Page 201 - Modelling in Transport Phenomena A Conceptual Approach
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Chapter 7
Unsteady- St at e Macroscopic
Balances
In this chapter we will consider unsteady-state transfer processes between the
phases by assuming no gradients within each phase. Since the dependent vari-
ables, such as temperature and concentration, are considered uniform within a
given phase, the resulting macroscopic balances are ordinary differential equations
in time.
The basic steps in the development of unsteady macroscopic balances are sim-
ilar to those for steady-state balances given in Chapter 6. These can be briefly
summarized as follows:
0 Define your system.
0 If possible, draw a simple sketch.
0 List the assumptions.
0 Write down the inventory rate equation for each of the basic concepts relevant
to the problem at hand.
0 Use engineering correlations to evaluate the transfer coefficients.
0 Write down the initial conditions: The number of initial conditions must be
equal to the sum of the order of differential equations written for the system.
0 Solve the ordinary differential equations.
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