conditions, and increased with the increase in φ.

At this stage, nanofluids are widely used in the field of enhanced heat transfer, such as in heat pipes, microchannels, heat sinks, and solar energy utilization [3,4,5,6,7,8], and a few scholars have studied the application of nanofluids in the field of liquid-cooled data centers, plus nanofluids as a new class of heat transfer cooling workpiece, providing a theoretical basis for their application in liquid-cooled cabinets. Nanofluid cooling is an emerging and promising technology that can bring multiple implications to liquid-cooled data centers. Nanofluids have good heat transfer properties and can effectively absorb and transfer heat. Compared with traditional cooling media, nanofluid can cool heat-concentrated equipment more effectively and improve cooling efficiency. Due to the better heat transfer properties of nanofluids, the same cooling effect can be achieved using a relatively low temperature of the cooling medium, thus reducing the cost of energy used for cooling. Nanofluid cooling provides a higher cooling capacity, enabling data centers to support higher-density server deployments and improve resource utilization. Nanofluid cooling reduces heat build-up, thereby reducing the risk of thermal limiting and thermal shutdown. This helps improve server performance and reliability and reduces the risk of hardware failure.

On the one hand, this paper takes a single-phase submerged liquid-cooled server as the research object, and selects five types of nanofluid, Cu–FC40, CuO–FC40, Al–FC40, Al₂O₃–FC40, and TiO₂–FC40, as cooling media to analyze the influence of fluid medium on the heat dissipation performance of the electronic components of the server. On the other hand, the comprehensive heat transfer performance of Al–FC40 nanofluid in the case of a nanoparticle volume fraction α of 1% to 5% and a flow rate u of 0.1 m/s to 0.5 m/s is studied, which lays a theoretical foundation for the application of nanofluid in liquid-cooled data centers.

2. Model Description

2.1. Mathematical Model

In this paper, a single-phase fluid model is chosen. That is, the nanoparticles in the nanofluid are considered to be uniformly distributed in the base fluid. The two are in thermal equilibrium. There is no relative slip velocity between the nanoparticles and the base fluid, and the fluid flow is considered to be incompressible steady-state laminar flow. Based on the above assumptions, the heat transfer control equation of nanofluid can be expressed as:

Continuity equation:

$$\frac{\partial }{\partial x_j}\left({\rho }_f{u}_j\right)=0$$

(1)

Momentum equation:

$$\frac{\partial }{\partial x_j}\left({\rho }_f{u}_i{u}_j\right)=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left[{\mu }_f\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)\right]$$

(2)

Energy equation:

$$\frac{\partial }{\partial x_j}\left({\rho }_f{c}_{pf}{Tu}_j\right)=\frac{\partial }{\partial x_j}\left[{\lambda }_f\frac{\partial T}{\partial x_j}\right]$$

(3)

where u_i and u_j are velocity components; x_i and x_j denote Cartesian coordinate components; p denotes flow field pressure; and T denotes temperature. The density ρ_f, kinetic viscosity μ_f, specific heat capacity c_pf, and thermal conductivity λ_f of the nanofluid are calculated according to the following equations [9,10].

$${\rho }_f=\left(1-\alpha \right){\rho }_w+\alpha {\rho }_p$$

(4)

$${\mu }_f=\left(1+0.025\alpha +0.015{\alpha }^2\right)\cdot {\mu }_w$$

(5)

$$c_{pf}{\rho }_f=\left(1-\alpha \right){\left(\rho c_p\right)}_w+\alpha {\left(\rho c_p\right)}_p$$

(6)

$${\lambda }_f=\frac{{\lambda }_p+\left(n-1\right){\lambda }_w-\left(n-1\right)\alpha \left({\lambda }_w-{\lambda }_p\right)}{{\lambda }_p+\left(n-1\right){\lambda }_w+\alpha \left({\lambda }_w-{\lambda }_p\right)}{\lambda }_w$$

(7)

where the subscripts w and p denote the corresponding thermal properties of the base liquid and nanoparticles, respectively; α denotes the volume fraction of nanoparticles; and n is the shape factor of the nanoparticles. Additionally, in this paper, nanoparticles are considered as regular spherical shapes, n = 3 [11].

