energy transport.pdf
TRANSCRIPT
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.