Modeling and Optimization of Gaseous Thermal Slip Flow in Rectangular Microducts Using a Particle Swarm Optimization Algorithm
Abstract
:1. Introduction
1.1. Rarefied Gas Flows
1.2. Artificial Neural Networks
1.3. Particle Swarm Optimization Algorithm
2. Mathematical Model
2.1. Hydrodynamic Analysis
2.2. Thermal Analysis
2.3. Solution Procedure
3. Results and Discussion
4. Conclusions
- The small tolerance values for the mean squared error function values and a very close correlation coefficient of 1 in the NN models proved that the NN models were suitable to use for predicting the Poiseuille Po and Nusselt Nu numbers.
- Without going back to the numerical data, the proposed models were used with the PSO algorithm to find the optimal values of Po and Nu.
- The optimal values of Po and Nu are found when and .
- The correlation coefficient of the models was greater than 0.95.
- The optimal values of the curves were determined when the curves became stable.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Morini et al. [36] | Sadeghi et al. [37] | Present Results | |
---|---|---|---|
0.2 | 9.46 | 9.464 | 9.519 |
0.4 | 8.65 | 8.654 | 8.721 |
0.6 | 8.25 | 8.248 | 8.331 |
0.8 | 8.08 | 8.076 | 8.178 |
1 | 8.04 | 8.033 | 8.159 |
Numerical | Exact [38] | % Difference | |
---|---|---|---|
0.001 | 24.031 | 23.7 | 1.3774 |
0.01 | 23.743 | 23.41 | 1.4025 |
0.02 | 23.432 | 22.24 | 5.0871 |
0.1 | 21.259 | 20.95 | 1.4535 |
0.2 | 19.182 | 18.89 | 1.5223 |
0.3 | 17.641 | 17.36 | 1.5929 |
0.4 | 16.514 | 16.24 | 1.6592 |
0.5 | 15.712 | 15.43 | 1.7948 |
0.6 | 15.164 | 14.87 | 1.9388 |
0.7 | 14.811 | 14.5 | 2.0998 |
0.8 | 14.608 | 14.28 | 2.2453 |
0.9 | 14.519 | 14.17 | 2.4037 |
1 | 14.514 | 14.14 | 2.5768 |
Numerical | Exact [38] | % Difference | |
---|---|---|---|
0.001 | 10.944 | 10.9 | 0.402 |
0.01 | 10.862 | 10.82 | 0.3867 |
0.02 | 10.773 | 10.47 | 2.8126 |
0.1 | 10.139 | 10.09 | 0.4833 |
0.2 | 9.519 | 9.46 | 0.6198 |
0.3 | 9.056 | 9 | 0.6184 |
0.4 | 8.721 | 8.66 | 0.6995 |
0.5 | 8.487 | 8.41 | 0.9073 |
0.6 | 8.331 | 8.25 | 0.9723 |
0.7 | 8.233 | 8.14 | 1.1296 |
0.8 | 8.178 | 8.08 | 1.1983 |
0.9 | 8.157 | 8.04 | 1.4344 |
1 | 8.159 | 8.04 | 1.4585 |
0.001 | 6.1658 | 1.4213 | 0.7164 |
0.25 | 5.1047 | 1.7625 | 1.0819 |
0.35 | 4.6786 | 1.8996 | 1.2287 |
0.5 | 4.0394 | 2.1051 | 1.4488 |
0.65 | 3.8048 | 2.1830 | 1.5590 |
0.75 | 3.6485 | 2.2348 | 1.6325 |
0.85 | 3.6156 | 2.2745 | 1.6816 |
1 | 3.5662 | 2.3341 | 1.7552 |
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Hamadneh, N.N.; Khan, W.A.; Khan, I.; Alsagri, A.S. Modeling and Optimization of Gaseous Thermal Slip Flow in Rectangular Microducts Using a Particle Swarm Optimization Algorithm. Symmetry 2019, 11, 488. https://doi.org/10.3390/sym11040488
Hamadneh NN, Khan WA, Khan I, Alsagri AS. Modeling and Optimization of Gaseous Thermal Slip Flow in Rectangular Microducts Using a Particle Swarm Optimization Algorithm. Symmetry. 2019; 11(4):488. https://doi.org/10.3390/sym11040488
Chicago/Turabian StyleHamadneh, Nawaf N., Waqar A. Khan, Ilyas Khan, and Ali S. Alsagri. 2019. "Modeling and Optimization of Gaseous Thermal Slip Flow in Rectangular Microducts Using a Particle Swarm Optimization Algorithm" Symmetry 11, no. 4: 488. https://doi.org/10.3390/sym11040488