Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with CWT (constant wall temperature) whose temperature is lower than the inlet temperature. The combined effect of viscous dissipation and compressibility is also investigated. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The stagnation temperature is fixed at 300K and the computations were done for the wall temperature of 250K, 280K, and 290K. The bulk temperature based on the static temperature and the total temperature are compared with those of the heated case and also compared with those of the incompressible flow in a conventional sized channel. The identical heat transfer coefficients are obtained for both heated and cooled cases of the incompressible flow. However, in the case of the gaseous flow in micro-channels, different heat transfer coefficients are obtained for each heated and cooled case. A correlation for the prediction of the heat transfer rate of the gaseous flow in the micro-channel is proposed.

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