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ABSTRACT
In this study, the fluid flow and heat transfer characteristics of turbulent forced convection of air flow through perforated circular pin fin heat sinks with constant heat flux are investigated numerically. Circular perforated pin fins are shown to have 8% larger averaged Nusselt numbers than the corresponding solid pin cases. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology (RSM) coupled with genetic algorithm (GA). The difference between the optimal thermal performance factor (η) which is calculated by regression function and obtained by using computational fluid dynamics (CFD) is less than 2%, and the numerical optimization shows that the enhancement of the objective function (η) can achieve 34%.
Nomenclature
| C1ε, C2ε, Cμ | = | turbulence model coefficient |
| Cp | = | specific heat of constant pressure (J/kg·K) |
| D | = | circular pin fin diameter (mm) |
| Dh | = | hydraulic diameter (mm) |
| d | = | perforation diameter (mm) |
| e | = | nondimensional perforation diameter |
| F | = | nondimensional perforation space |
| f | = | friction factor |
| f0 | = | friction factor of original case |
| H | = | channel height (mm) |
| I | = | turbulent intensity |
| k | = | thermal conductivity (W/m·K) |
| k | = | turbulent kinetic energy (J/kg) |
| L | = | length of test section (mm) |
| Lin | = | length of inlet section (mm) |
| Lout | = | length of outlet section (mm) |
| = | averaged Nusselt number | |
| = | averaged Nusselt number of original case | |
| P | = | pressure (Pa) |
| ΔP | = | pressure difference between inlet and outlet boundary (Pa) |
| p | = | space of pin fin (mm) |
| q″ | = | heat flux (kW/m2) |
| Re | = | Reynolds number |
| s | = | perforation space (mm) |
| T | = | temperature (K) |
| u, v, w | = | velocity component at x, y, z direction |
| x, y, z | = | Cartesian coordinate component |
| ε | = | turbulent kinetic dissipation (J/kg·s) |
| η | = | thermal performance factor |
| μ | = | viscosity coefficient (N·s/m2) |
| μt | = | turbulent viscosity coefficient (N·s/m2) |
| ρ | = | density (kg/m3) |
| = | Reynolds stress (Pa) | |
| = | Reynolds heat flux (W/m2) | |
| σk, σε | = | turbulent coefficient |
| Subscripts | = | |
| in | = | inlet |
| out | = | outlet |
| f | = | fluid |
| s | = | solid |
| Superscripts | = | |
| = | vector | |
| = | time-averaged value |
Nomenclature
| C1ε, C2ε, Cμ | = | turbulence model coefficient |
| Cp | = | specific heat of constant pressure (J/kg·K) |
| D | = | circular pin fin diameter (mm) |
| Dh | = | hydraulic diameter (mm) |
| d | = | perforation diameter (mm) |
| e | = | nondimensional perforation diameter |
| F | = | nondimensional perforation space |
| f | = | friction factor |
| f0 | = | friction factor of original case |
| H | = | channel height (mm) |
| I | = | turbulent intensity |
| k | = | thermal conductivity (W/m·K) |
| k | = | turbulent kinetic energy (J/kg) |
| L | = | length of test section (mm) |
| Lin | = | length of inlet section (mm) |
| Lout | = | length of outlet section (mm) |
| = | averaged Nusselt number | |
| = | averaged Nusselt number of original case | |
| P | = | pressure (Pa) |
| ΔP | = | pressure difference between inlet and outlet boundary (Pa) |
| p | = | space of pin fin (mm) |
| q″ | = | heat flux (kW/m2) |
| Re | = | Reynolds number |
| s | = | perforation space (mm) |
| T | = | temperature (K) |
| u, v, w | = | velocity component at x, y, z direction |
| x, y, z | = | Cartesian coordinate component |
| ε | = | turbulent kinetic dissipation (J/kg·s) |
| η | = | thermal performance factor |
| μ | = | viscosity coefficient (N·s/m2) |
| μt | = | turbulent viscosity coefficient (N·s/m2) |
| ρ | = | density (kg/m3) |
| = | Reynolds stress (Pa) | |
| = | Reynolds heat flux (W/m2) | |
| σk, σε | = | turbulent coefficient |
| Subscripts | = | |
| in | = | inlet |
| out | = | outlet |
| f | = | fluid |
| s | = | solid |
| Superscripts | = | |
| = | vector | |
| = | time-averaged value |