Free-Forced Convection in the Entry Region of a Heated Straight Pipe

The developing flow in the entry region of a horizontal pipe whose temperature is held constant and higher than the entry fluid temperature is analyzed. The asymptotic solution of the developing flow near the entrance of the heated straight pipe, distance 0(a), is obtained by perturbing the solution of the developing flow in an unheated straight pipe. The displacement of the boundary layer induces radial-directional and downward motion of the fluid particles in the inviscid core flow. The combination of these two motions results in two vortices developing along the pipe. The temperature in the core flow equals the entry fluid temperature. The forced convection boundary layer is affected by the buoyancy force and the axial pressure gradient induced by the boundary-layer displacement, and so is the heat transfer rate. The axial velocity has a concave profile with its maximum off the center line near the entrance, and it grows toward a uniformly distributed profile downstream. The downward stream caused by the displacement of the secondary boundary layer forces the axial velocity profile to turn counterclockwise continuously along the pipe if the flow is from left to right. The competition of two displacement effects supplies the physical explanation of why the flow pattern and the temperature distribution in heated pipes differ due to different degrees of heating.