Free Convection: Another mode of heat transfer is natural (free) convection. A number of correlations have been developed which are functions of Prandtl number (Pr), Grashof number (Gr), geometry and orientation of the heat transfer surface. See Table 5.2, where Nu is the Nusselt number, L is the characteristic length. The product Gr·Pr is termed as Raleigh number (Ra). Values of a and m are reported in Table 5.3.

For ideal gases β is equal to 1/T. For liquids, this value is calculated from density data. For water, this value is obtained from steam tables. Air properties are calculated at the film temperature that is the average of surface and bulk temperatures.

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: