Convection is the mode of heat transfer that involves conduction as well as bulk fluid motion. The rate of convection heat transfer in external flow is expressed by Newton’s law of cooling as


where Ts is the surface temperature and TX! is the free-stream temperature. The heat transfer coefficient h is usually expressed in the dimensionless form as the Nusselt number as Nu = hLc /k where Lc is the characteristic length. The characteristic length for noncircular tubes is the hydraulic diameter Dh defined as Dh = 4Ac /p where Ac is the cross-sectional area of the tube and p is its perimeter. The value of the critical Reynolds number is about 5 X 105 for flow over a flat plate, 2 X 105 for flow over cylinders and spheres, and 2300 for flow inside tubes.

The average Nusselt number relations for flow over a flat plate are:



which is valid for 3.5 < Re < 80,000 and 0.7 < Pr < 380. The fluid properties are evaluated at the film temperature Tf = (TX! + Ts)/2 in the case of a cylinder, and at the free- stream temperature TX! (except for ms , which is evaluated at the surface temperature Ts) in the case of a sphere.

The Reynolds number for internal flow and the hydraulic diameter are defined as


The flow in a tube is laminar for Re < 2300, turbulent for Re > 4,000, and transitional in between.

The length of the region from the tube inlet to the point at which the boundary layer merges at the centerline is the hydro- dynamic entry length Lh. The region beyond the entrance region in which the velocity profile is fully developed is the hydrodynamically fully developed region. The length of the region of flow over which the thermal boundary layer develops and reaches the tube center is the thermal entry length Lt. The region in which the flow is both hydrodynamically and thermally developed is the fully developed flow region. The entry lengths are given by


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