Thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in parabolic trough solar receiver tube

Journal Pre-proof Thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in parabolic trough solar receiver tube

Hao Peng, Wenhua Guo, Meilin Li PII:

S0360-5442(19)32259-5

DOI:

https://doi.org/10.1016/j.energy.2019.116564

Reference:

EGY 116564

To appear in:

Energy

Received Date:

22 April 2019

Accepted Date:

16 November 2019

Please cite this article as: Hao Peng, Wenhua Guo, Meilin Li, Thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in parabolic trough solar receiver tube, Energy (2019), https://doi.org/10.1016/j.energy.2019.116564

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Journal Pre-proof Thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in parabolic trough solar receiver tube Hao Peng*, Wenhua Guo, Meilin Li ( Institute of Thermal Engineering, Shanghai Maritime University, Shanghai 201306, China) *Corresponding Author, Tel: +86-21-38282951; E-mail: [email protected]

Abstract Parabolic trough collectors (PTCs) are widely applied in concentrated solar energy utilization, and the further improvement of PTC’s efficiency is usually restricted by heat transfer performance of parabolic trough solar receiver (PTR) tube. With the aim to enhance the heat transfer performance of PTR tube, liquid metal based nanofluid (i.e. the suspension of nano-scale powders in liquid metal) is proposed as working fluid due to its superior thermal transport properties. The thermal-hydraulic and thermodynamic performances of two types of liquid metal based nanofluids including gallium (Ga)-copper (Cu) and Ga-carbon nanotube (CNT) in PTR tube are numerically investigated. Monte Carlo Ray-Trace Method is used to obtain actual distribution of non-uniform heat flux on receiver tube wall, and four parameter turbulence model is adopted considering the low Prandtl number of liquid metal based nanofluid. The numerical method is validated by the experimental data. The results show that the presence of Cu and CNT can enhance the forced convection heat transfer of pure Ga in PTR tube, and the average enhancement degrees can reach up to 34.5% and 45.2% respectively under present conditions. Also, the frictional pressure drops of Ga-Cu and Ga-CNT nanofluids are larger than that of pure Ga at the same Reynolds number. With the increase of nano-powder concentration, the total entropy generation decreases and the exergetic efficiency increases. The thermodynamic performance of Ga-CNT nanofluid is better than that of Ga-Cu nanofluid under the same condition. Keywords: liquid metal; nanofluid; parabolic trough solar receiver; non-uniform heat flux; thermodynamic performance 1

Journal Pre-proof Nomenclature Aa

the aperture area of collector (m2)

Be

Bejan number (-)

Cp

specific heat (J kg-1 K-1)

dp din DB DT Do Di E f fdrag g

nano-powder size (nm) inner diameter of test tube (mm) Brownian diffusion coefficient thermophoresis diffusion coefficient receiver tube outer diameter (m) receiver tube inner diameter (m) exergy flow (W) friction factor (-) drag function (-) gravitational acceleration (m s-2)

Gr

Grashof number (-)

h H I kθ L m N NBT Nu P Pr q Qu Ri Re S Sg Sg,fr Sg,th

Sg

forced convection heat transfer coefficient (W m-2 K-1) enthalpy (J kg-1) direct normal irradiance (W m-2) average square temperature fluctuation (K2) receiver tube length (m) mass flow rate (kg s-1) augmentation entropy generation number (-) the ratio of Brownian motion to thermophoretic diffusivities Nusselt number (-) average static pressure (Pa) Prandtl number (-) heat flux (W m-2) useful heat (W) Richardson number (-) Reynolds number (-) velocity deformation tensor (s-1) total entropy generation rate (W K-1) frictional entropy generation (W K-1) thermal entropy generation (W K-1)

2

total entropy generation rate per unit volume (W m-3 K-1)  frictional entropy generation rate per unit Sg,fr volume (W m-3 K-1)  thermal entropy generation rate per unit Sg,th volume (W m-3 K-1) T temperature (K) u,v,w x, y, z velocity component (m s-1) V Volume (m3) V velocity (m s-1) turbulent heat flux vector (m K s-1) Vm T  Reynolds stress tensor (m2 s-2) VmVm Greek symbols α acceleration (m s-2) α thermal diffusivity (m2 s-1) αt,m turbulent thermal diffusivity (m2 s-1) εθ Dissipation rate of temperature fluctuations (K2 s-1 ) ηex exergetic efficiency θ λ λeff λt µ ρ

circle angle (°) thermal conductivity (W m-1 K-1) effective thermal conductivity (W m-1 K-1) turbulent thermal conductivity (W m-1 K-1) molecular viscosity (Pa s)

σ

stress tensor (-)

density (kg m-3)

φ volume fraction (-) ψ solar elevation angle (°) Subscripts dr,f drift velocity for liquid metal dr,p drift velocity for nano-powder f liquid metal in inlet m nanofluid out outlet pf slip velocity p nano-powder

Journal Pre-proof 1. Introduction In recent years, liquid metal has been used in concentrated solar power (CSP) technologies as a new type of working fluid due to its high thermal conductivity and good high-temperature thermal stability [1]. The existing researches on solar central receiver systems (CRSs) showed that the utilization of liquid metal leads to the enhancement of forced convection heat transfer in central receiver tube and then the improvement of CRS’s thermal efficiency [2-5]. For another type of widely used CSP system, parabolic trough collector (PTC), the enhancement of heat transfer performance is a vital problem needed to be solved for the further improvement of system’s thermal efficiency [6-8]. In view of the superior thermal transport properties of liquid metal, the utilization of liquid metal as working fluid in PTC may become an efficient method to enhance the heat transfer. As the liquid metal based nanofluid (i.e. the suspension of nano-scale powders in liquid metal) has higher thermal conductivity than the host liquid metal [9], the PTC system using liquid metal based nanofluid has potential for achieving higher heat transfer enhancement degree. For the design and optimization of a PTC system using liquid metal based nanofluid, the thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in the PTR tube should be basic knowledge. To understand the thermal-hydraulic performance, the effects of nano-powder type and concentration on the forced convection heat transfer coefficient as well as pressure drop of liquid metal based nanofluid in the PTR tube under realistic non-uniform heat flux distribution should be investigated. To evaluate the thermodynamic performance, entropy generation and exergy analysis are useful tools [10-12], and the effects of nano-powder type and concentration on thermal entropy generation, frictional entropy generation and exergetic efficiency of liquid metal based nanofluid should be analyzed. 3

Journal Pre-proof The existing researches on the thermal-hydraulic performance of liquid metal based nanofluids are mainly aimed at the forced convection heat transfer and pressure drop in microchannels under uniform heat flux [13-15]. Sarafraz et al. [13, 14] experimentally investigated the thermal-hydraulic performance of gallium-copper oxide (Ga-CuO) and indium-copper oxide (In-CuO) in a microchannel. They found that the presence of CuO enhances the heat transfer coefficient and pressure drop of pure Ga or In, while the maximum enhancements of heat transfer coefficients for pure Ga and In occur at CuO mass fractions of 10 and 8 wt% respectively. Sarafraz et al. [15] also experimentally studied the thermal-hydraulic performance of gallium-aluminum oxide (Ga-Al2O3) in a microchannel. Their results showed that the addition of Al2O3 increases the heat transfer coefficient and pressure drop of pure Ga, while the maximum increment of heat transfer coefficient occurs at Al2O3 mass fraction of 10 wt% and the increment degree for pressure drop ranges from 9.1% to 23%. Due to the existing of non-uniform heat flux distribution, the thermal-hydraulic performance of liquid metal based nanofluid in PTR tube is different from those in microchannel reported by the above researches, and needs to be disclosed. The existing researches on the thermal-hydraulic or thermodynamic performance of nanofluids in PTR tubes are focused on the nanofluids based on water [16-19], thermal /synthetic oil [12, 20-28] and ethylene glycol [29, 30]. The nano-powder types in these researches include Cu [12, 20, 21], Si [29], Al2O3 [16, 17, 23-27], CuO [16, 27, 28], TiO2 [18, 19, 27], SiO2 [18] and carbon nanotube (CNT) [22, 29, 30]. The results showed that the presence of nano-powders can increase the forced convection heat transfer coefficient of base fluid, and causes the decrease of entropy generation and increase of exergetic efficiency. Due to the difference in thermophysical properties such as thermal conductivity and viscosity, the thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid may be different from those of nanofluids in the above researches, and should be investigated. 4

Journal Pre-proof In the present study, a numerical simulation on turbulent forced convection heat transfer and flow of liquid metal based nanofluid in a PTR tube under non-uniform heat flux has been carried out; the effects of nano-powder type and concentration on the thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid have been analyzed.

2. Physical problem description The physical model is based on conventional LS-2 parabolic trough solar collector (PTC) module, which is the basis for the design of many PTCs and tested by Dudley et al. [31] at Sandia National Laboratory (SNL), as schematically shown in Fig. 1. The PTC system mainly consists of a parabolic collector and a parabolic trough receiver (PTR). The parabolic collector, which is made of an array of parabolic shaped mirrors, reflects the solar radiation onto PTR. The PTR is fixed at the focal line of PTC, which consists of a glass envelop and a receiver tube covered with a selective coating. The receiver tube absorbs solar energy and transforms it into heat, and the working fluid flowing inside receiver tube takes away heat through convection. A vacuum gap is formed between the glass envelope and the receiver tube to reduce conduction and convection heat loss.

Fig. 1. Schematic diagram of parabolic trough solar receiver (PTR) tube.

5

Journal Pre-proof Since the present study is aimed to apply liquid metal based nanofluid as working fluid in PTC, the physical problem is focused on the forced convection heat transfer and flow of liquid metal based nanofluid in a PTR tube. The PTR tube is a circular stainless steel tube with length (L) of 4.06 m, outer diameter (Do) of 70 mm and inner diameter (Di) of 64 mm. The heat flux distributed on the PTR tube surface is non-uniform in consistent with the actual practice. The central angle (θ) of receiver tube ranges from 0 to 360o, and the solar elevation angle (ψ) (i.e. the angle between central normal of parabola and horizontal plane) is set at 90o. Two types of liquid metal based nanofluids, including gallium (Ga)-copper (Cu) and Ga-carbon nanotube (CNT) are investigated in the present study. The reasons for choosing Cu and CNT are as follows. (1) To understand the nano-powder shape effects on the thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid, zero- and one-dimensional nano-powders are considered. (2) Cu has relatively higher thermal conductivity (about 401 W m-1 K-1) and lower cost among zero-dimensional nano-powders, and is typically adopted for the preparation of liquid metal based nanofluids [9]. (3) CNT is a representative one-dimensional nano-powder with high thermal conductivity, and CNT nanofluids are widely applied in solar collectors [32]. Ga is suitable for preparing liquid metal based nanofluids (as done in the references [9, 13, 15]) due to the following advantages. (1) Among the conventional liquid metals, Ga is hardly corrosive to stainless steel tube surface [15]. (2) Ga has a low melting point (the melting point is about 303 K, close to room temperature) [9], which is convenient for preparing nanofluid at atmospheric pressure and needs lower energy consumption for keeping the fluid state. (3) The thermal conductivity of Ga is 28.7 W m -1 K -1, which is much higher than that of molten salt (about 0.5 W m -1 K -1) or thermal oil (about 0.1 W m-1 K-1); therefore, it is expected to achieve high heat transfer performance. 6

Journal Pre-proof In order to understand the influence of nano-powder concentration on the forced convection heat transfer and flow of liquid metal in PTR tube, the liquid metal based nanofluids with four nano-powder volume fractions (φp) of 2, 5, 8 and 10 vol% are investigated. As a basic flow mode in PTR tube, fully-developed turbulent flow is focused in the present study, and Reynolds number (Re) ranges from 50000 to 300000. For simplifying the physical problem, some assumptions are made as follows. The fluid flow is considered to be two-dimensional and incompressible. The buoyancy force and viscous dissipation are neglected. The natural convection effect is negligible when Richardson number (Ri=Gr/Re2) is less than 0.1 [8]. Under present conditions, the value of Ri ranges from 1.72×10-5 to 4.25×10-3, which is far less than 0.1; thus, the natural convection effect can be neglected.

3. Mathematical model and numerical implementation 3.1 Governing Equations The continuity, momentum, energy and volume fraction equations based on two-phase mixture model are used to describe the flow and heat transfer of liquid metal based nanofluid at steady state. Continuity equation:

  ρmVm   0

(1)

Momentum equation:





ρm Vm Vm   σ   ρm VmVm    φf ρf Vdr,f Vdr,f  φp ρpVdr,pVdr,p   ρm g

(2)

Energy equation:



  φpVp ρp H p  φf Vf ρf H f     λeff T    ρm Cp,m Vm T 



(3)

Volume fraction equation:

  φp ρpVm     φp ρpVdr,p  7

(4)

Journal Pre-proof where the subscripts m, f and p refer to the nanofluid, liquid metal (Ga) and nano-powder (Cu or CNT), respectively; Cp, H, T, ρ, λeff and φ are the specific heat, enthalpy, temperature, density, effective thermal conductivity and volume fraction, respectively; σ is the stress tensor; VmVm is the Reynolds stress tensor, which represents the average product of velocity fluctuations, and can be solved by the Reynolds stress transport equation; Vm T  is the turbulent heat flux vector, which represents the average product of velocity and temperature fluctuations, and can be solved by the turbulent heat flux transport equation; Vm , Vdr,p and Vdr,f are the averaged velocity, drift velocity for nano-powder (secondary phase) and drift velocity for liquid metal (primary phase), respectively. The effective thermal conductivity λeff can be calculated by Eq. (5).

λeff  φp  λp  λt   φf  λf  λt 

(5)

where λt is the turbulent thermal conductivity. The stress tensor σ is determined as follows. σ =  PI + μm S

S = Vm   Vm 

(6) T

(7)

where S is the velocity deformation tensor, P is the average static pressure, and μm is the mixture molecular viscosity. The averaged velocity Vm , drift velocity for nano-powder Vdr,p , and drift velocity for liquid metal Vdr,f can be calculated as follows.

Vm 

ρp φpVp  ρf φf Vf ρm

(8)

Vdr,p  Vp  Vm

(9)

Vdr,f  Vf  Vm

(10)

The slip velocity is defined as the velocity of nano-powder (secondary phase) relative to the 8

Journal Pre-proof velocity of liquid metal (primary phase), expressed as follows. Vp f  Vp  Vf

(11)

The relationship between drift velocity ( Vdr,p ) and slip velocity ( Vp f ) is written as

ρp φp

Vdr,p  Vp f 

ρm

Vfp

(12)

The slip velocity ( Vp f ) is calculated by Eq. (13) proposed by Manninen et al. [33].

Vp f 

d p2 ρp

ρ

p

18 μf f d rag

 ρm  ρp

α

(13)

where d p is the nano-powder size, α is the acceleration determined by Eq. (14), and f drag is the drag function calculated by Eq. (15) proposed by Schiller and Naumann [34].

α = g  Vm  Vm 1  0.15 Rep0.687 f d rag   0.0183 Rep

(14) Rep  1000 Rep  1000

(15)

where g is gravitational acceleration, and Reynolds number (Rep) is calculated as

Rep 

Vm d p ρm μm

(16)

3.2 Turbulence model The liquid metal based nanofluid in the present study has low Prandtl number (Pr) ranging from 0.0184~0.0239. For low-Pr fluids, the time scales of temperature and velocity fields are rather different, and the standard constant turbulent Pr model predictions are not sufficiently accurate [5, 35]. By introducing two additional equations for the average square temperature fluctuation (kθ) and its dissipation (εθ), the four parameter turbulence model proposed by Manservisi and Menghini [36] can provide accurate predictions for low-Pr fluids. In the present study, the four parameter turbulence model is applied, and a more detailed description of the model can be found in Ref. [35, 36].

9

Journal Pre-proof 3.3 Boundary conditions

The boundary conditions are as follows. (1) Near-wall approach is used to boundary condition for the turbulent variables. (2) Inlet: constant velocity and temperature condition, u = v = 0, w=win, T = Tin = 473.15 K. (3) Outlet: fully developed condition, u / x  v / x  w / x  p / x  T / x  0 . (4) The non-uniform heat flux distribution is determined by Monte Carlo Ray-Trace Method (MCRT Method) as demonstrated by Cheng et al. [37]. The local heat flux on outer tube wall (qwall) is calculated by multiplying the direct normal irradiance (DNI) I with the local concentration ratio (LCR), i.e. qwall=I·LCR. The value of I is set to be 1000 W m-2. This value is a typical peak value of terrestrial solar irradiance on surfaces at sea level facing the sun’s rays under clear sky conditions around solar noon, and used as a rating condition for PTR [8]. The relationship between LCR and central angle (θ) of receiver tube is shown in Fig. 2.

