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ABSTRACT
In order to obtain the optimal structure size of a microchannel heat sink (MCHS) with arc-shaped grooves and ribs according to the actual demand, multiple parameters that influence the performance of the microchannel are analyzed by combining the multi-objective evolutionary algorithm (MOEA) with computational fluid dynamics (CFD). The design variables include the relative groove height, relative rib height and relative rib width, and the two objective functions are to minimize the total thermal resistance and pumping power in constant volume flow rate. The influences of the design variables on the two objective functions are analyzed by CFD firstly. The results show that each design variable has a different impact on the two functions. The competitive relationship between the two objective functions is depicted in plots of the Pareto front obtained by MOEA. Pareto sensitivity analysis is carried out to find that the relative rib height has the most significant impact on the two objective functions.
Nomenclature
| A | = | area, mm2 |
| Λ | = | mean free path of fluid, m |
| cp | = | special heat capacity, kJ/(kg K) |
| Dh | = | hydrodynamic diameter, mm |
| e1 | = | groove height, mm |
| e2 | = | rib height, mm |
| H | = | height of microchannel, mm |
| Kn | = | Knudsen number |
| k | = | thermal conductivity, W/(m K) |
| L | = | length, mm |
| N | = | number of microchannel |
| Pp | = | pumping power, W |
| Δp | = | pressure drop, Pa |
| R2 | = | coefficient of multiple determination |
| Rth | = | thermal resistance, K/W |
| Q | = | heat flux, W/m2 |
| T | = | temperature, K |
| u | = | liquid velocity in microchannel, m/s |
| W | = | width, mm |
| Greek symbols | = | |
| α | = | design variable, e1/Dh |
| β | = | design variable, e2/Dh |
| γ | = | design variable, L4/L2 |
| ξ | = | regression coefficient |
| μ | = | dynamic viscosity, kg/(m s) |
| ρ | = | density, kg/m3 |
| Subscripts | = | |
| avg | = | average value |
| ch | = | channel |
| f | = | fluid |
| i | = | inlet |
| max | = | maximum value |
| o | = | outlet |
| s | = | substrate |
Nomenclature
| A | = | area, mm2 |
| Λ | = | mean free path of fluid, m |
| cp | = | special heat capacity, kJ/(kg K) |
| Dh | = | hydrodynamic diameter, mm |
| e1 | = | groove height, mm |
| e2 | = | rib height, mm |
| H | = | height of microchannel, mm |
| Kn | = | Knudsen number |
| k | = | thermal conductivity, W/(m K) |
| L | = | length, mm |
| N | = | number of microchannel |
| Pp | = | pumping power, W |
| Δp | = | pressure drop, Pa |
| R2 | = | coefficient of multiple determination |
| Rth | = | thermal resistance, K/W |
| Q | = | heat flux, W/m2 |
| T | = | temperature, K |
| u | = | liquid velocity in microchannel, m/s |
| W | = | width, mm |
| Greek symbols | = | |
| α | = | design variable, e1/Dh |
| β | = | design variable, e2/Dh |
| γ | = | design variable, L4/L2 |
| ξ | = | regression coefficient |
| μ | = | dynamic viscosity, kg/(m s) |
| ρ | = | density, kg/m3 |
| Subscripts | = | |
| avg | = | average value |
| ch | = | channel |
| f | = | fluid |
| i | = | inlet |
| max | = | maximum value |
| o | = | outlet |
| s | = | substrate |