LAMINAR MIXED CONVECTION IN A VERTICAL .3. HEAT-TRANSFER PROBLEMS

Numerical results are presented for the case of heat transfer by laminar combined free and forced convection in a vertical tube with uniform wall temperature in the following range of parameters: -200 less-than-or-equal-to Gr/Re less-than-or-equal-to 500 and 0.1 less-than-or-equal-to Pr less-than-or-equal-to 10 000. Basing on the derived theoretical model [1] and the analysis of fluid flow phenomena [2] the selected characteristic profiles of local and bulk dimensionless temperture as well as local and mean Nusselt number for both cases: heating and cooling of fluid are presented and discussed. Free convection may influence heat transfer rate significantly, especially in the region of parabolic velocity profile distortion. In an upflow free convection aids forced convection at heating, while it opposes forced convection at cooling in terms of heat transfer rate. This is illustrated by the bulk temperature curves. The mixed convection bulk temperature curves are situated below the "pure" forced convection curves for heating, which means that heat transfer is being enhanced. For cooling on the contrary, they are located above the forced convection curves which is an evidence for slower heat transfer rate in this case. With aided free and forced convection local and mean Nusselt number may reach values up to 80% higher than those for pure forced convection. With opposed free and forced convection values of local and mean Nusselt number are up to 40% smaller in comparison with the case Gr/Re = 0. In all the cases they reach the final value of 3.657 at the end of the thermal development region (z* congruent-to 1). The discrepancies depend strongly on Gr/Re ratio (free convection) and Prandtl number. Among obtained results they were found to be the greatest in the case Gr/Re = 500 and Pr = 10 000. The deformations of Nusselt number curves in comparison with the classical case ("pure" forced convection) reach their maximum at the same point, where the parabolic profile of axial velocity undergoes the maximal distortion, i.e. at z* congruent-to 0.03 [2]. A local maximum of local Nusselt number at z* congruent-to 0.04 may be evidently observed in Fig. 9 for Pr = 1. In this case "the point of maximum distortion of parabolic velocity profile" is shifted towards the greater values of axial coordinate as a result of neglection of axial heat conduction, which is especially important for small Prandtl numbers. Buoyancy effects should be taken into consideration, when analyzing non-isothermal laminar flows of fluids with strongly temperature - dependent density. Neglection of these phenomena may lead to considerable errors in heat transfer calculations.