Simultaneously developing flow and heat transfer in circular and parallel-plates microchannels with velocity slip and temperature jump

Abstract

The entrance effect has an important influence on the heat transfer characteristics in microchannels. It is necessary to determine the influence to design microchannel heat sinks properly. In this work, the simultaneously developing flow and convective heat transfer were investigated numerically inside circular and parallel-plates microchannels. The effects of the Knudsen number (0–0.1) and Peclet number (25–1000) on the local Nusselt number were taken into consideration in the slip flow regime. The numerical results were calculated via an incompressible and steady computational fluid dynamics algorithm under the boundary conditions of the velocity slip and temperature jump. The user-defined functions were used to achieve the velocity slip boundary condition, and a thermal resistance model was first proposed to easily impose the temperature jump boundary condition. The numerical approach was verified using both the analytic solutions of the thermally developing flow and the exact solutions of the fully developed flow, which was then employed to obtain the influences of the axial heat conduction and the rarefaction on the local Nusselt number of the simultaneously developing flow. The results of the apparent friction factor and the heat transfer coefficient were graphically presented as functions of the Knudsen number, Reynolds number or Peclet number, and non-dimensional axial length. It was found that the effect of the axial heat conduction on the entrance effect can be ignored when Pe > 500. The heat transfer performance of the simultaneously developing flow can be predicted by the results of the thermally developing flow when the Knudsen number is large enough. General correlations were also proposed for the apparent friction coefficients, local Nusselt number in circular and parallel-plates microchannels.