Combined Geometrical Optimisation of a Square Microchannel with Smoothed Corners
Abstract
:1. Introduction
2. Mathematical Model
2.1. Performance Evaluation Criteria
2.2. Entropy Generation Number
2.3. Graetz–Brinkman Problem
3. Results
3.1. Nusselt Number Correlation
3.2. Microchannel Geometry Optimisation
3.2.1. FG1a Criterion
3.2.2. FG1b Criterion
3.2.3. FG2a Criterion
3.2.4. FG2b Criterion
3.2.5. VG2a Criterion
3.2.6. VG2b Criterion
4. Conclusions
- -
- The constrained heated perimeter and cross-sectional area almost invariably exhibit an improvement from the reference configuration when the corners are smoothed. The sole exception is criterion FG1b. The comparison with a standard modelisation in the case of the VG2a criterion proves that viscous heating plays a crucial role, showing that the increase in the objective function is more substantial when viscous dissipation is present, if the constrained heated perimeter and cross-sectional area are are considered.
- -
- The constrained characteristic length and hydraulic diameter never yield better results if the corners are smoothed, the FG2a criterion being the only exception; for the FG1a and VG2a criteria, there is a local maximum for in-between values of the smoothing parameter corresponding to a minimum improvement of F when the characteristic length is fixed, albeit limited to about ;
- -
- Some plots exhibit maxima and minima for some in-between values of the smoothing radius, but the trend is primarily monotonous.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
EGM | Entropy generation minimisation |
EGN | Entropy generation number |
FG | Fixed Geometry |
MFD | Micro-flow device |
PEC | Performance evaluation criteria |
VG | Variable Geometry |
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Criteria | |||||
---|---|---|---|---|---|
FG1a | ↑ | 1 | 1 | 1 | |
FG1b | 1 | ↓ | 1 | 1 | |
FG2a | ↑ | 1 | 1 | 1 | |
FG2b | 1 | ↓ | 1 | 1 | |
VG2a | ↑ | 1 | 1 | 1 | |
VG2b | 1 | ↓ | 1 | 1 |
Constraint | |
---|---|
b | |||||||
---|---|---|---|---|---|---|---|
0 | 0 |
Test Case | |||||||||
---|---|---|---|---|---|---|---|---|---|
(a) | 1 | 0 | 10 | 35 | 15 | ||||
(b) | 1 | 0 | 10 | 35 | 15 | ||||
(c) | 1 | 0 | 10 | 1 | 35 | 15 | 1375 |
1 | 0 | 60 | 30 | 1900 |
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Lorenzini, M.; Suzzi, N. Combined Geometrical Optimisation of a Square Microchannel with Smoothed Corners. Energies 2024, 17, 2666. https://doi.org/10.3390/en17112666
Lorenzini M, Suzzi N. Combined Geometrical Optimisation of a Square Microchannel with Smoothed Corners. Energies. 2024; 17(11):2666. https://doi.org/10.3390/en17112666
Chicago/Turabian StyleLorenzini, Marco, and Nicola Suzzi. 2024. "Combined Geometrical Optimisation of a Square Microchannel with Smoothed Corners" Energies 17, no. 11: 2666. https://doi.org/10.3390/en17112666
APA StyleLorenzini, M., & Suzzi, N. (2024). Combined Geometrical Optimisation of a Square Microchannel with Smoothed Corners. Energies, 17(11), 2666. https://doi.org/10.3390/en17112666