Fig. 2. Relationship between local concentration ratio (LCR) and central angle (θ) of receiver tube. 3.4 Entropy generation determination and exergy analysis Local entropy generation rate can be determined from the velocity and temperature fields under

10

Journal Pre-proof non-uniform heat flux. The total entropy generation rate per unit volume ( Sg ) are expressed as the  ) and frictional entropy generation rate ( Sg,fr  ) caused by sum of thermal entropy generation rate ( Sg,th

the heat transfer and fluid friction irreversibility respectively.   Sg,th  Sg  Sg,fr

(17)

The thermal entropy generation rate is calculated by Eq. (18).

  Sg,th

λ T

2

 T 

2



αt,m λ T α T2

 

2

(18)

On the right side of Eq. (18), the first item represents the entropy generated by heat transfer with mean temperature, and the second item represents the entropy generated by heat transfer with fluctuating temperature due to turbulence; α and αt,m are the thermal diffusivity and turbulent thermal diffusivity respectively. The frictional entropy generation rate is calculated by Eq. (19).

  Sg,fr

μ  ui u j  ui ρε     T   x j  xi   x j T

(19)

On the right side of Eq. (19), the first item represents the entropy generated by direct dissipation, and the second item represents the entropy generated by turbulent dissipation. The total entropy generation rate in the entire domain with volume of V is calculated by integrating entropy generation rate per unit volume, as shown in Eq. (20).

Sg   Sg dV

(20)

The useful heat delivered to the liquid metal based nanofluid can be calculated by  p,m Tout  Tin  Qu  mC

(21)

where m is the mass flow rate; Cp,m is the specific heat capacity; Tout and Tin are the outlet temperature and inlet temperature, respectively. 11

Journal Pre-proof The exergy output from the PTR can be written as Eq. (22), which takes into account the effect of pressure drop on the exergy output [38].

T  p,mTam ln  out Eu  Qu  mC  Tin

 ΔP  am  -mT ρmTm 

(22)

The available solar exergy is determined by the following equation proposed by Petela [39].

 4  T  1  T 4  Es  Aa I 1   am    am    3  Tsun  3  Tsun  

(23)

In Eqs. (22) and (23), Tm is the average temperature of the inlet and outlet; Tam is the ambient temperature, and set to be 300 K in the present study; Tsun is the sun temperature, and the value is set to be 5800 K [39]; Aa is the aperture area of collector with the value of 27.49 m2 .

The exergetic efficiency is defined as the ratio of useful exergy output to exergy input, as shown below. ηex 

Eu Es

(24)

3.5 Numerical procedure The non-uniform heat flux boundary condition and two additional equations for average square temperature fluctuation (kθ) and its dissipation (εθ) in turbulence model are implemented by User Defined Functions (UDFs). The governing equations are discretized by the finite volume method (FVM). The SIMPLE algorithm is used for pressure-velocity coupling. The convective terms in equations for momentum, turbulent kinetic energy as well as dissipation rate, temperature fluctuation as well as its dissipation rate, and energy are all discretized by the second-order upwind scheme. The pressure is discretized by PRESTO! scheme. The convergence criteria to terminate the solutions for

12

Journal Pre-proof continuity, momentum and turbulence parameters are all 10-6, and that for energy is 10-8. 3.6 Grid independence checking The structured non-uniform hexahedral grid is adopted in the present simulation. In order to ensure the accuracy and validity of numerical results, a grid independence checking was performed using four different grid resolutions (cell number of 20000, 100000, 400000 and 1760000) at Reynolds number Re=50000 and Re=300000 for pure Ga. The predicted Nusselt number (Nu) and friction factor (f) with these four different grid systems are listed in Table 1. It can be seen that the deviations of Nu between two neighboring grids decrease from 2.1% to 0.5%, while the deviations of f between two neighboring grids decrease from 0.97% to 0.39% at Re=50000. The deviations of Nu between two neighboring grids decrease from 2.4% to 0.4%, while the deviations of f between two neighboring grids decrease from 1.12% to 0.28% at Re=300000. Therefore, the third grid system (cell number of 400000) is selected considering the balance between numerical accuracy and computation time. Table 1. Grid independence checking.

Re=50000

Re=300000

Grid Number

20000

100000

400000

1760000

Predicted Nu

7.18

7.11

7.07

7.03

Error (%)

2.1

1.1

0.5

Baseline

Predicted f

0.00521

0.00520

0.00518

0.00516

Error (%)

0.97

0.78

0.39

Baseline

Predicted Nu

23.96

23.65

23.49

23.40

Error (%)

2.4

1.1

0.4

Baseline

Predicted f

0.00360

0.00359

0.00357

0.00356

Error (%)

1.12

0.84

0.28

Baseline

4. Experimental validation 4.1 Preparation of liquid metal based nanofluids Ga-Cu and Ga-CNT nanofluids with nano-powder concentrations (φp) of 2, 5, 8 and 10 vol% were prepared. Ga was purchased from Yantai Aibang Electronic Materials Co., Ltd., China. Cu

13

Journal Pre-proof nanoparticles (mean diameter of 50 nm) and CNTs (mean length of 1.5 µm and mean outer diameter of 80 nm) were purchased from Suzhou Hengqiu Graphene Co., Ltd, China. The preparation procedure contained the following steps: (1) The required mass of Cu nanoparticles or CNTs were weighed by a digital electronic balance (measurement range of 10 mg to 210 g, and a maximum error of 0.1 mg), and then dispersed into deionized (DI) water with volume of 1000 mL. (2) Non-ionic surfactant nonylphenolethoxilate (NPE) was added into water-Cu or water-CNT mixture for dispersing Cu nanoparticles or CNTs uniformly, and NPE concentrations used for water-Cu and water-CNT mixtures are 800 ppm and 1000 ppm respectively. (3) The water-Cu or water-CNT mixture containing NPE was vibrated by an ultrasonic processor for 15 min to stabilize the dispersion of nano-powders. (4) Ga was added to water-Cu or water-CNT mixture containing NPE, then the mixture was heated up to 120 ℃ to evaporate the water and surfactant. The photographs of pure Ga and prepared Ga-Cu and Ga-CNT nanofluids (φp=10 vol% as an example) are shown in Fig. 3. The time-settlement experiments showed that the stable dispersion of Cu nanoparticles or CNTs can be maintained for more than one week, which is much longer than the time needed for thermophysical properties and forced convention heat transfer measurements.

(a) Ga

(b) Ga-Cu

(c) Ga-CNT

Fig. 3. Photographs of pure Ga and prepared Ga-Cu and Ga-CNT nanofluids (φp=10 vol%).

14

Journal Pre-proof 4.2 Measurement of thermophysical properties of liquid metal based nanofluids The density, viscosity, specific heat and thermal conductivity of Ga-Cu and Ga-CNT nanofluids with nano-powder concentrations (φp) of 2, 5, 8 and 10 vol% were experimentally measured since these thermophysical properties are essential for evaluating the forced convection heat transfer and pressure drop performance. The density was determined by the density bottle method. The viscosity was measured by Ubbelohde viscometer. The specific heat was measured by differential scanning calorimeter (DSC, NETZSCH 200F3). The thermal conductivity was measured using Thermal Constants Analyzer (TPS 2500S) which is based on the transient plane source technique. The measured density, viscosity, specific heat and thermal conductivity of Ga-Cu and Ga-CNT nanofluids with nano-powder concentrations (φp) of 2, 5, 8 and 10 vol% are listed in Table 2. With the increase of φp from 0 to 10 vol%, the density is increased by 3.7% for Ga-Cu nanofluid and decreased by 6.5% for Ga-CNT nanofluid, the viscosity are increased by 26.6% and 27.2% for Ga-Cu and Ga-CNT nanofluids respectively, the specific heat are increased by 1.2% and 3.0% for Ga-Cu and Ga-CNT nanofluids respectively, and the thermal conductivity are increased by 31.2% and 70.8% for Ga-Cu and Ga-CNT nanofluids respectively. It also can be seen that the maximum deviations of measured density, viscosity, specific heat and thermal conductivity from the predictions by the correlations listed in Table 3 are 0.05%, 2.63%, 0.36% and 2.05%, respectively. Table 2. Measured thermophysical properties of liquid metal based nanofluids and their deviations from model predictions. Deviation (%)

Viscosity (Pas)

Deviation (%)

8300 2100 6048 6091

0.03

— — 0.0018 0.00187

0.91

Specific heat (Jkg-1K-1) 420 709 381.5 382.5

6159

0.02

0.00202

1.49

384

Density (kgm-3) Cu CNT Ga Ga-Cu (φp=2 vol%) Ga-Cu (φp=5 vol%)

15

0.01

Thermal conductivity (Wm-1K-1) 401 3000 28.7 30.8

0.02

33.2

Deviation (%)

Deviation (%)

1.03 2.05

Journal Pre-proof Ga-Cu (φp=8 vol%) Ga-Cu (φp=10 vol%) Ga-CNT (φp=2 vol%) Ga-CNT (φp=5 vol%) Ga-CNT (φp=8 vol%) Ga-CNT (φp=10 vol%)

6231

0.04

0.00216

1.85

385

0.16

35.3

1.52

6270

0.05

0.00228

2.63

386

0.15

37.7

1.98

5967

0.03

0.00188

0.69

383.5

0.08

33.1

1.03

5853

0.04

0.00202

1.49

386

0.36

38.8

1.02

5733

0.01

0.00216

1.85

390

0.28

44.8

1.01

5655

0.03

0.00229

2.18

393

0.17

49.0

1.03

Note: Thermophysical properties of pure Ga, Cu and CNT are provided by manufacturers, and those of Ga-Cu and Ga-CNT nanofluids are obtained in the present study.

