CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 331
Example
Let us have a metal rod. One end of this rod has an initial temperature of 1000 K and the other
300 K. The rod is not at thermal equilibrium—its temperature is different at different positions.
The system undergoes transition to the state of equilibrium during which its temperature changes
with time at every location. As the temperatures equalize, energy is transported from areas with
a higher temperature to those with a lower temperature.Note:Processes in which transition to equilibrium is accelerated by external disturbances,
e.g. by stirring, are not considered transport processes.10.1.2 Flux and driving force
The fluxJzin the direction of axiszis defined as the amount of a certain quantityXwhich
passes through unit area perpendicular to this axis per unit time
Jz=1
S
dX
dτ. (10.1)
In general, the flux is a vector with components (Jx,Jy,Jz) in the direction of axesx,y,z.
The flux in the direction of axiszis caused by thedriving forceFz. Driving force means a
change of an intensive quantity with location (this quantity will be the same everywhere in the
system after equilibrium is attained). To be more precise, if we denote the intensive quantity
using the symbolY, the driving force in the direction of the axiszwill be equal to the derivative
Fz=dY
dz. (10.2)
Note: The termdriving forceindicates that the quantityFzshould have the physical
meaning of strength. This, however, is not always so.In general, driving force is a gradient of the quantityY, i.e. a vector with components
(Fx,Fy,Fz) in the direction of axesx,y,z.