FREE CONVECTIVE DRAFT INDUCED BY THERMAL AND CONCENTRATION GRADIENTS INSIDE AN ISOTHERMAL, VERTICAL CYLINDER†

Laminar, free convective flow through a vertical cylinder induced by the thermal and concentration buoyancy forces is investigated. The numerical studies involve development of a steady-state, two-dimensional heat and mass transfer model for the moist air core of the vertical tube. The stream function-vorticity method is employed to simplify the governing, coupled conservation equations which were then numerically solved by the successive over-relaxation (SOR) and alternating direction implicit ((ADI) methods.

A graphical correlation was found between dimensionless flow rate and dimensionless tube length as a function of the buoyancy force ratio N = Gr/Grc. Excellent agreement was obtained for the dimensionless flow rale results with those of Davis and Perona¹⁶ and Kageyama and Izumi¹³ for the case when only the-thermal buoyancy force is considered.

The combined buoyancy force from thermal and species diffusion provides larger local Nusselt Nu and local Sherwood Sh numbers relative to the case when just one buoyancy force is accounted for. Both local Nu and local Sh are seen to asymptotically approach a constant value as flow develops.