Table 3. Calculation methods for thermophysical properties of liquid metal based nanofluid. Thermophysical property Correlation for calculating thermophysical property

ρm = φp ρp  1  φp  ρf

Density, kg m-3

μf

μm 

Viscosity, Pa s [40]

1  φ  C  1  φ  C  φC  (n  1) λ  φ  n  1  λ  λ  λ λ   n  1 λ  φ  λ  λ  2.5

p

Specific heat, J kg-1 K-1 [41] Thermal conductivity, W

m-1

K-1

p,m

[42]

λm 

λp

p

f

p,f

p,p

p

f

p

f

p

f

p

f

p

n

3



ζ: Sphericity of nano-powders 4.3 Experimental setup and method for forced convection heat transfer Figure 4 shows the experimental setup for testing the forced convection heat transfer coefficient and pressure drop for liquid metal based nanofluids, which consists of a flow loop, measuring instruments and a data acquisition system. The flow loop includes a test section, a heating unit, a heat exchanger, a constant temperature tank, and a electromagnetic pump. The test section is a straight stainless steel tube with a length of 800 mm, inner diameter of 10 mm and outer diameter of 14 mm. The test section is heated trough a heating flexible tape linked to a DC power supply, and insulated with fiberglass and rubber insulation to prevent heat loss. The liquid metal based nanofluids are forced through the flow loop by the electromagnetic pump (DC EMP). Two pressure transducers (GE Druck PTX5072, ±0.2% accuracy) are placed at the inlet and outlet of test tube for measuring the pressure drop. The flow rate is measured using electromagnetic flowmeter (Omega, FMG71B, ±0.3% accuracy).

16

Journal Pre-proof To measure the wall temperature, 12 T-type thermocouples (with the precision of ±0.1 ℃) are mounted at different axial positions on the test tube surface. To measure the bulk temperatures of liquid metal based nanofluids, 2 T-type thermocouples (with the precision of ±0.1 ℃) are inserted into the flow at the inlet and outlet of test tube.

Fig. 4. Schematic diagram of experimental setup for forced convection heat transfer. The heat supplied to the test section can be calculated as Qsup  UI

(25)

where U and I are the electrical voltage and current, respectively. The heat absorbed by liquid metal based nanofluid can be determined by  p,m Tout  Tin  Qabs  mC

(26)

where m is the mass flow rate; Cp,m is the specific heat of liquid metal based nanofluid; Tout and Tin are the outlet and inlet temperatures, respectively. 17

Journal Pre-proof In the present study, the error between heat supplied to test section (Qsup) and heat absorbed by test fluid (Qabs) is less than 3%. To further improve the accuracy, the average heat transfer rate (Qave) is used for determining the heat transfer coefficient, defined as follows:

Qave 

Qsup  Qabs

(27)

2

The forced convection heat transfer coefficient (h) can be calculated as

h

Qave

(28)

 din L Twi  Tf 

where din and L are the inner diameter and length of test tube respectively; Tf and Twi are the average temperatures of test fluid and inner tube wall, and calculated by Eqs. (29) and (30) respectively. Tf  (Tout  Tin ) 2

(29)

 12  Twi    Tw  i   12  i 1 

(30)

where Twi(i) is the inner wall temperature at i measurement points and calculated as Twi  i   Two  i  

Qave ln  ro ri  2 L

,

 i  1, 2,3...12 

(31)

where Two(i) is the outer wall temperature at i measurement points, ro and ri are the outer and inner diameters of test tube respectively, and λ is the thermal conductivity of stainless steel. The maximum uncertainties of heat transfer coefficient (h) and pressure drop (ΔP) are calculated to be 9.1% and 8.3%, respectively. 4.4 Comparison between model predictions and experimental data Two types of models have been commonly used to simulate the nanofluid flow, i.e. two-phase mixture model [23, 43, 44] and single-phase model [20, 45]. In the two-phase mixture model, the movement between solid and fluid molecule is considered and the Brownian motion as well as thermophoresis migration of nano-powders can be reflected [46]. In the single-phase model, the 18

Journal Pre-proof accurate thermophysical properties of nanofluid need to be known [47]. In the present study, the two-phase mixture model is adopted to simulate the turbulent forced convection of liquid metal based nanofluid. In order to validate the accuracy of this numerical method, the forced convection heat transfer coefficients and pressure drops predicted by two-phase mixture model and single-phase model with input of measured thermophysical properties are compared with the experimental data. Figures 5 (a) and (b) show the comparison of forced convection heat transfer coefficients (h) and pressure drops (ΔP) for Ga-Cu and Ga-CNT nanofluids among two-phase mixture model predictions under uniform heat flux, single-phase model predictions with input of measured thermophysical properties and experimental data. The heat flux is 18758 W m-2, and Re is 20000. The maximum deviations of h predicted by two-phase mixture model from experimental data are 9.2% and 7.6% for Ga-Cu and Ga-CNT nanofluids respectively, while those of h predicted by single-phase model from experimental data are 11.2% and 12.4% for Ga-Cu and Ga-CNT nanofluids respectively. The maximum deviations of ΔP predicted by two-phase mixture model from experimental data are 4.1% and 6.3% for Ga-Cu and Ga-CNT nanofluids respectively, while those of ΔP predicted by single-phase model from experimental data are 6.2% and 9.2% for Ga-Cu and Ga-CNT nanofluids respectively. The comparison results indicate that the numerical method based on two-phase mixture model can ensure the prediction accuracy for forced convection heat transfer coefficient and pressure drop.

19

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(a) Comparison of h

(b) Comparison of ΔP Fig. 5. Comparison of heat transfer coefficients (h) and pressure drops (ΔP) among two-phase mixture model predictions, single-phase model predictions and experimental data under uniform heat flux. Figures 6 (a) and (b) show the comparison of forced convection heat transfer coefficients (h) and pressure drops (ΔP) for Ga-Cu and Ga-CNT nanofluids inside the PTR tube under non-uniform heat flux among two-phase mixture model predictions and single-phase model predictions with input of measured thermophysical properties. The condition of Re=20000 is selected for analysis. The maximum deviations of h predicted by two-phase mixture model from single-phase model are 3.2%

20

Journal Pre-proof and 4.9% for Ga-Cu and Ga-CNT nanofluids respectively. The maximum deviations of ΔP predicted by two-phase mixture model from single-phase model are 2.1% and 3.1% for Ga-Cu and Ga-CNT nanofluids respectively.

(a) Comparison of h

(b) Comparison of ΔP Fig. 6. Comparison of heat transfer coefficients (h) and pressure drops (ΔP) among two-phase mixture model predictions, single-phase model predictions under non-uniform heat flux.

21

Journal Pre-proof 5. Results and discussion 5.1 Thermal-hydraulic performance 5.1.1 Temperature distribution Figure 7 shows the three-dimensional temperature distribution on receiver tube surface for Ga-CNT nanofluids with different concentrations, and Reynolds number (Re) is fixed at 100000 as a representative example. The temperature distribution along circumferential direction is non-uniform, which is consistent with the non-uniform heat flux distribution. The hot spots occur in high heat flux region, and the temperature difference existing in each cross-section is increased along flow direction. With the increase of CNT concentration, the temperature gradient along flow direction in high heat flux region and the maximum temperature are significantly decreased, which indicates that the presence of nano-powders can enhance the forced convection heat transfer performance of liquid metal.

