Page 359 - Design and Operation of Heat Exchangers and their Networks

Dynamic analysis of heat exchangers and their networks 345

With modern computer technology and numerical methods, there is
no problem to simulate dynamic responses of multistream heat exchangers.
However, the numerical methods have some limitations, mainly numerical
errors and time-consuming computation. Therefore, great efforts have
been done to get more accurate, simple, and rapid dynamic simulations.
By introducing four connection matrices, Luo et al. (2002) obtained a
general solution of steady-state performance of multistream parallel
channel heat exchangers and their networks with arbitrary arrangements.
Their dynamic responses have also been investigated (Roetzel et al., 2002;
Luoetal.,2003). Later, the analytical solution of the dynamic responses
of multistream parallel channel plate-fin heat exchangers was obtained
by Roetzel and Luo (2003) by means of the Laplace transform and numer-
ical inverse transform. These general solutions will be presented here
in detail.

7.3.1 General model for multipass/multistream
heat exchangers
Consider a generalized multistream heat exchanger that consists of M fluid
00
0
channels, M w solid walls, N stream entrances, and N stream exits. N and
0
N can be different due to stream splitting and junction. The fluid flowing
00
through a channel can exchange heat with all solid walls. Each pipes or
mixing node in which several fluid streams are mixed and split again
(such as a manifold or a header) is considered as a channel. If the heat loss
to the surrounding should be taken into account, for example, there is no
thermal insulation outside the exchanger, the temperature of the sur-
rounding is taken as a boundary condition with known temperature var-
iation with time.
The assumptions used in the analysis are as follows: (1) The mass flow rate
and fluid temperature in each channel are uniform over the cross section per-
pendicular to the flow direction, and there is no axial heat dispersion (plug
flow); (2) the axial heat conduction in the solid wall and the fluid is
neglected; (3) there is no lateral heat resistances across the wall thickness;
(4) the heat transfer coefficients and the properties of the fluids and wall
materials are constant, and there is no phase change in the exchanger; (5)
there is no thermal interconnection between the walls. The governing equa-
tion system can be written as

M w
C i ∂t i _ ∂t i ¼ X U ik ð t w,k t i Þ ð i ¼ 1, 2, …, MÞ (7.108)
L i ∂τ + C i ∂x L i
k¼1