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Note that the McAdams equation requires only a knowledge of the bulk temperature, whereas the Sieder-Tate expression also requires the wall temperature. Many people prefer equation I.7 for that reason.

Nusselt found that short tubes could be represented by the expression

For noncircular ducts, the concept of equivalent diameter can be employed, so that all the correlations for circular systems can be used.

Forced Convection in Flow Normal to Single Tubes and Banks. This circumstance is encountered frequently, for example air flow over a tube or pipe carrying hot or cold fluid. Correlations of this phenomenon are called semi-empirical and take the form Nud = C(ReD)m. Hilpert, for example, recommends the values given in Table 1.8. These values have been in use for many years and are considered accurate.

Flows across arrays of tubes (tube banks) may be even more prevalent than single tubes. Care must be exercised in selecting the appropriate expression for the tube bank. For example, a staggered array and an in-line array could have considerably different heat-transfer characteristics. Kays and London6 have documented many of these cases for heat-exchanger applications. For a general estimate of order-of-magnitude heat-transfer coefficients, Colburn's equation

is acceptable.

### Free Convection Around Plates and Cylinders.

In free convection phenomena, the basic relationships take on the functional form Nu = /(Gr, Pr). The Grashof number replaces the Reynolds number as the driving function for flow.

In all free convection correlations it is customary to evaluate the fluid properties at the mean film temperature Tm, except for the coefficient of volume expansion P, which is normally evaluated at the temperature of the undisturbed fluid far removed from the surface—namely, T/. Unless otherwise noted, this convention should be used in the application of all relations quoted here.

Table I.9 gives the recommended constants and exponents for correlations of natural convection for vertical plates and horizontal cylinders of the form Nu = C • Ram. The product Gr • Pr is called the Rayleigh number (Ra) and is clearly a dimensionless quantity associated with any specific free convective situation.

### I.3.3 Radiation Heat Transfer

Radiation heat transfer is the most mathematically complicated type of heat transfer. This is caused primarily by the electromagnetic wave nature of thermal radiation. However, in certain applications, primarily high-temperature, radiation is the dominant mode of heat transfer. So it is imperative that a basic understanding of radiative heat transport be available. Heat transfer in boiler and fired-heater enclosures is highly dependent upon the radiative characteristics of the surface and the hot combustion gases. It is known that for a body radiating to its surroundings, the heat rate is

where e is the emissivity of the surface, o is the Stefan-Boltzmann constant, o = 0.1713 x 10- 8 Btu/hr ft2 • R4. Temperature must be in absolute units, R or K. If e = 1 for a surface, it is called a "blackbody," a perfect emitter of thermal energy. Radiative properties of various surfaces are given in Appendix II. In many cases, the heat exchange between bodies when all the radiation emitted by one does not strike the other is of interest. In this case we employ a shape factor Fj to modify the basic transport equation. For two blackbodies we would write

Range of Nr6D |

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