2.2. Nanofluid Physical Parameters

In submerged liquid cooling, the coolant occupies an important position, and the core aim of submerged liquid cooling is to submerge the electronic components in the coolant to achieve efficient heat dissipation. After reviewing the relevant literature, FC–40 was selected as the coolant base fluid for this paper’s numerical simulation study, and its thermal and physical parameters are shown in

Table 1. Thermophysical parameters of the base fluid.

Coolant Base Fluid	λ (W/(m·K))	cp (J/(kg·K))	µ (kg/(m·s))	ρ (kg/m3)
FC–40	0.065	1100	0.0034	1850

.

Among them, thermal conductivity λ is the key parameter for heat transfer in fluid flow. The thermal conductivity of the nanofluids is shown in

Table 2. Thermal conductivity of nanofluids.

Nanofluids	Cu–FC40	CuO–FC40	Al–FC40	Al2O3–FC40	TiO2–FC40
λ (W/(m·K))	0.071028	0.071015	0.071025	0.070996	0.070848
Increment	9.274%	9.254%	9.269%	9.225%	8.997%

. Nanofluids have greater thermal conductivity compared with conventional fluids, and the thermal conductivity of Cu–FC40 is slightly higher compared with the other four types of nanofluid under the same working conditions.

2.3. Physical Model

Physical models of the liquid-cooled server and chip cooler are shown in Figure 1. The server consists of a CPU, GPU, PCI–E, hard disk, memory sticks and other electronic components, and the server is 915 mm long, 445 mm wide, and 85 mm high [1].

The dimensional parameters of the server components are shown in

Table 3. Dimensions of liquid-cooled server components.

Part Name	CPU	GPU	PCI-E	Hard Disk	Memory Stick
Size (mm)	75 × 55 × 5	55 × 55 × 5	85 × 65 × 15	85 × 65 × 15	130 × 35 × 1.5
Quantity	2	8	2	4	8

.

2.4. Boundary Conditions

The boundary conditions for the model solution are as follows:

(1)

The entry boundary of the server is set to velocity inlet.

(2)

The inlet flow rate is 0.1 m/s; the fixed inflow temperature is 300 K.

(3)

The exit boundary of the server is set to pressure outlet.

(4)

The heat-generating electronic components are equivalent to a volumetric heat source with uniform heat flow density.

The heat power consumption of the liquid-cooled server components is shown in

Table 4. Heating and power consumption of server components.

Part Name	CPU	GPU	PCI-E	Hard Disk	Memory Stick
Power consumption (W)	250	300	20	20	15

.

The overall grid division diagram and the local grid division profile are shown in Figure 2.

The numerical calculation in this paper is based on Fluent simulation software, and the solution algorithm uses a SIMPLE algorithm. The residual value of the convergence index is 10⁻⁴, and the residual value of the energy equation is 10⁻⁶. The average surface temperature monitoring amount of the heat sink is set, and the calculation results can be considered to have converged when the monitoring amount no longer produces a large change with an increase in the number of calculation iteration steps.

3. Data Processing and Analysis

3.1. Analysis of the Effects of Nanofluid Categories on Flow Heat Transfer

3.1.1. Core Component Temperature Analysis

A temperature cloud map of the liquid-cooled server core components when FC–40 and Cu–FC40, CuO–FC40, Al–FC40, Al₂O₃–FC40, TiO₂–FC40, the five types of nanofluid, are used as cooling media is shown in Figure 3. It can be seen from the figure that the temperature distribution of the core element is close to that of the core element under the flowing heat transfer state of each type of coolant, but the difference lies in the temperature interval values. With five types of nanofluid, the core element temperature range is roughly 324 K–367 K, while with coolant base fluid FC–40, the core element temperature range is roughly 326 K–372 K; the temperature range is reduced by 6.5%. In the flowing heat transfer state of nanofluid, the base fluid has greater thermal conductivity compared to the base fluid, which can cool the server core components to a lower temperature faster in the heat transfer process.

The flow heat transfer effects of FC–40 and of the five types of nano-coolant on reference indicators such as GPU surface temperature, heat sink surface temperature, overall server maximum temperature, and server outlet maximum temperature are shown in Figure 4, Figure 5, Figure 6 and Figure 7.

