# Natural convection heat transfer on surfaces of copper micro-wires

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## Abstract

The natural convection heat transfer characteristics and mechanism for copper micro-wires in water and air were investigated experimentally and numerically. The wires with diameters of 39.9, 65.8 and 119.1 μm were placed horizontally in water inside of a sealed tube and in air of a large room, respectively. Using Joule heating, the heat transfer coefficients and Nusselt numbers of natural convection for micro-wires in ultra pure water and air were obtained. A three dimensional incompressible numerical model was used to investigate the natural convection, and the prediction with this model was in reasonable accordance with the experimental results. With the decrease of micro-wire diameter, the heat transfer coefficient of natural convection on the surface of micro-wire becomes larger, while the *Nu* number of natural convection decreases in water and air. Besides, the change rate of *Nu* number in water decreases apparently with the increase of heat flux and the decrease of wire diameter, which is larger than that in air. The thickness of boundary layer on the wall of micro-wire becomes thinner with the decrease of diameter in both water and air, but the ratio of boundary layer thickness in water to the diameter increases. However, there is almost no change of this ratio for natural convection in air. As a result, the proportion of conduction in total heat transfer of natural convection in water increases, while the convective heat transfer decreases. The velocity distribution, temperature field and the boundary layer in the natural convection were compared with those of tube with conventional dimension. It was found that the boundary layer around the micro-wire is an oval-shaped film on the surface, which was different from that around the conventional tube. This apparently reduces the convection strength in the natural convection, thus the heat transfer presents a conduction characteristic.

## Keywords

Heat Transfer Boundary Layer Heat Flux Heat Transfer Coefficient Natural Convection## List of symbols

*D*Outer diameter of micro-wire (m)

*F*Surface area of micro-wire (m

^{2})*Gr*Grashof number

*h*Heat transfer coefficient (W/m

^{2}K)*I*Current (A)

*k*Thermal conductivity (W/m K)

*L*Length of micro-wire (m)

*Nu*Nusselt number

*Q*_{cov}Quantity of the heat transfer of natural convection, W

*Q*_{R}Quantity of radiant heat transfer (W)

*Ra*Rayleigh number

*R*Resistance of micro-wire (Ω)

*ΔT*Temperature difference between micro-wire and room or deionized water (K)

*T*Average temperature of micro-wire (K)

*U*Voltage (V)

*u*Velocity of x-direction (m/s)

*v*Velocity of y-direction (m/s)

*W*Velocity of y-direction (m/s)

- x
x-direction coordinate

*y*y-direction coordinate

*z*z-direction coordinate

## Greek symbols

*ϕ*Measuring uncertainty

*ρ*Density (kg/m

^{3})

## Subscripts

*c*Cool side

*eff*Effective value

*W*Micro-wire

## Notes

### Acknowledgments

The authors acknowledge the financial support of the National Science Foundation of China (Grant 51176105), Science Foundation of Shandong Province (ZR2011EEQ015).

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