Fully developed natural counterflow in a long horizontal pipe with different end temperatures.
The temperature difference applied across the two ends of a horizontal duct generates a natural counterflow in which colder fluid along the bottom of the duct towards the warm end while a warmer stream flows in the opposite dierection along the top. The paper presents an asymptotic solution of the velocity and temperature distributions in the middle portion of a long horizontal pipe with conduction wall. The influence of circumferential heat conduction through the pipe wall on the temperature distribution in the fluid has been investigated. An analytical expression has been established for the net axial heat-transfer rate by counterflow natural convection. The present results for the temperature distribution in the pipe wall are compared with numerical results reported recently. (A)