Page 281 - Bird R.B. Transport phenomena

Thermal Conductivity and the

Mechanisms of Energy Transport

§9.1 Fourier's law of heat conduction (molecular energy transport)
§9.2 Temperature and pressure dependence of heat conductivity
§9.3° Theory of thermal conductivity of gases at low density
§9.4° Theory of thermal conductivity of liquids

§9.5° Thermal conductivity of solids
§9.6° Effective thermal conductivity of composite solids
§9.7 Convective transport of energy
§9.8 Work associated with molecular motions

It is common knowledge that some materials such as metals conduct heat readily,
whereas others such as wood act as thermal insulators. The physical property that de-
scribes the rate at which heat is conducted is the thermal conductivity k.
Heat conduction in fluids can be thought of as molecular energy transport, inasmuch
as the basic mechanism is the motion of the constituent molecules. Energy can also be
transported by the bulk motion of a fluid, and this is referred to as convective energy trans-
port; this form of transport depends on the density p of the fluid. Another mechanism is
that of diffusive energy transport, which occurs in mixtures that are interdiffusing. In addi-
tion, energy can be transmitted by means of radiative energy transport, which is quite dis-
tinct in that this form of transport does not require a material medium as do conduction
and convection. This chapter introduces the first two mechanisms, conduction and con-
vection. Radiation is treated separately in Chapter 16, and the subject of diffusive heat
transport arises in §19.3 and again in §24.2.
We begin in §9.1 with the definition of the thermal conductivity к by Fourier's law
for the heat flux vector q. In §9.2 we summarize the temperature and pressure depen-
dence of к for fluids by means of the principle of corresponding states. Then in the next
four sections we present information about thermal conductivities of gases, liquids,
solids, and solid composites, giving theoretical results when available.
Since in Chapters 10 and 11 we will be setting up problems by using the law of con-
servation of energy, we need to know not only how heat moves into and out of a system
but also how work is done on or by a system by means of molecular mechanisms. The na-
ture of the molecular work terms is discussed in §9.8. Finally, by combining the conduc-
tive heat flux, the convective energy flux, and the work flux we can create a combined
energy flux vector e, which is useful in setting up energy balances.

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