(a) Pure Ga

(b) Ga-CNT (φp=2 vol%)

(c) Ga-CNT (φp=5 vol%)

(d) Ga-CNT (φp=8 vol%) 22

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(e) Ga-CNT (φp=10 vol%) Fig. 7. Three-dimensional temperature distribution on receiver tube surface for Ga-CNT nanofluids with different concentrations. Figure 8 shows the two-dimensional temperature distribution for Ga-Cu nanofluids at different Reynolds number (Re) in the cross-section of z=2.03, and Cu concentration is fixed at 8 vol% as a representative example. As the flow is fully turbulent and Richardson number (Ri) <<1 under present simulation conditions, the natural convection driven by buoyancy can be neglected. The relatively low velocity near the wall causes higher temperature in this region, and the non-uniform heat flux distribution results in the distortion of circumferential temperature isotherms. With the increase of Re, the thickness of velocity and thermal boundary layer are decreased, causing the enhancement of forced convection heat transfer; thus, the average temperature in the cross-section decreases gradually and the temperature distribution tends to be uniform.

(a) Re=50000

(b) Re=100000

23

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(c) Re=150000

(d) Re=200000

(e) Re=250000

(f) Re=300000

Fig. 8. Two-dimensional temperature distribution for Ga-Cu nanofluids at different Reynolds number. Figures 9 (a) and (b) show the temperature difference (ΔTmax-min) between maximum temperature (i.e. outlet temperature) and minimum temperature (i.e. inlet tube temperature) for Ga-Cu and Ga-CNT nanofluids, respectively. ΔTmax-min is an important indicator for evaluating the temperature gradient and thermal stress on receiver tube wall. The large thermal stress caused by non-uniform temperature may lead to the rupture of tube, thus the system security will be enhanced with the decrease of ΔTmax-min. From Fig. 9, it can be seen that ΔTmax-min is reduced with the increase of Reynolds number (Re), and the reduction degree becomes smaller for higher Re. With the increase of nano-powder concentration (φp), ΔTmax-min is also decreased. At Re of 200000 as an example, comparing to pure Ga, ΔTmax-min are decreased by 5.2%, 9.5%, 19.2% and 24.3% for Ga-Cu nanofluids with φCu of 2, 5, 8 and 10 vol% respectively, and decreased by 5.5%, 13.8%, 19.9% and 25.6% for Ga-CNT nanofluids with φCNT of 2, 5, 8 and 10 vol% respectively.

24

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(a) Ga-Cu

(b) Ga-CNT Fig. 9. Temperature difference (ΔTmax-min) between maximum temperature and minimum temperature for Ga-Cu and Ga-CNT nanofluids. 5.1.2 Heat transfer and pressure drop characteristics Figures 10 (a) and (b) show the forced convection heat transfer coefficients (h) for Ga-Cu and Ga-CNT nanofluids, respectively. It can be seen that h increases with the increase of Reynolds number (Re) at fixed nano-powder concentration (φp). At φp of 5 vol% as an example, with the increase of Re from 50000 to 300000, h are increased by 234.9% and 250.6% for Ga-Cu and Ga-CNT nanofluids

25

Journal Pre-proof respectively. This phenomenon might be caused by the reduction of boundary layer thickness with the increase of Re.

(a) Ga-Cu

(b) Ga-CNT Fig. 10. Forced convection heat transfer coefficients (h) for Ga-Cu and Ga-CNT nanofluids. From Fig. 10, it also can be seen that forced convection heat transfer coefficient (h) increases with the increase of nano-powder concentration (φp) at fixed Reynolds number (Re). Compared to pure Ga, h averagely increase by 5.5%, 14.3%, 26.5% and 34.5% for Ga-Cu nanofluids with φCu of 2, 5, 8 and 10 vol% respectively, while averagely increase by 9.7%, 21.2%, 35.9% and 45.2% for Ga-CNT nanofluids 26

Journal Pre-proof with φCNT of 2, 5, 8 and 10 vol% respectively. It indicates that the presence of nano-powders enhances the forced convection heat transfer of liquid metal, and the enhancement effect of CNT is higher than that of Cu. This phenomenon might be explained as follows. (1) Effect of nano-powders on the thermophysical properties of liquid metal The presence of nano-powders (Cu or CNT) increases the thermal conductivity (λ) of pure liquid metal (Ga) due to Brownian motion of nano-powders, formation of molecular-level liquid layer at the liquid/nano-powder interface, heat transport inside nano-powders and effect of nano-powder clustering. λCNT (about 3000 W m-1 K-1) is much larger than λCu (about 401 W m-1 K-1), and the contact of cylindrical CNTs can form chain-like low-resistance heat conduction path [48]; thus, λGa-CNT is larger than λGa-Cu. In the present study, the experimental results show that at nano-powder concentrations (φp) of 2, 5, 8 and 10 vol%, λGa-CNT are 7.6%, 16.9%, 27.0% and 30.2% larger than λGa-Cu respectively, which causes the enhancement effect of CNT on forced convection heat transfer coefficient to be higher than that of Cu. (2) Effect of nano-powders on the flow characteristics of liquid metal The nano-powders can reduce of thermal boundary layer thickness. The irregular micro-motions of nano-powders can enhance momentum exchange and increase the intensity of turbulence [49]. The number of vortexes, vorticity and turbulent kinetic energy increase with the increase of nano-powder concentration [50]. Therefore, the addition of nano-powders can augment the thermal energy transfer from the receiver tube wall to the nanofluid. (3) Effect of nano-powder migration Figure 11 schematically shows the physical process of nano-powder migration in PTR tube. The distribution of nano-powders in PTR tube is affected by Brownian motion and thermophoresis [51]. 27

Journal Pre-proof Brownian motion promotes the nano-powder motion in the opposite direction of the concentration gradient and tends to make the nanofluid more uniform, while the thermophoresis causes the nano-powder migration in the opposite direction of the temperature gradient (i.e. from hotter to colder region) and causes the nanofluid to be non-uniform [52]. The uniformity degree of nano-powder distribution is determined by the opposite effects of Brownian motion and thermophoresis, and can be evaluated by NBT, which is defined as the ratio of Brownian motion to thermophoretic diffusivities [52]. NBT is proportional to DB/DT, and DB ( DB  kBT ) and DT ( DT =β μf φ ) represent Brownian diffusion 3πμf d p

ρf

coefficient and thermophoresis diffusion coefficient respectively. In the present study, NBT of Ga-CNT nanofluid is 45% less than that of Ga-Cu nanofluid, indicating that the thermophoresis effect is stronger for Ga-CNT nanofluid. According to the boundary condition, the heat flux on the lower surface of PTR tube (qlw) is higher than that on the upper surface (quw), implying that the direction of temperature gradient is towards the lower surface. Therefore, the stronger thermophoresis effect for Ga-CNT nanofluid causes more nano-powders to accumulate at the upper surface, and then the local viscosity at the lower surface decreases, which results in the increase of momentum value and higher heat transfer performance through convection effect [52].

Fig. 11. Schematic of nano-powder migration process in PTR tube. Figures 12 (a) and (b) show the frictional pressure drops (ΔP) for Ga-Cu and Ga-CNT nanofluids,

28

Journal Pre-proof respectively. It can be seen that ΔP increases with the increase of Reynolds number (Re). At φp of 5 vol% as an example, with the increase of Re from 50000 to 300000, ΔP are increased by 23.8 times and 24.4 times for Ga-Cu and Ga-CNT nanofluids respectively. ΔP increases with the increase of nano-powder concentration (φp). Compared to pure Ga, ΔP averagely increase by 9.9%, 27.6%, 46% and 63.4% for Ga-Cu nanofluids with φCu of 2, 5, 8 and 10 vol% respectively, while averagely increase by 11.2%, 33.4%, 58.2% and 80.9% for Ga-CNT nanofluids with φCNT of 2, 5, 8 and 10 vol% respectively. The reason for this phenomenon is that the viscosity and collision rate of nano-powders increase with the increase of nano-powder concentration.

(a) Ga-Cu

29

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(b) Ga-CNT Fig. 12. Frictional pressure drops (ΔP) for Ga-Cu and Ga-CNT nanofluids. 5.1.3 Overall thermal-hydraulic performance evaluation To evaluate the overall thermal-hydraulic performance of liquid metal based nanofluid in the PTR tube, the performance evaluation criteria (PEC) and thermal-hydraulic performance parameter (η) are adopted, as done in the references [53, 54] and [55, 56] respectively.

