Laminar Free Convection Flow Rate in a Vertical Tube (Its measurement and Theoretical Prediction)

This paper treats the average mass velocity of laminar free convection inside a heated or cooled vertical tube situated in a large space. A one-dimensional model is proposed by applying the Poiseuille flow and the Graetz solution for forced convection in a tube and by considering both the pressure losses at the tube inlet and exit and in the hydrodynamic developing region. The average mass velocity of air is measured by means of the deflection of a fine quartz fiber in a cross-flow. The agreement between the theory and experiment is very good for the cases where the tube is partly heated and partly adiabatic, where the tube is partly heated and partly cooled, and with temperature stratification existing in the ambient fluid. At the same time, the effects of tube-to-ambient temperature difference, a reference temperature of the stratified ambient fluid, the tube length-to-diameter ratio and fluid's physical properties in the tube on the average mass velocity are clarified.