Natural Heat Convection in a Vertical Circular Tube

Pure natural heat convection fields in the entrance region of a heated vertical circular tube, in which the temperature and velocity profiles were developing simultaneously, were solved by a numerical method of finite difference. And then the characteristics of heat transfer were obtained. The analysis presented here was based on the assumption that the inlet velocity profile is uniform. It was verified analytically and numerically that, for the case of uniform wall temperature, the inlet velocity U1 has an asymptotic value 1/8 as the tube length approaches infinity. As for the case of uniform heat flux at the wall, U1 is directly proportional to √(L/p)r over the range L>Le, where Le is the entrance length. The relationship between the dimensionless pipe length L and dimensionless suction velocity U1 was also obtained, using Pr=0.72, for both the wall conditios. In the case that the pipe length is semi-infinite and the wall temperature is uniform, a relationship between Pr and thermal, as well as hydrodynamic, entrance length was obtained for Pr=0.01, 0.1, 0.72, 1.0, 10 and 100, and some interesting irregularities of developing velocity profiles were also observed except for the case Pr=1.0.