PEC =

η=

hm /hf

(32)

 ΔPm / ΔPf 

1/3

 Num / Nuf  1/3  fm / ff 

(33)

 Num / Nuf  hm /hf λ ρ  η= =  f  f  1/3 1/3  fm / ff   ΔPm / ΔPf  λm  ρm 

1/3

μ   m   μf 

2/3

(34)

Figure 13 shows the performance evaluation criteria (PEC) and thermal-hydraulic performance parameter (η) for Ga-Cu and Ga-CNT nanofluids. It can be seen that PEC increases with the increase of nano-powder concentration (φp) at fixed Reynolds number (Re). At fixed φp, PEC increases first and then decreases with the increase of Re. For Ga-Cu and Ga-CNT nanofluids, the highest values of PEC occur at φp=10 vol% and Re=250000. The values of PEC for Ga-CNT nanofluids are averagely 4.1% 30

Journal Pre-proof higher than those for Ga-Cu nanofluids. η for Ga-CNT nanofluids are all less than 1, and η for Ga-Cu nanofluids are greater than 1 at middle Re and high φp. η of Ga-Cu and Ga-CNT nanofluids are less than PEC, and this phenomenon is mainly caused by the significant increase of thermal conductivity with the increase of nano-powder concentration.

(a) PEC for Ga-Cu

(b) PEC for Ga-CNT

(c) η for Ga-Cu

(d) η for Ga-CNT

Fig. 13. Performance evaluation criteria (PEC) and thermal-hydraulic performance parameter (η) for Ga-Cu and Ga-CNT nanofluids.

5.2 Thermodynamic performance 5.2.1 Entropy generation analysis Figures 14 and 15 show the frictional entropy generation (Sg,fr) and thermal entropy generation (Sg,th) for liquid metal based nanofluids, respectively. At fixed nano-powder concentration (φp), Sg,fr

31

Journal Pre-proof increases and Sg,th decreases with the increase of Re. Also, Sg,fr increases and Sg,th decreases with the increase of φp at fixed Re. With the increase of φp from 0 to 10 vol%, Sg,fr averagely increase by 105.8% and 152.2% for Ga-Cu and Ga-CNT nanofluids respectively, and Sg,th averagely decrease by 22.9% and 35.6% for Ga-Cu and Ga-CNT nanofluids respectively. The possible reasons for above phenomenon are as follows. (1) With the increase of Re, the shear stress and frictional pressure drop increase, leading to the increase of friction irreversibility. This consequently enhances the forced convection heat transfer, and lowers the temperature difference between fluid and tube wall, resulting in the decrease of heat transfer irreversibility. (2) With the increase of nano-powder concentration, both the thermal conductivity and viscosity of liquid metal based nanofluid increase, causing the enhancement of heat transfer and the increase of fluid frictional resistance.

(a) Ga-Cu

32

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(b) Ga-CNT Fig. 14. Frictional entropy generation (Sg,fr) for liquid metal based nanofluids.

(a) Ga-Cu

33

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(b) Ga-CNT Fig. 15. Thermal entropy generation (Sg,th) for liquid metal based nanofluids. Figure 16 shows the distribution of frictional entropy generation (Sg,fr) and thermal entropy generation (Sg,th) in the cross-section of z=2.03 for liquid metal based nanofluid (Ga-CNT nanofluid with concentration of 10 vol% as a representative example). From Fig. 16, it can be seen that in the vicinity of receiver tube wall, Sg,fr and Sg,th are large due to high velocity as well as temperature gradient; while in the central region of receiver tube, Sg,fr and Sg,th are relatively small due to low velocity as well as temperature gradient. The isolines of Sg,fr are nearly concentric circles, while Sg,th in the lower part of cross-section is higher than that in the upper part since the heat flux and temperature distribution are non-uniform.

(a) Sg,fr for pure Ga

(b) Sg,th for pure Ga 34

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(c) Sg,fr for Ga-CNT (φp=10 vol%)

(d) Sg,th for Ga-CNT (φp=10 vol%)

Fig. 16. Cross-sectional distribution of frictional entropy generation (Sg,fr) and thermal entropy generation (Sg,th). Figure 17 shows the total entropy generation (Sg) for liquid metal based nanofluids. It can be seen that with the increase of Reynolds number (Re), Sg decreases at nano-powder concentrations (φp) of 0, 2 and 5 vol%, while Sg first decreases and then increases at φp of 8 and 10 vol%. At nano-powder concentrations (φp) of 2, 5, 8 and 10 vol%, Sg for Ga-Cu nanofluids are 4.4%, 10.4%, 15% and 18.9% less than that of pure Ga, while those for Ga-CNT nanofluids are 8.3%, 18.4%, 25.7% and 29.7% less than that of pure Ga. Under present simulation conditions, the optimal point corresponding to minimum entropy generation occurs at φp=10% and Re=250000 for both Ga-Cu and Ga-CNT nanofluids. The effects of Re and φp on Sg might be explained as follows. Firstly, with the increase of Re, the increase extent of frictional entropy generation (Sg,fr) is always smaller than the decrease extent of thermal entropy generation (Sg,th) at lower φp, while the increase extent of Sg,fr is firstly smaller and then larger than the decrease extent of Sg,th at higher φp. Secondly, with the increase of φp, the increase extent of Sg,fr is always smaller than the decrease extent of Sg,th.

35

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(a) Ga-Cu

(b) Ga-CNT Fig. 17. Total entropy generation (Sg) for liquid metal based nanofluids. Figure 18 shows Bejan number (Be) for liquid metal based nanofluids. Be represents the fraction of thermal entropy generation in total entropy generation, and is defined as Be=Sg,th/Sg. In Fig. 18, at relatively low Reynolds number (Re<150000), the values of Be range from 0.95 to 1, indicating the thermal entropy generation contribution is predominant. With the further increase of Re, Be decreases sharply due to the enhanced frictional entropy generation contribution. It also can be seen that Be decreases with the increase of nano-powder concentration (φp), which is caused by the decrease of heat 36

Journal Pre-proof transfer irreversibility and the increase of friction irreversibility.

(a) Ga-Cu

(b) Ga-CNT Fig. 18. Bejan number (Be) for liquid metal based nanofluids. In order to evaluate thermodynamic performance of liquid metal based nanofluid, the augmentation entropy generation number is defined as Eq. (35).

N

Sg,nf Sg,bf

(35)

where Sg,nf and Sg,bf are the total entropy generation rates for liquid metal based nanofluid and pure

37

Journal Pre-proof liquid metal respectively. Figure 19 shows the augmentation entropy generation number (N) for liquid metal based nanofluids. Reynolds number (Re) is fixed at 100000 as a representative example. It can be seen that N for Ga-Cu nanofluids and Ga-CNT nanofluids with different nano-powder conentrations (φp) are all less than 1, which means the presence of nano-powders can reduce the degree of irreversibility and improve the thermodynamic performance of liquid metal. N of Ga-CNT nanofluids are 4.2%, 9.1%, 13.4% and 15.1% less than those of Ga-Cu nanofluids at φp of 2, 5, 8 and 10 vol% respectively, indicating that the thermodynamic performance of Ga-CNT nanofluid is better than that of Ga-Cu nanofluid under the same condition.

Fig. 19. Augmentation entropy generation number (N) for liquid metal based nanofluids. 5.2.2 Exergetic performance Figure 20 shows the exergetic efficiency (ηex) for liquid metal based nanofluids. It can be seen that ηex decreases with the increase of Reynolds number (Re) at fixed nano-powder concentration (φp). At φp of 10 vol% as an example, with the increase of Re from 50000 to 300000, ηex are decreased by 3.36% and 5.23% for Ga-Cu and Ga-CNT nanofluids respectively. It also can be seen that ηex slightly

38

Journal Pre-proof increases with the increase of φp at fixed Re. At φp of 2, 5, 8 and 10 vol%, ηex for Ga-Cu nanofluids are averagely 0.34%, 0.57%, 0.91% and 1.31% higher than that of pure Ga respectively, while ηex for Ga-CNT nanofluids are averagely 0.40%, 0.87%, 1.32% and 1.65% higher than that of pure Ga respectively.

(a) Ga-Cu

(b) Ga-CNT Fig. 20. Exergetic efficiency (ηex) for liquid metal based nanofluids.

