Page 345 - Modelling in Transport Phenomena A Conceptual Approach

Chapter 9

Steady-State Microscopic

Balances With Generation

This chapter is the continuation of Chapter 8 with the addition of the genera-
tion term in the inventory rate equation. The breakdown of the chapter is the
same as Chapter 8. Once the governing equations for the velocity, temperature
or concentration are developed, the physical significance of the terms appearing in
these equations are explained and the solutions are given in detail. Obtaining the
macroscopic level design equations by integrating the microscopic level equations
over the volume of the system is also presented.

9.1 MOMENTUM TRANSPORT

For steady transfer of momentum, the inventory rate equation takes the form

Rate of Rate of
( momentum in ) - ( momentum out
Rate of
+ ( momentum generation ) = 0 (9.1-1)

In Section 5.1 it was shown that momentum is generated as a result of forces acting
on a system, i.e., gravitational and pressure forces. Therefore, EQ. (9.1-1) may also
be expressed as

Rate of Rate of Forces acting
( momentum in ) - ( momentum out on a system = 0 (9.1-2)
As in Chapter 8, our analysis will again be restricted to cases in which the following
assumptions hold:

325