**SUMMA****R****Y**

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 *Newtonâ€™s law of cool**ing *as

where *T**s *is the surface temperature and *T*X! is the free-stream temperature. The heat transfer coefficient *h *is usually expressed in the dimensionless form as the *Nusselt number *as Nu = *hL**c */*k *where *L**c *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 *T**f *= (*T*X! + *T**s*)/2 in the case of a cylinder, and at the free- stream temperature *T*X! (except for m*s *, which is evaluated at the surface temperature *T**s*) 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 L**h**. *The region beyond the entrance region in which the velocity profile is fully developed is the *hy**drodynamically 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 L**t**. *The region in which the flow is both hydrodynamically and thermally developed is the *fully developed flow region. *The entry lengths are given by