Laminar free convection flow rate in a vertical tube

This paper considers the flow rate of a laminar free convection inside a fully heated or a partly heated and partly cooled vertical tube placed in a large space. A theory based on a one-dimensional model which uses the Graetz solution for forced convection in a tube and which considers the pressure losses at the tube inlet and exit and in the hydrodynamic developing region is proposed for the range Gr Pr < 100. For the fully heated tube, the theory is compared with a two-dimensional numerical analysis and actual measurements using a quartz fiber anemometer. Their agreement is good when proper values of pressure loss coefficients are used in the theory. For the partly heated and partly cooled or partly adiabatic tube in thermally stratified and non-stratified ambients, the agreement between the theory and the experiment is also good. The effects of the tube-to-ambient temperature difference, the representative temperature of the stratified ambient, the tube length-to-diameter ratio and the temperature dependence of fluid properties upon the average mass velocity inside the tube are also clarified.