EFFECTS OF AXIAL DIFFUSION ON LAMINAR HEAT TRANSFER WITH LOW PÉ CLET NUMBERS IN THE ENTRANCE REGION OF THIN VERTICAL TUBES

Abstract

Laminar upward and downward flows with mixed convection in a thin vertical tube with a short uniformly heated section were investigated numerically. Calculations were performed by solving the elliptic Navier-Stokes and energy equations for slow flows of air ( Pr = 0.7) corresponding to low Reynolds numbers from 20 to 500 and a wide range of Grashof numbers. Results reveal that axial diffusion plays a significant role in preheating the fluid upstream from the entrance of the heat transfer region for both aiding and opposing buoyancy, with a stronger effect for the latter, and can lead to flow reversal. By mapping the conditions that correspond to significant preheating and flow reversal on a Grashof-Reynolds plane, it has become possible to establish criteria that determine (1) when the upstream boundary conditions can be applied at the entrance of the heated section and ( 2) when the elliptical formulation is necessary to describe the flow field accurately.