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ABSTRACT
In this study, numerical calculations using single- and two-phase models of CuO/water nanofluid forced convection in a three-dimensional C-shaped channel with constant heat flux are investigated. The laminar heat transfer enhancement using a nanofluid in a chaotic flow is first validated with the available data in the literature and the maximum discrepancy is within 3%; then further it is extended to design the C-shaped geometry. In addition, after comparisons of the numerical results with single- and two-phase models, the multiparameter constrained the optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid laminar convection of three-dimensional C-shaped channels. The thermal performance factors predicted by the regression function for the C-shaped channel case are in good agreement with the numerical results of CFD, with the difference being within 10%.
Nomenclature
| B | = | width of C-shaped channel, mm |
| Cp | = | specific heat, J/kg · K |
| D | = | channel height/depth, mm |
| Dh | = | hydraulic diameter, mm |
| dp | = | particle diameter, nm |
| E | = | performance factor |
| F | = | friction factor |
| H | = | height of C-shaped channel, mm |
| H | = | average convection heat transfer coefficient, W/m2 · K |
| K | = | thermal conductivity, W/m · K |
| L | = | test section length, mm |
| Lin | = | upstream length, mm |
| Lout | = | downstream length, mm |
| = | average Nusselt number | |
| N | = | normal vector |
| P | = | pressure, N/m2 |
| q″ | = | heat flux, W/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| u, v, w | = | velocity component, m/s |
| V | = | velocity, m/s |
| W | = | depth of C-shaped channel, mm |
| x, y, z | = | Cartesian x, y, z-coordinates |
| Greek Symbols | = | |
| ρ | = | density of the working fluid, kg/m3 |
| μ | = | dynamic viscosity, N · s /m2 |
| τ | = | shear stress, Pa |
| φ | = | volume fraction |
| κ | = | Boltzmann constant, 1.381 × 10−23 J/K |
| Subscripts | = | |
| Avg | = | average |
| Bf | = | base fluid |
| Dr | = | drift |
| Eff | = | effective |
| F | = | fluid |
| In | = | inlet |
| K | = | secondary phase |
| M | = | mixture |
| Nf | = | nanofluid |
| P | = | particle |
| S | = | solid |
| W | = | wall |
| 0 | = | smooth channel |
Nomenclature
| B | = | width of C-shaped channel, mm |
| Cp | = | specific heat, J/kg · K |
| D | = | channel height/depth, mm |
| Dh | = | hydraulic diameter, mm |
| dp | = | particle diameter, nm |
| E | = | performance factor |
| F | = | friction factor |
| H | = | height of C-shaped channel, mm |
| H | = | average convection heat transfer coefficient, W/m2 · K |
| K | = | thermal conductivity, W/m · K |
| L | = | test section length, mm |
| Lin | = | upstream length, mm |
| Lout | = | downstream length, mm |
| = | average Nusselt number | |
| N | = | normal vector |
| P | = | pressure, N/m2 |
| q″ | = | heat flux, W/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| u, v, w | = | velocity component, m/s |
| V | = | velocity, m/s |
| W | = | depth of C-shaped channel, mm |
| x, y, z | = | Cartesian x, y, z-coordinates |
| Greek Symbols | = | |
| ρ | = | density of the working fluid, kg/m3 |
| μ | = | dynamic viscosity, N · s /m2 |
| τ | = | shear stress, Pa |
| φ | = | volume fraction |
| κ | = | Boltzmann constant, 1.381 × 10−23 J/K |
| Subscripts | = | |
| Avg | = | average |
| Bf | = | base fluid |
| Dr | = | drift |
| Eff | = | effective |
| F | = | fluid |
| In | = | inlet |
| K | = | secondary phase |
| M | = | mixture |
| Nf | = | nanofluid |
| P | = | particle |
| S | = | solid |
| W | = | wall |
| 0 | = | smooth channel |
Acknowledgment
We really appreciate the Ministry of Science and Technology of Taiwan for supporting this project under contract no. NSC102-2221-E-006-173-MY3.