Analytical Solution of Temperature Field in Micro-Poiseuille Flow With Constant Wall Temperature

The analytical study of microchannels has been considered as a preliminary approach to alleviate the difficulties which are normally encountered in numerical and experimental studies. Among the analytical solutions, those with high robustness and low complexities are certainly more attractive. In this work, we present a theoretical approach to predict the temperature field in micro-Poiseuille channel flow with constant wall temperature. The use of power series method simplifies the solution in the current analytical approach. The current analytical derivations are examined for channels with both hot-wall and cold-wall conditions. The current solutions agree well with the numerical solutions for a wide range of Knudsen numbers. Contrary to the past analytical solutions and in spite of using a simple and robust approach, the current formulations predict the temperature field in the channel readily.