It is still in suspense for the effects of slip velocity and structural parameters on the heat transfer on a super-hydrophobic surface. It is thus necessary to study it in both theory and experiments. In this paper, the convective heat transfer with constant heat flux condition inside a circular microchannel was investigated. The velocity and temperature profiles when slip velocity exists were derived firstly, and then the heat transfer coefficient and Nusselt number were obtained. Furthermore, an effective conduction model for the super-hydrophobic surface with different structural parameters was proposed and the thermal resistance of the surface with trapped air was calculated. Finally, the effective heat transfer coefficient of super-hydrophobic surface was found with the integration of heat transfer coefficient and surface thermal resistance. The calculation results show that 1) the slip of fluid on a super-hydrophobic surface makes the temperature profile inside the channel more uniform, and the heat transfer coefficient or Nusselt number increased, 1.8 times higher maximally under constant heat flux condition; 2) the thermal resistance of super-hydrophobic surface increases with trapped air volume; 3) the effective heat transfer coefficient on super-hydrophobic surface declines seriously with trapped air volume, especially with the trapped air area; 4) there exists a critical thickness for the trapped air on a super-hydrophobic surface with given surface structural parameters, under which the effective heat transfer coefficient is not less than that on normal surfaces without slip. Therefore, it is necessary to consider the structural parameters of super-hydrophobic surfaces, such as rib height and distance between ribs, so that the heat transfer on the super-hydrophobic surface will not be impacted by the trapped air.

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