Analytic solution of fully developed flow and heat transfer for variable density fluid in tube

The concept and its inferences for fully developed flow and heat transfer in a tube with variable density fluid were presented. According to the concept and the inferences, the mathematical model for the flow and heat transfer of an ideal gas in the tube was solved analytically and the analytical solutions of dimensionless velocity and temperature were obtained, which gives a parabolic distribution of dimensionless velocity. A numerical simulation was performed for the argon flow and heat transfer considering density variation in the tube. The dimensionless velocity and temperature fields obtained by the numerical simulation are in good agreement with the above analytical solutions behind an entrance area, which indicates that the fully developed concept and analytical solutions of the flow and heat transfer in a tube with variable density fluid are reasonable in the range of calculation parameters in this paper.