Page 257 - Modelling in Transport Phenomena A Conceptual Approach

Chapter 8

Steady-State Microscopic

Balances Without

Generation

So far we have considered macroscopic balances in which quantities such as temper-
ature and concentration varied only with respect to time. As a result, the inventory
rate equations are written by considering the total volume as a system and the re-
sulting governing equations turn out to be the ordinary differential equations in
time. If the dependent variables such as velocity, temperature and concentration
change as a function of both position and time, then the inventory rate equations
for the basic concepts are written over a differential volume element taken within
the volume of the system. The resulting equations at the microscopic level are
called the equations of change.
In this chapter we will consider steady-state microscopic balances without in-
ternal generation. Therefore, the governing equations will be either ordinary or
partial differential equations in position. It should be noted that the treatment
for heat and mass transport is different from the one for momentum transport.
The main reasons for this are: (i) momentum is a vector quantity while heat and
mass are scalar, (ii) in heat and mass transport the velocity appears only in the
convective flux term, while it appears both in the molecular and convective flux
terms for the case of momentum transfer.

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