Page 336 - Design and Operation of Heat Exchangers and their Networks

322 Design and operation of heat exchangers and their networks

disturbances in inlet fluid temperatures, mass flow rates, and heat transfer
coefficients was proposed by Luo et al. (2003). This general solution can also
be applied to the dynamic simulation of multipass tube bundle heat
exchangers and plate heat exchangers. Their algorithm was further extended
to multistream plate-fin heat exchangers of which the fin dynamics should
be taken into account (Roetzel and Luo, 2003).
In this chapter, the mathematical models for transient analysis of heat
exchangers are introduced. The analytical solutions and numerical proce-
dures for plate heat exchangers, shell-and-tube heat exchangers, multistream
plate-fin heat exchangers, and heat exchanger networks are provided with
examples in detail.

7.1 Mathematical model for transient analysis
of heat exchangers

Till now, a lot of mathematical models were developed for the dynamic
analysis of heat exchangers. The commonly used mathematical models for
predicting dynamic behavior of heat exchangers can be classified into the
lumped parameter model, the distributed parameter model, the cell model,
the axial dispersion model, and the numerical computation model.
The lumped parameter model simplifies the spatially distributed thermal
systems into a number of discrete “lumps” and assumes that the temperature
difference inside each lump is negligible. Therefore, the fluid and wall tem-
peratures are only the functions of time. The lumped parameter model
greatly simplifies the mathematical model describing the transient behavior
of a heat exchanger, so that the analytical solutions of the outlet fluid tem-
perature responses can be easily obtained.
A commonly used model for the steady-state and transient thermal anal-
ysis of heat exchangers is the distributed parameter model, which is based on
the plug-flow assumption. In the distributed parameter model, the fluid
velocity and temperature are assumed to be constant across any cross section
of the flow channel. There are no velocity and thermal boundary layers adja-
cent to the inner wall of the flow passage. Therefore, the temperature dis-
tribution is one dimensional along the flow channel, and the whole
temperature field is one dimensional in a parallel-flow heat exchanger
and is two dimensional in a crossflow heat exchanger.
In the cases of flow maldistributions, the ideal plug flow greatly deviates
from the real flow pattern. One way to correct this deviation is the applica-
tion of dispersion model. By introducing an axial dispersion term into the