Development and Analyses of Artificial Intelligence (AI)-Based Models for the Flow Boiling Heat Transfer Coefficient of R600a in a Mini-Channel
Abstract
:1. Introduction
2. Basic Idea of Support Vector Machines (SVMs)
3. An Overview of ANNs
4. An Overview of the Existing Correlations
4.1. Magdalena Piasecka Correlation
4.2. Dutkowski Correlation
4.3. Li and Wu Correlation
5. Results and Discussion
5.1. Development of the ANN-Based Model
5.2. Development of an SVR-Based Model
5.3. Comparative Study
5.4. Parametric Study
5.4.1. Effect of Heat Flux and Vapor Quality on the Heat Transfer Coefficient of R600a
5.4.2. Effect of Mass Flux on the Heat Transfer Coefficient, h of R600a
5.4.3. Effect of Saturation Temperature on the Heat Transfer Coefficient of R600a
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
C | cost function |
dh | hydraulic diameter, m |
f (m) | regression function |
G | mass flux, kg/m2·s |
hlv | latent heat of vaporization, J/kg |
K(mi mj) | kernel function |
L | Lagrangian multiplier (dual form) |
mi | input vector |
ni | output vector |
qw | heat flux density, W/m2 |
Q2ext | leave-one-out cross validation for test dataset |
Q2Loo | leave-one-out cross validation for training dataset |
w | weight vector |
x | vapor quality |
z | bias term |
Greek Symbols | |
Γ | surface development parameter |
ε | loss function |
γ | regularization parameter |
α and α* | Lagrangian multiplier |
ϕ(mi) | high dimensional feature function for input space m |
K | thermal conductivity, W/m·K |
μ | dynamic viscosity, kg/m·s |
ρ | density, kg/m3 |
σ | surface tension, N/m |
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Hidden Layer 1 Neurons | % Residual Variance |
---|---|
2 | 8.27490 |
3 | 10.72571 |
4 | 4.03148 |
5 | 4.51386 |
6 | 8.74758 |
7 | 3.22918 (Optimal value) |
8 | 3.99854 |
9 | 4.41057 |
10 | 6.25276 |
11 | 5.57635 |
12 | 4.74811 |
13 | 6.90271 |
14 | 4.34555 |
15 | 4.46499 |
Statistical Indices | Train Data | Test Data |
---|---|---|
AARE (%) | 4.12 | 5.14 |
R | 0.9884 | 0.9842 |
RMSE | 0.8142 | 0.8608 |
SD | 4.7469 | 5.2438 |
MRE | 0.0412 | 0.0514 |
MAE (%) | 1.02 | 1.05 |
Q2LOO (Train data), Q2ext (Test data) | 0.9832 | 0.9685 |
Model | C | γ = 1/2σ2 | ε | Kernel Type | Loss Function | Number of Support Vectors | Number of Training Points |
---|---|---|---|---|---|---|---|
Heat transfer coefficient, h | 4907.6 | 1.3486 | 0.001 | RBF | ε-insensitive | 175 | 255 |
Statistical Indices | Train Data | Test Data |
---|---|---|
AARE (%) | 2.05 | 1.15 |
R | 0.9978 | 0.9991 |
RMSE | 0.3241 | 0.2365 |
SD | 5.4354 | 4.8343 |
MRE | 0.02045 | 0.0115 |
MAE (%) | 0.41 | 0.28 |
Q2LOO (Train data), Q2ext (Test data) | 0.9955 | 0.9986 |
Correlations | Model Evaluation Indices | |||||
---|---|---|---|---|---|---|
AARE (%) | R2 | RMSE | SD | MRE | MAE (%) | |
SVR (Present study) | 1.15 | 0.9981 | 0.2365 | 4.8343 | 0.0115 | 0.28 |
ANN (Present study) | 5.14 | 0.9685 | 0.8608 | 5.2438 | 0.0514 | 1.05 |
Piasecka [24] | 62.52 | 0.1600 | 35.61 | 14.0801 | 6.252 | 33.2313 |
Dutkowski [24,25] | 43.89 | 0.2624 | 15.32 | 12.2 | 4.3893 | 13.68 |
Li and Wu [26] | 47.68 | 0.0095 | 16.19 | 17.78 | 4.76 | 18.35 |
Absolute Deviation (AD) (%) | % of ANN Model Predicted Values | Cumulative Score | % of SVR Model Predicted Values | Cumulative Score |
---|---|---|---|---|
AD < 5 | 61.96 | 61.96 | 93.73 | 93.73 |
5 < AD < 10 | 23.53 | 85.49 | 5.09 | 98.82 |
AD > 10 | 14.51 | 100 | 1.18 | 100 |
Total | 100 | 100 |
Absolute Deviation (AD) (%) | % of ANN Model Predicted Values | Cumulative Score | % of SVR Model Predicted Values | Cumulative Score |
---|---|---|---|---|
AD < 5 | 68.75 | 68.75 | 96.88 | 96.88 |
5 < AD < 10 | 28.12 | 96.87 | 3.12 | 100 |
AD > 10 | 3.13 | 100 | 0.00 | |
Total | 100 | 100 |
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Parveen, N.; Zaidi, S.; Danish, M. Development and Analyses of Artificial Intelligence (AI)-Based Models for the Flow Boiling Heat Transfer Coefficient of R600a in a Mini-Channel. ChemEngineering 2018, 2, 27. https://doi.org/10.3390/chemengineering2020027
Parveen N, Zaidi S, Danish M. Development and Analyses of Artificial Intelligence (AI)-Based Models for the Flow Boiling Heat Transfer Coefficient of R600a in a Mini-Channel. ChemEngineering. 2018; 2(2):27. https://doi.org/10.3390/chemengineering2020027
Chicago/Turabian StyleParveen, Nusrat, Sadaf Zaidi, and Mohammad Danish. 2018. "Development and Analyses of Artificial Intelligence (AI)-Based Models for the Flow Boiling Heat Transfer Coefficient of R600a in a Mini-Channel" ChemEngineering 2, no. 2: 27. https://doi.org/10.3390/chemengineering2020027