39

Journal Pre-proof 5.3 Performance comparison for Cu and CNT nanofluids between present study and existing researches The comparison of thermal-hydraulic and thermodynamic performance for Cu and CNT nanofluids between present study and existing researches are listed in Table 4. It can be seen that the presence of Cu or CNTs can increase the forced convection heat transfer coefficient of base fluid and decrease the entropy generation rate. The heat transfer enhancement degree or entropy generation rate decrease degree caused by nano-powders are influenced by the thermophysical properties of base fluid. Table 4. Comparison of thermal-hydraulic and thermodynamic performance for Cu and CNT nanofluids between present study and existing researches Base fluid

Tin

Re

Nano-powder concentration

Mwesigye et al. [12]

Therminol®VP-1

350 ~ 650 K

3560 ~ 1150000

0 ~ 6 vol%

Mwesigye et al. [20]

Therminol®VP-1

400 ~ 650 K

18000 ~ 2660000

0 ~ 6 vol%

Benabderrahmane et al. [21]

Synthetic oil

573 K

257056

1 vol%

Present study

Ga

473.15 K

50000 ~ 300000

0 ~ 10 vol%

Mwesigye et al. [22]

Therminol®VP-1

400 ~ 650 K

20000 ~ 1300000

0 ~ 2.5 vol%

Ethylene glycol

320 K

–

0 ~ 0.3 vol%

Ga

473.15 K

50000 ~ 300000

0 ~ 10 vol%

References

Nano-powder type

Kasaeian et al. [29]

Cu

CNT

Present study

Nano-powder effects Heat transfer coefficient is maximally enhanced by 32% Entropy generation rate is maximally decreased by 30% Heat transfer coefficient is maximally enhanced by 6.4% Entropy generation rate is maximally decreased by 17% Local Nusselt number is enhanced by 9.0% Heat transfer coefficient is maximally enhanced by 34.5% Entropy generation rate is maximally decreased by 18.9% Heat transfer coefficient is maximally enhanced by 234% Entropy generation rate is maximally decreased by 70% Heat transfer coefficient is enhanced by 20% at CNT concentration of 0.2 vol% Heat transfer coefficient is maximally enhanced by 45.2% Entropy generation rate is maximally decreased by 29.7%

6. Conclusions (1) The temperature difference between maximum and minimum temperatures of PTR tube with liquid metal is reduced with the presence of Cu or CNT. These findings indicates that the liquid metal based nanofluid reduces the thermal stress caused by non-uniform temperature and then enhance the PTC system’s security. 40

Journal Pre-proof (2) The forced convection heat transfer coefficients of Ga-Cu and Ga-CNT nanofluids are higher than that of pure Ga at the same Reynolds number. At nano-powder concentrations of 2, 5, 8 and 10 vol%, the enhancement degrees for Ga-Cu nanofluids are 5.5%, 14.3%, 26.5% and 34.5% respectively, while those for Ga-CNT nanofluids are 9.7%, 21.2%, 35.9% and 45.2% respectively. The enhancement effect of CNT on forced convection heat transfer is higher than that of Cu. (3) The frictional pressure drops of Ga-Cu and Ga-CNT nanofluids are larger than that of pure Ga at the same Reynolds number. At nano-powder concentrations of 2, 5, 8 and 10 vol%, the increase degrees for Ga-Cu nanofluids are 9.9%, 27.6%, 46% and 63.4% respectively, while those for Ga-CNT nanofluids are 11.2%, 33.4%, 58.2% and 80.9% respectively. (4) With the increase of nano-powder concentration, the total entropy generation decreases and the exergetic efficiency increases. The presence of nano-powders can reduce the degree of irreversibility and improve the thermodynamic performance of liquid metal; the thermodynamic performance of Ga-CNT nanofluids is better than that of Ga-Cu nanofluids under the same condition.

Acknowledgements The authors gratefully acknowledge the supports by the Key Program of Shanghai Science and Technology Commission (Grant No. 16040501600).

References [1] N. Lorenzin, A. Abánades. A review on the application of liquid metals as heat transfer fluid in Concentrated Solar Power technologies. International Journal of Hydrogen Energy 41 (2016) 6990–6995. [2] N. Boerema, G. Morrison, R. Taylor, G. Rosengarten. Liquid sodium versus Hitec as a heat transfer fluid in solar thermal central receiver systems. Solar Energy 86 (2012) 2293–2305. 41

Journal Pre-proof [3] J. Pacio, Th. Wetzel. Assessment of liquid metal technology status and research paths for their use as efficient heat transfer fluids in solar central receiver systems. Solar Energy 93 (2013) 11–22. [4] A. Fritsch, J. Flesch, V. Geza, Cs. Singer, R. Uhlig, B. Hoffschmidt. Conceptual study of central receiver systems with liquid metals as efficient heat transfer fluids. Energy Procedia 69 (2015) 644–653. [5] L. Marocco, G. Cammi, J. Flesch, Th. Wetzel. Numerical analysis of a solar tower receiver tube operated with liquid metals. International Journal of Thermal Sciences 105 (2016) 22–35. [6] S.A. Kalogirou. A detailed thermal model of a parabolic trough collector receiver. Energy 48 (2012) 298–306. [7] X.T. Gong, F.Q. Wang, H.Y. Wang, J.Y. Tan, Q. Z. Lai, H.Z. Han. Heat transfer enhancement analysis of tube receiver for parabolic trough solar collector with pin fin arrays inserting. Solar Energy 144 (2017) 185–202. [8] C. Chang, A. Sciacovelli, Z.Y. Wu, X. Li, Y.L. Li, M.Z. Zhao, J. Deng, Z.F. Wang, Y.L Ding. Enhanced heat transfer in a parabolic trough solar receiver by inserting rods and using molten salt as heat transfer fluid. Applied Energy 220 (2018) 337–350. [9] K.Q. Ma, J. Liu. Nano liquid-metal fluid as ultimate coolant. Physics Letters A 361 (2007) 252–256. [10] S.A. Kalogirou, S. Karellas, V. Badescu, K. Braimakis. Exergy analysis on solar thermal systems: A better understanding of heir sustainability. Renewable Energy 85 (2016) 1328–1333. [11] R. Loni, E. Askari Asli-Ardeh, B. Ghobadian, A.B. Kasaeian, E. Bellos. Energy and exergy investigation of alumina/oil and silica/oil nanofluids in hemispherical cavity receiver: Experimental Study. Energy 164 (2018) 275–287. 42

Journal Pre-proof [12] A. Mwesigye, Z.J Huan, J.P. Meyer. Thermal performance and entropy generation analysis of a high concentration ratio parabolic trough solar collector with Cu-Therminol®VP-1 nanofluid. Energy Conversion and Management 120 (2016) 449–465. [13] M.M. Sarafraz, H. Arya, M. Arjomandi. Thermal and hydraulic analysis of a rectangular microchannel with gallium-copper oxide nano-suspension. Journal of Molecular Liquids 263 (2018) 382–389. [14] M.M. Sarafraz, M. Arjomandi. Thermal performance analysis of a microchannel heat sink cooling with copper oxide-indium (CuO/In) nano-suspensions at high-temperatures. Applied Thermal Engineering 137 (2018) 700–709. [15] M.M. Sarafraz, M. Arjomandi. Demonstration of plausible application of gallium nano-suspension in microchannel solar thermal receiver: Experimental assessment of thermohydraulic performance of microchannel. International Communications in Heat and Mass Transfer 94 (2018) 39–46. [16] S.E. Ghasemi, A.A. Ranjbar. Thermal performance analysis of solar parabolic trough collector using nanofluid as working fluid: A CFD modelling study. Journal of Molecular Liquids 222 (2016) 159–166. [17] P.D. Tagle-Salazar, K.D.P. Nigam, C.I. Rivera-Solorio. Heat transfer model for thermal performance analysis of parabolic trough solar collectors using nanofluids. Renewable Energy 125 (2018) 334–343. [18] E.C. Okonkwo, E.A. Essien, E. Akhayere, M. Abid, D. Kavaz, T.A.H. Ratlamwala. Thermal performance analysis of a parabolic trough collector using water-based green-synthesized nanofluids. Solar Energy 170 (2018) 658–670. [19] J. Subramani, P.K. Nagarajan, O. Mahian, R. Sathyamurthy. Efficiency and heat transfer 43

