Page 449 - Modelling in Transport Phenomena A Conceptual Approach
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Chapter 10
Unsteady-State Microscopic
Balances Without
Generation
The presence of the accumulation term in the inventory rate equation complicates
the mathematical problem since the resulting equation is a partial differential equa-
tion even if the transport takes place in onedirection. The solution of partial dif-
ferential equations not only depends on the structure of the equation itself, but
also on the boundary conditions. Systematic treatment of momentum, energy, and
mass transport based on the types of the partial differential equation as well as
the boundary conditions is a formidable task and beyond the scope of this text.
Therefore, only some representative examples on momentum, energy, and mass
transport will be covered in this chapter.
10.1 MOMENTUM TRANSPORT
Consider an incompressible Newtonian Auid contained between two large parallel
plates of area A, separated by a distance B as shown in Figure 10.1. The system is
initially at rest but at time t = 0, the lower plate is set in motion in the z-direction
at a constant velocity V while the upper plate is kept stationary. It is required to
determine the development of velocity profile as a function of position and time.
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