Design Analysis of Heat Sink Using the Field Synergy Principle and Multitarget Response Surface Methodology
Abstract
:1. Introduction
2. Methodology
2.1. Field Synergy Principle (FSP)
2.2. Response Surface Methodology
3. Design Analysis
3.1. Heat Sink Model
- There will be a steady-state heat transfer.
- The fluid in the chamber is three-dimensional forced convection.
- The working fluid has an incompressible density.
- The model space’s walls are all nonslip surfaces.
- There is little radiation impact.
3.2. Boundary Conditions
3.3. Experiment Measuring
- (A)
- Measuring range: −40 °C to 500 °C
- (B)
- Resolution: 0.06 °C
- (C)
- Accuracy: ±2 °C or ±2% of reading, whichever was greater
- (A)
- Measuring range: 2~30 m/s
- (B)
- Resolution: 0.1 m/s
- (C)
- Accuracy: 2–10 m/s (±3% ± 0.5); 10–30 m/s (±3% ± 0.8)
3.4. Results and Discussion
B − 0.0212188A × C + 0.00760208B × C
4. Conclusions
- We investigated the effects of wall velocity on heat transport due to the field synergy angle. The effectiveness of heat dissipation increased with the synchromesh of the display field.
- The gradient and velocity field changes were not coordinated, which prevented the velocity field change from keeping up with the temperature difference between the fins. This resulted in a higher field synergy angle of the fins in the second half.
- When the synergy angle was employed to show the fins’ effects in heat transfer, the research findings supported the design combination. It is important to show the effectiveness of the heat-dissipation effect.
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
cp | Heat capacity, J/(kg∙K) |
h | Heat transfer coefficient, W/(m2∙K) |
k | Thermal conductivity, W/(m∙K) |
l | Length, m |
Nu | Nusselt number, dimensionless |
Pr | Prandtl number, dimensionless |
Q | Conduction heat source, W/m2 |
Re | Reynold’s number, dimensionless |
t | Time, s |
T | Temperature, K |
U | Fluid velocity field, m/s. |
Mean velocity vector, m/s. | |
u | Velocity in the x direction, m/s. |
v | Velocity in the y direction, m/s. |
w | Velocity in the z direction, m/s. |
x | Spatial coordinate |
Xi | Input factor |
y | Spatial coordinate |
yi | Output value |
Y | Reaction variables |
z | Spatial coordinate |
Greek symbols | |
Velocity boundary layer thickness, m | |
Temperature boundary layer thickness, m | |
Fluid density, kg/m3 | |
μ | Dynamic viscosity, Pa/s |
ν | Kinematic viscosity, m2/s |
Field synergistic angle | |
▽T | Temperature gradient vector, K |
ij | Coefficient of the linear and quadratic terms |
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1. Material | ||
Name | Material | Thermal conductivity [W/(m·K)] |
Heat Sink | Aluminum 6063-T83 | 201 |
Chamber | Acrylic plastic | 0.18 |
Heat source | Al2O3-Aluminum oxide | 30 |
Thermal insulation coating material | Owens–Corning fiberglass | 0.018 |
Heat sticks | Red copper | 385 |
Fluid | Air | 0.026 |
2. Turbulence mode: k-ω | ||
Condition attribute | Parameter | Position |
k-ω | Incompressible flow | Inside the entire chamber |
Wall | Wall function (no slippage) | Except for entrance, exit, fan |
Entrance | 1 m/s | Wall rear |
Export | 1 atm | Wall |
Fan 1 | PQ curve | Above the fin |
Fan 2 | PQ curve | Chamber fan |
3. Heat transfer mode | ||
Condition attribute | Parameter | Position |
Heat transfer | Ambient temperature: 25 °C | The whole chamber |