Journal Pre-proof improvements in a parabolic trough solar collector using TiO2 nanofluids under turbulent flow regime. Renewable Energy 119 (2018) 19–31. [20] A. Mwesigye, J.P. Meyer. Optimal thermal and thermodynamic performance of a solar parabolic trough receiver with different nanofluids and at different concentration ratios. Applied Energy 193 (2017) 393–413. [21] A. Benabderrahmane, M. Aminallah, S. Laouedj, A. Benazza, J.P. Solano. Heat transfer enhancement in a parabolic trough solar receiver using longitudinal fins and nanofluids. Journal of Thermal Science 25 (2016) 410–417. [22] A. Mwesigye, Í.H. Yı lmaz, J.P. Meyer. Numerical analysis of the thermal and thermodynamic performance of a parabolic trough solar collector using SWCNTs-Therminol®VP-1nanofluid. Renewable Energy 119 (2018) 844–862. [23] E. Kaloudis, E. Papanicolaou, V. Belessiotis. Numerical simulations of a parabolic trough solar collector with nanofluid using a two-phase model. Renewable Energy 97 (2016) 218–229. [24] T. Sokhansefat, A.B. Kasaeian, F. Kowsary. Heat transfer enhancement in parabolic trough collector tube using Al2O3/synthetic oil nanofluid. Renewable and Sustainable Energy Reviews 33 (2014) 636–644. [25] S.E. Ghasemi, A.A. Ranjbar. Effect of using nanofluids on efficiency of parabolic trough collectors in solar thermal electric power plants. International Journal of Hydrogen Energy 42 (2017) 21626–21634. [26] H. Khakrah, A. Shamloo, S. K. Hannani. Exergy analysis of parabolic trough solar collectors using Al2O3/synthetic oil nanofluid. Solar Energy 173 (2018) 1236–1247. [27] A. Allouhi, M. Benzakour Amine, R. Saidur, T. Kousksou, A. Jamila. Energy and exergy analyses 44

Journal Pre-proof of a parabolic trough collector operated with nanofluids for medium and high temperature applications. Energy Conversion and Management 155 (2018) 201–217. [28] E. Bellos, C. Tzivanidis, D. Tsimpoukis. Enhancing the performance of parabolic trough collectors using nanofluids and turbulators. Renewable and Sustainable Energy Reviews 91 (2018) 358–375. [29] A. Kasaeian, R. Daneshazarian, F. Pourfayaz. Comparative study of different nanofluids applied in a trough collector with glass-glass absorber tube. Journal of Molecular Liquids 234 (2017) 315–323. [30] M.M. Tafarroj, R. Daneshazarian, A. Kasaeian. CFD modeling and predicting the performance of direct absorption of nanofluids in trough collector. Applied Thermal Engineering 148 (2019) 256–269. [31] V. Dudley, G. Kolb, M. Sloan, D. Kearney. SEGS LS2 solar collector-test results. Report of Sandia National Laboratories. SAN94-1884 (1994). [32] H. Kim, J. Ham, C. Park, H. Cho. Theoretical investigation of the efficiency of a U-tube solar collector using various nanofluids. Energy 94 (2016) 497–507. [33] M. Manninen, V. Taivassalo, S. Kallio. On the mixture model for multiphase flow. VTT Publications 288, Technical Research Center of Finland (1996). [34] L. Schiller, A. Naumann. A drag coefficient correlation. Z. Ver. Dtsch. Ing. 77 (1935) 318–320. [35] S. Manservisi, F. Menghini. Triangular rod bundle simulations of a CFD k-ε-kθ-εθ heat transfer turbulence model for heavy liquid metals. Nuclear Engineering and Design 273 (2014) 251–270. [36] S. Manservisi, F. Menghini. A CFD four parameter heat transfer turbulence model for engineering applications in heavy liquid metals. International Journal of Heat and Mass Transfer 69 (2014) 312–326. [37] Z.D. Cheng, Y.L. He, J. Xiao, Y.B. Tao, R.J. Xu. Three-dimensional numerical study of heat transfer characteristics in the receiver tube of parabolic trough solar collector. International 45

Journal Pre-proof Communications in Heat and Mass Transfer 37 (2010) 782–787. [38] E. Bellos, C. Tzivanidis, I. Daniil, K. A. Antonopoulos. The impact of internal longitudinal fins in parabolic trough collectors operating with gases. Energy Conversion and Management 135 (2017) 35–54. [39] R. Petela. Exergy of undiluted thermal radiation. Solar Energy 74 (2003) 469–488. [40] H.C. Brinkman. The viscosity of concentrated suspensions and solution. J. Chem. Phys. 20 (1952) 571–581. [41] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transfer 11 (2) (1998) 151–170. [42] R.L. Hamilton, O.K. Crosser. Thermal conductivity of heterogeneous two component systems. Ind Eng Chem Fundam 1(3) (1962) 187–191. [43] X.M. Zhou, Y.N. Jiang, X.F. Li, K.Y. Cheng, X.L. Huai, X.D. Zhang, H.L. Huang. Numerical investigation of heat transfer enhancement and entropy generation of natural convection in a cavity containing nano liquid-metal fluid. International Communications in Heat and Mass Transfer 106 (2019) 46–54. [44] Y. Abbassi, A.S. Shirani, S. Asgarian. Two-phase mixture simulation of Al2O3/water nanofluid heat transfer in a non-uniform heat addition test section. Progress in Nuclear Energy 83 (2015) 356–364. [45] H.W. Chiam, W.H. Azmi, N.M. Adam, M.K.A.M. Ariffin. Numerical study of nanofluid heat transfer for different tube geometries-A comprehensive review on performance. International Communications in Heat and Mass Transfer 86 (2017) 60–70. [46] Sh.M. Vanaki, P. Ganesan, H.A.Mohammed. Numerical study of convective heat transfer of 46

Journal Pre-proof nanofluids: A review. Renewable and Sustainable Energy Reviews 54 (2016) 1212–1239. [47] M. Hejazian, M.K. Moraveji, A. Beheshti. Comparative study of Euler and mixture models for turbulent flow of Al2O3 nanofluid inside a horizontal tube. International Communications in Heat and Mass Transfer 52 (2014) 152–158. [48] H.F. Jiang, Q. Zhang, L. Shi. Effective thermal conductivity of carbon nanotube-based nanofluid. Journal of the Taiwan Institute of Chemical Engineers 55 (2015) 76–81. [49] W.Z. Cui, M.L. Bai, J.Z. Lv, L. Zhang, G.J. Li, M. Xu. On the flow characteristics of nanofluids by experimental approach and molecular dynamics simulation. Experimental Thermal and Fluid Science 39 (2012) 148–157. [50] J.Z. Lv, C.Z. Hu, M.L. Bai, L.Y. Li, L. Shi, D.D. Gao. Visualization of SiO2-water nanofluid flow characteristics in backward-facing step using PIV. Experimental Thermal and Fluid Science 101 (2019) 151–159. [51] M.A. Sharafeldin, G. Gróf, O. Mahian. Experimental study on the performance of a flat-plate collector using WO3/Water nanofluids. Energy 141 (2017) 2436–2444. [52] F. Hedayati, G. Domairryba. Nanoparticle migration effects on fully developed forced convection of TiO2–water nanofluid in a parallel plate microchannel. Particuology 24 (2016) 96–107. [53] W. Wang, Y.N. Zhang, K.S. Lee, B.X. Li. Optimal design of a double pipe heat exchanger based on the outward helically corrugated tube. International Journal of Heat and Mass Transfer 135 (2019) 706–716. [54] H.E. Ahmed, M.Z. Yusoff, M.N.A. Hawlader, M.I. Ahmed, B.H. Salman, A.Sh. Kerbeet. Turbulent heat transfer and nanofluid flow in a triangular duct with vortex generators. International Journal of Heat and Mass Transfer 105 (2017) 495–504. 47

Journal Pre-proof [55] S. Singh, S. Chander, J.S.Saini. Thermo-hydraulic performance due to relative roughness pitch in V-down rib with gap in solar air heater duct-Comparison with similar rib roughness geometries. Renewable and Sustainable Energy Reviews 43 (2015) 1159–1166. [56] R.L Webb, E.R.G. Eckert. Application of rough surfaces to heat exchanger design. International Journal of Heat and Mass Transfer 15 (1972) 1647–1658.

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Conflict of Interest Form

We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property.

Author's email: [email protected]

Hao Peng

[email protected] Wenhua Guo [email protected] Meilin Li

Journal Pre-proof Highlights 

Liquid metal based nanofluid is proposed as working fluid for parabolic trough collector.

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Thermophysical properties of gallium-copper and gallium-carbon nanotube nanofluids are experimentally measured.

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Thermal-hydraulic performance of liquid metal based nanofluids are investigated.

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Entropy generation and exergetic efficiency of liquid metal based nanofluids are analyzed.