THERMAL CONDUCTIVITY AND THE

MECHANISMS OF ENERGY

TRANSPORT

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 describes the rate at

which heat is conducted is the thermal conductivity

k.

Heat conduction in fluids can be thought of as

molecular energy transport.

Energy can also be transported by the bulk motion of

a fluid, and this is referred to as convective energy

transport; this form of transport depends on the

density ρ of the fluid.

FOURIER'S LAW OF HEAT

CONDUCTION(MOLECULAR ENERGY

TRANSPORT)

This equation, which serves to define k, is the one-dimensional form of

Fourier's law of heat conduction.

Then we can write an equation like for each of the coordinate directions:

Three-dimensional form of

Fourier's law

This equation describes the molecular transport of heat in isotropic

media. By "isotropic" we mean that the material has no preferred

direction, so that heat is conducted with the same thermal conductivity

k in all directions.

In addition to the thermal conductivity k, a quantity known as the thermal

diffusivity a is widely used. It is defined as

EXAMPLE

TEMPERATURE AND PRESSURE

DEPENDENCE OF THERMAL

CONDUCTIVITY

The thermal conductivities of gases at low

density increase with increasing temperature,

whereas the thermal conductivities of most

liquids decrease with increasing temperature.

EXAMPLE

CONVECTIVE TRANSPORT OF

ENERGY

Energy may also be transported by the bulk

motion of the fluid. In Fig. 9.7-1 we show three

mutually perpendicular elements of area dS at

the point P, where the fluid velocity is v. The

volume rate of flow across the surface element dS

perpendicular to the x-axis is vxdS.

The rate at which energy is being swept across

the same surface element is then

If we now multiply each of the three expressions

by the corresponding unit vector and add, we

then get, after division by dS

= Convective energy flux vector

WORK ASSOCIATED WITH

MOLECULAR MOTIONS

Work flux

The combined energy flux vector e:

The e vector is the sum of

(a) the convective energy flux,

(b) the rate of doing work (per unit area) by

molecular mechanisms, and

(c) the rate of transporting heat (per unit area) by

molecular mechanisms.