Prandtl-number effects on vertical buoyant jets in forced and mixed convection regimes

In the present paper, we propose a detailed numerical study of the influence of Prandtl number on the hydrodynamic and thermal behaviour of a laminar buoyant free jet. Both round and plane nozzle geometry configurations are studied and compared. Variations of properties like viscosity and thermal conductivity with temperature are neglected. For a given fluid, Prandtl number variation with temperature is also neglected. On the other hand, the variation of density with temperature is only taken into account in terms of the gravity force. The influences of buoyancy and condition at the exit of the nozzle are examined for both geometry configurations (round and plane). Two cases are considered for the latter: uniform or parabolic velocity and temperature profiles. The Prandtl number effect on the jet flow characteristics is studied in both convection regimes: forced and mixed.Solution of the incompressible Navier–Stokes equations is accomplished by a finite difference method. For numerical stability of the scheme, discretization of the governing equations is performed on a staggered mesh. The results, which are presented in the form of graphs and compared with those obtained analytically by other authors; show a suitable agreement far from the exit of the nozzle. These authors replace the emission conditions at the exit of the nozzle by considering two constraints of integration: conservation of momentum and energy, which are checked for whatever profile is used. The results demonstrate first that the effect of the emission conditions, of velocity and temperature, are significant in the region close to the jet exit, in which the flow is governed mainly by the inertias forces. This effect is true for all Prandtl numbers and is consistent with results found in other studies. Secondly, the effect of Prandtl number is significant in the plume region in which the jet flow is influenced by buoyant forces.