Page 440 - Bird R.B. Transport phenomena

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Chapter 4

Interphase Transport in

Nonisothermal Systems

§14.1 Definitions of heat transfer coefficients

§14.2 Analytical calculations of heat transfer coefficients for forced convection through
tubes and slits
§14.3 Heat transfer coefficients for forced convection in tubes
§14.4 Heat transfer coefficients for forced convection around submerged objects
§14.5 Heat transfer coefficients for forced convection through packed beds
§14.6° Heat transfer coefficients for free and mixed convection

§14.7° Heat transfer coefficients for condensation of pure vapors on solid surfaces

In Chapter 10 we saw how shell energy balances may be set up for various simple
problems and how these balances lead to differential equations from which the tem-
perature profiles may be calculated. We also saw in Chapter 11 that the energy bal-
ance over an arbitrary differential fluid element leads to a partial differential
equation—the energy equation—which may be used to set up more complex prob-
lems. Then in Chapter 13 we saw that the time-smoothed energy equation, together
with empirical expressions for the turbulent heat flux, provides a useful basis for
summarizing and extrapolating temperature profile measurements in turbulent sys-
tems. Hence, at this point the reader should have a fairly good appreciation for the
meaning of the equations of change for nonisothermal flow and their range of applic-
ability.
It should be apparent that all of the problems discussed have pertained to systems
of rather simple geometry and furthermore that most of these problems have contained
assumptions, such as temperature-independent viscosity and constant fluid density. For
some purposes, these solutions may be adequate, especially for order-of-magnitude esti-
mates. Furthermore, the study of simple systems provides the stepping stones to the dis-
cussion of more complex problems.
In this chapter we turn to some of the problems in which it is convenient or necessary
to use a less detailed analysis. In such problems the usual engineering approach is to for-
mulate energy balances over pieces of equipment, or parts thereof, as described in Chapter
15. In the macroscopic energy balance thus obtained, there are usually terms that require
estimating the heat that is transferred through the system boundaries. This requires know-
ing the heat transfer coefficient for describing the interphase transport. Usually the heat
transfer coefficient is given, for the flow system of interest, as an empirical correlation of

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