The diagram shows that, considering the coolant base fluid FC–40 flow heat exchange as the reference base, the highest GPU temperature ranking is Al–FC40 > TiO₂–FC40 > Al₂O₃–FC40 > CuO–FC40 > Cu–FC40; the lowest GPU temperature ranking is Al–FC40 < Cu–FC40 < CuO–FC40 < TiO₂–FC40 < Al₂O₃–FC40; the highest temperature ranking of the heat sink is Al–FC40 > TiO₂–FC40 > Al₂O₃–FC40 > CuO–FC40 > Cu–FC40; the lowest temperature ranking of the heat sink is Cu–FC40 < CuO–FC40 < Al₂O₃–FC40 < TiO₂–FC40 < Al–FC40; the overall highest temperature of the server is ranked as TiO₂–FC40 > Al–FC40 > Al₂O₃–FC40 > CuO–FC40 > Cu–FC40; and the temperature of the server outlet is ranked as Al–FC40 > TiO₂–FC40 > Al₂O₃–FC40 > Cu–FC40 > CuO–FC40. Compared to FC–40, the five types of nanofluid on the performance of the flow heat transfer in the liquid-cooled server is better, which shows that the surface temperature of the core element is lower and the temperature of the server outlet is higher, indicating that the nanofluid can take away more heat from the core element of the server. Among them, the Al–FC40 nanofluid has better heat transfer performance compared with the other four types of nanofluid, which shows that the lowest temperature of the GPU surface is 326.5 K; the lowest temperature of chip heat sink surface is 347.8 K; the highest temperature of the server as a whole is 392.4 K; and the temperature of the liquid outlet is 385.6 K.

3.1.2. Analysis of Average Nusselt Number Nu and Frictional Resistance Coefficient f

The average Nusselt number Nu is a criterion number used to characterize the intensity of convective heat transfer, and Nu is introduced in this paper as an evaluation index for the heat transfer performance of nanofluid flow.

$$Nu=\frac{{hD}_h}{{\lambda }_f}$$

(8)

$$D_h=\frac{2ab}{a+b}$$

(9)

where h denotes the average convective heat transfer coefficient, W/(m²·K); D_h denotes the characteristic size, m; λ_f denotes the fluid thermal conductivity, W/(m·K); and a and b, respectively, denote the server width and height, m.

In addition, enhanced heat transfer should not come at the cost of a significant increase in frictional resistance, so an analysis of the frictional resistance coefficient needs to be carried out, with the frictional resistance coefficient f expressed as:

$$f=\frac{{2D}_h\Delta P}{\rho {Lu}^2}$$

(10)

where ΔP denotes server import and export pressure drop, Pa; ρ denotes the fluid density, kg/m³; L denotes the server length, m; and u denotes the fluid flow rate, m/s.

As shown in Figure 8, under the same working conditions, the average Nu numbers of the five types of nanofluid under enhanced heat transfer are ranked as Al₂O₃–FC40 > Al–FC40 > TiO₂–FC40 > CuO–FC40 > Cu–FC40, and the frictional resistance coefficients f are ranked as Cu–FC40 > CuO–FC40 > TiO₂–FC40 > Al₂O₃–FC40 > Al–FC40. Among them, the Cu–FC40 nanofluid has the smallest Nu and the largest f; the Al–FC40 nanofluid has a slightly lower Nu than the Al₂O₃–FC40 nanofluid; and the Al–FC40 nanofluid has the smallest f.

As the analysis of the above data concluded that Al–FC40 nanofluid flow has the best heat transfer effect, so it was chosen for the subsequent study to discuss the effect of nanoparticle volume fraction α and fluid flow rate u on the heat transfer performance.

3.2. Analysis of the Effect of Nanoparticle Volume Fraction α on Heat Transfer in Fluid Flow

The thermal conductivity of the Al–FC40 nanofluid with a nanoparticle volume fraction α of 1–5% was analyzed, and the results are shown in Figure 9, where the growth rate of λ_f relative to the base fluid FC–40 gradually increases with increasing α. The thermal conductivity of the Al-FC40 nanofluid increased by 3.03%, 6.12%, 9.27%, 12.49%, and 15.77% compared to the base fluid with α of 1–5%, respectively.

Figure 10 shows the maximum and minimum temperature data of the GPU surface of the server component at different volume fractions of Al nanoparticles. In the process of increasing α, the maximum and minimum GPU temperatures continue to decrease. α = 1%, the maximum GPU surface temperature is 370.1 K, and the minimum temperature is 327.8 K; α = 5%, the maximum GPU surface temperature is 364.3 K and the minimum temperature is 325.4 K. The decrease in the maximum GPU temperature from 1% to 5% of α is 1.6%; the decrease in the minimum GPU temperature is 0.7%, which shows that the increase in α can effectively reduce the surface temperature of server components.

3.3. Analysis of the Effect of Server Inlet Flow Rate u on Fluid Flow Heat Transfer

A nanofluid with a median volume fraction α of 3% was used as the analysis object, and the flow heat transfer simulation was carried out under different working conditions by varying the server inlet flow rate u. The flow heat transfer characteristics of u to the nanofluid were studied, as shown in Figure 11. With the gradual acceleration of u, the maximum and minimum GPU temperatures decrease accordingly. u = 0.1 m/s, the maximum GPU surface temperature is 367.7 K and the minimum temperature is 326.5 K; u = 0.5 m/s, the maximum GPU surface temperature is 359.2 K and the minimum temperature is 323.8 K. The maximum GPU temperature decreases by 2.3%; the minimum GPU temperature decreases by 0.8%. As u accelerates, the nanofluid perturbation is enhanced, the degree of convective heat transfer within the server is strengthened, and the cooling medium can carry more heat away from the surface of the GPU as it flows through it, thus presenting a decrease in the GPU surface temperature as u accelerates.

As shown in Figure 12, the relationship between the average Nusselt number Nu and the frictional drag coefficient f with u is shown. As u increases, Nu in the server gradually increases, and the increase becomes less and less; f in the server gradually decreases, and the decreasing trend becomes more and more flat. u increases from 0.1 m/s to 0.2 m/s, and the increase in Nu and the decreasing trend of f are both at maximum. This means that increasing the inlet flow rate of the server appropriately can improve the heat transfer of the nanofluid, and the larger the flow rate, the more intense the fluid disturbance in the server, thus achieving the goal of enhanced heat transfer; the increase in Nu and the decrease in f from 0.2 m/s to 0.5 m/s are both increasing and decreasing, which means that it is unrealistic to expect an improvement in heat transfer performance by increasing the inlet flow rate of the server without restriction. This will not only increase the energy consumption of nanofluid transport, but will also make it difficult to maintain a stable and uniform suspension of nanoparticles in the nanofluid at too fast a flow rate.

4. Conclusions

In this paper, a liquid-cooled server is used as the research object, and the computational fluid dynamics method is used to simulate the flow heat transfer of five types of nanofluid, respectively, using coolant FC–40 heat transfer as the reference benchmark. The following conclusions are drawn:

(1)

The nanofluid has greater thermal conductivity compared to the base fluid, which can carry away more heat from electronic core components under the same working conditions.

(2)

Among the five types of nanofluid flow heat transfer, Al–FC40 nanofluid has the best comprehensive heat transfer effect. The lowest temperature of the GPU surface is 326.5 K; the lowest temperature of the chip heat sink surface is 347.8 K; the highest temperature of the server as a whole is 392.4 K; and the temperature of the outlet is 385.6 K. The frictional resistance coefficient f of the Al–FC40 nanofluid is the smallest under the same working condition.

(3)

With an increase in α and the acceleration of u, the surface temperature of the server components can be effectively reduced. However, it is unrealistic to expect an improvement in heat transfer performance by increasing the volume fraction of nanoparticles and increasing the inlet flow rate of the server without restriction, which will not only increase the energy consumption of nanofluid transport, but will also make it difficult to maintain uniform stability of nanoparticles in the nanofluid.

The results of the above study can provide a technical-level reference for the application of nanofluid in liquid-cooled data centers. Nanofluid cooling as an innovative cooling technology provides an attractive and promising option for liquid-cooled data centers. In this paper, simulation software is used to conduct an experimental study of nanofluid cooling applied to submerged liquid cooling; however, the actual effect of its application needs to be further verified in practice by building an experimental platform, and at the same time, factors such as its cost, maintenance requirements, and environmental sustainability need to be considered.