Page 169 - Modelling in Transport Phenomena A Conceptual Approach

Chapter 6

Steady- St at e Macroscopic

Balances

The use of correlations in the determination of momentum, energy and mass trans
fer from one phase to another under steady-state conditions was covered in Chap
ter 4. Although some examples of Chapter 4 make use of steady-state macroscopic
balances, systematic treatment of these balances for the conservation of chemical
species, mass and energy was not presented. The basic steps in the development
of steady-state macroscopic balances are as follows:
Define your system: A system is any region which occupies a volume and has
a boundary.
If possible, draw a simple sketch: A simple sketch helps in the understanding
of the physical picture.
0 List the assumptions: Simplify the complicated problem to a mathematically
tractable form by making reasonable assumptions.

Write down the inventory rate equation for each of the basic concepts relevant
to the problem at hand: Since the accumulation term vanishes for steady-state
cases, macroscopic inventory rate equations reduce to algebraic equations.
Note that in order to have a mathematically determinate system, the number
of independent inventory rate equations must be equal to the number of
dependent variables.
Use engineering correlations to evaluate the transfer coeficients: In macro-
scopic modeling, empirical equations that represent transfer phenomena from
one phase to another contain transfer coefficients, such as the heat transfer
coefficient in Newton’s law of cooling. These coefficients can be evaluated by
using engineering correlations given in Chapter 4.
Solve the algebraic equations.

149