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

Laminar upward and downward flows with mixed convection in a thin vert ical tube with a short uniformly heated section were investigated nume rically. Calculations were performed by solving the elliptic Navier-St okes and energy equations for slow flows of air (Pr = 0.7) correspondi ng 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 transfe r region for both aiding and opposing buoyancy, with a stronger effect for the latter, and can lead to flow reversal. By mapping the conditi ons that correspond to significant preheating and low reversal on a Gr ashof-Reynolds plane, a 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 formul ation is necessary to describe the flow field accurately.