Solid heat transfer | Depending on the material type | Fins, fans, thermal insulation, shells |
Fluid heat transfer | Air | Inside the chamber |
Initial value | 25 °C | Overall |
Heat source | 80 W | Heat source |
Thin layer | Heat paste: Layer thickness: 50 μm With ST-350 | Between the fins and the thermal bars |
Temperature | Entry temperature: 25 °C | Chamber rear |
Outflow | Export | Fan and drain on both sides |
Node number | 20743 |
Tetrahedron elements number | 122097 |
Triangle elements number | 34126 |
Minimum element quality | 0.005516 |
Average element quality | 0.5344 |
Element volume ratio | 9.048 × 10−8 |
Mesh volume | 1.944 × 108 |
Item | A Fin Height (mm) | B Heat Sink Angle (Degree) | C Fin Aliquots | Field Synergy Angle (Y1) | Fin Average Temperature (°C) (Y2) |
---|---|---|---|---|---|
1 | 30 | 0 | 3 | 90.605 | 67.715 |
2 | 40 | 30 | 3 | 90.089 | 59.309 |
3 | 40 | 30 | 5 | 87.953 | 59.793 |
4 | 30 | 30 | 5 | 87.953 | 59.793 |
5 | 50 | 30 | 5 | 87.953 | 59.793 |
6 | 30 | 0 | 7 | 91.303 | 68.211 |
7 | 40 | 0 | 5 | 92.779 | 58.428 |
8 | 50 | 60 | 3 | 87.007 | 54.403 |
9 | 50 | 0 | 3 | 93.409 | 51.529 |
10 | 40 | 30 | 5 | 87.953 | 59.793 |
11 | 50 | 0 | 7 | 92.568 | 57.225 |
12 | 40 | 30 | 7 | 89.076 | 63.077 |
13 | 40 | 30 | 5 | 87.953 | 59.793 |
14 | 30 | 60 | 7 | 88.778 | 67.924 |
15 | 50 | 60 | 7 | 87.832 | 58.260 |
16 | 40 | 30 | 5 | 87.953 | 59.793 |
17 | 40 | 30 | 5 | 87.953 | 59.793 |
18 | 40 | 30 | 5 | 87.953 | 59.793 |
19 | 40 | 60 | 5 | 85.823 | 59.320 |
20 | 30 | 60 | 3 | 86.097 | 65.586 |
Response Surface Regression: Y1 versus A, B, C Estimated Regression Coefficients for Y1 | ||
---|---|---|
Term | Coefficient | p value |
A | 88.1320 | 0 |
B | 0.4033 | 0.095 |
C | −2.5127 | 0 |
A × A | 0.2350 | 0.308 |
B × B | −0.4475 | 0.309 |
C × C | 0.9005 | 0.056 |
A × B | 1.1820 | 0.018 |
A × C | −0.5131 | 0.062 |
B × C | −0.4244 | 0.113 |
R-Sq(adj) = 89.69% |
Response Surface Regression: Y2 versus A, B, C Estimated Regression Coefficients for Y2 | ||
---|---|---|
Term | Coefficient | p value |
A | 4.08896 | 0 |
B | −0.07892 | 0 |
C | 0.00512 | 0.696 |
A × A | 0.02773 | 0.054 |
B × B | 0.00481 | 0.847 |
C × C | −0.01071 | 0.668 |
A × B | 0.02748 | 0.284 |
A × C | 0.01355 | 0.364 |
B × C | 0.01638 | 0.277 |
R-Sq(adj) = 66.99% |
Item | Fin Height | Heat Sink Angle | Fin Aliquots | Fin’s Bottom Field Synergy | Fin’s Middle Field Synergy | Fin’s Top Field Synergy |
---|---|---|---|---|---|---|
Best combination | 50 mm | 60° | 5 | 53.476 | 73.581 | 42.039 |
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Lin, M.-C.; Lin, R.-F. Design Analysis of Heat Sink Using the Field Synergy Principle and Multitarget Response Surface Methodology. Energies 2022, 15, 8399. https://doi.org/10.3390/en15228399
Lin M-C, Lin R-F. Design Analysis of Heat Sink Using the Field Synergy Principle and Multitarget Response Surface Methodology. Energies. 2022; 15(22):8399. https://doi.org/10.3390/en15228399
Chicago/Turabian StyleLin, Ming-Che, and Ruei-Fong Lin. 2022. "Design Analysis of Heat Sink Using the Field Synergy Principle and Multitarget Response Surface Methodology" Energies 15, no. 22: 8399. https://doi.org/10.3390/en15228399
APA StyleLin, M. -C., & Lin, R. -F. (2022). Design Analysis of Heat Sink Using the Field Synergy Principle and Multitarget Response Surface Methodology. Energies, 15(22), 8399. https://doi.org/10.3390/en15228399