E5.4 Natural Convection

Example 5.4: The outside surface of a pipe (0.1388 ft outside diameter) is maintained at 110 °F. If the ambient air is 90 °F (1 atm), estimate the heat loss by free convection from a unit length of this pipe.

Solution: The film temperature is

The properties of air at 100 °F can be found from properties table as

The characteristic length of a circular pipe, L

The driving force for heat transfer is equal to the difference between surface temperature (t_s) and ambient temperature (t_a).

It is convenient to use the value of g as 4.17´10⁸ ft/h². One can definitely use 32.2 ft/s² for g but units have to be consistent.

Grashof number, (Gr)

Prandtl number (Pr):

Raleigh number, (Ra or Y):

The Nusselt number (Nu) is found by using appropriate values of a and m that depend upon the geometry of the heat transfer surface. For a horizontal pipe, these values can be read from Table 5.3 as

Nusselt number, Nu:

Heat transfer coefficient, h:

Heat transfer area, A:

Heat transfer rate, Q: