Free and forced convection in the entry region of a heated vertical channel

Abstract An analytical solution for the fluid flow and heat transfer in the entry region of a heated vertical channel is presented. The conditions of constant wall temperature and constant wall heat flux are studied. Different axial length scales are revealed by the analytical solution. These scales distinguish the regions of different convective mechanisms that a developing flow has to pass through before reaching its fully-developed state. The solution also indicates that natural convection eventually becomes the dominant heat transfer mode if Gr > Re for constant wall temperature, and Gr2 > Re for constant wall heat flux. If natural convection is a dominant mode, the evidence suggests that moving periodic and recirculating cells are generated. This provides an explanation of why reverse transition is observed, and laminar flow is maintained in a heated vertical tube for Re