Preference Parameters for the Calculation of Thermal Conductivity by Multiparticle Collision Dynamics
Abstract
:1. Introduction
2. Numerical Model
2.1. MPCD Implementation
2.2. Calculation of Thermal Conductivity
2.3. Definition of Nondimensional Parameters
3. Analysis of Various Effect Factors
3.1. Effect of Time-Step and Coarse-Grained Mass
3.2. Effect of Bin Size
3.3. Effect of Rotation Angle
3.4. Effect of Temperature
4. Thermal Conductivity Calculations
4.1. Thermal Conductivity of Ar
4.2. Thermal Conductivity of Water
4.3. Thermal Conductivity of Cu-Water Nanofluid
5. Conclusions
- (1)
- The method proposed is applicable as long as suitable MPCD parameters are selected. It is suitable for various systems, such as argon, water and nanofluids. The computational accuracy was ensured, and the deviations of argon, water and Cu-water nanofluid were 3.4%, 1.5% and 1.2%, respectively.
- (2)
- The combined rotation angle (90°, 180°, 270°) with a probability of (1/6, 1/6, 4/6) may be preferential for calculating the thermal conductivity. The reason could be the isotropy of the simulation system.
- (3)
- The adaptive time-steps were 1.0, 0.35 and 0.35 for argon, water and copper-water nanofluid respectively, because argon has a greater weight compared to water. The underlying mechanism may be the different interaction intensity between different particles. It can be interpreted by the different parameters, and , in L-J potential for different molecules.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
a | Bin size |
Stochastic rotation matrix | |
e | Local energy |
fcc | Lattice constant |
Time-step | |
j | Local momentum |
k | Thermal conductivity |
kB | Boltzmann constant |
m | Mass of fluid particle |
M | Mass of coarse-grained particle |
N | Number of particles |
Q | Heat flux |
Position vector | |
Thermostats | |
Time | |
T | Temperature |
Velocity | |
x | z-coordinate |
Rotation angle | |
Mean free path | |
Average number density | |
Scale parameter of L-J potential | |
Well depth of L-J potential | |
Superscript and subscript | |
b | Solvents/fluid |
i | ith particle |
p | Solutes/particle |
th cell |
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Lattice Constant | fcc = 1.550 | |||||
Bin size | 1.000 | 1.250 | 1.465 | 1.685 | 1.780 | 1.983 |
Number density | 1.590 | 3.370 | 5.140 | 7.810 | 9.110 | 12.720 |
Lattice Constant | fcc = 1.750 | |||||
Bin size | 1.000 | 1.250 | 1.465 | 1.685 | 1.780 | 1.983 |
Number density | 1.782 | 3.778 | 5.771 | 8.788 | 10.250 | 14.310 |
Lattice Constant | fcc = 1.950 | |||||
Bin size | 1.000 | 1.250 | 1.465 | 1.685 | 1.780 | 1.983 |
Number density | 2.003 | 4.000 | 6.470 | 9.840 | 11.500 | 16.020 |
Case Number | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | |||||||
CRA | 130° | 90° | 180° | 90° | 180° | 270° | 90° | 180° | 270° | 90° | 180° | 270° |
Probability | 1 | 1/2 | 1/2 | 1/3 | 1/3 | 1/3 | 1/6 | 2/6 | 3/6 | 1/6 | 1/6 | 4/6 |
TC | 3.1241 | 3.1548 | 3.1476 | 3.2304 | 3.2714 | |||||||
Case Number | Case 6 | Case 7 | Case 8 | Case 9 | Case 10 | |||||||
CRA | 135° | 90° | 270° | 90° | 270° | 360° | 90° | 270° | 360° | 90° | 270° | 360° |
Probability | 1 | 1/2 | 1/2 | 1/3 | 1/3 | 1/3 | 1/6 | 2/6 | 3/6 | 1/6 | 1/6 | 4/6 |
TC | 3.1453 | 3.2159 | 5.2538 | 7.0564 | 11.2008 |
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Wang, R.; Zhang, Z.; Li, L.; Zhu, Z. Preference Parameters for the Calculation of Thermal Conductivity by Multiparticle Collision Dynamics. Entropy 2021, 23, 1325. https://doi.org/10.3390/e23101325
Wang R, Zhang Z, Li L, Zhu Z. Preference Parameters for the Calculation of Thermal Conductivity by Multiparticle Collision Dynamics. Entropy. 2021; 23(10):1325. https://doi.org/10.3390/e23101325
Chicago/Turabian StyleWang, Ruijin, Zhen Zhang, Long Li, and Zefei Zhu. 2021. "Preference Parameters for the Calculation of Thermal Conductivity by Multiparticle Collision Dynamics" Entropy 23, no. 10: 1325. https://doi.org/10.3390/e23101325
APA StyleWang, R., Zhang, Z., Li, L., & Zhu, Z. (2021). Preference Parameters for the Calculation of Thermal Conductivity by Multiparticle Collision Dynamics. Entropy, 23(10), 1325. https://doi.org/10.3390/e23101325