Page 384 - Design and Operation of Heat Exchangers and their Networks

Dynamic analysis of heat exchangers and their networks 367

7.4 Dynamic behavior of multistream parallel channel
plate-fin heat exchangers

Since the first dynamic model presented and solved by Anzelius (1926) for
the heat transfer between a porous medium and a fluid passing through it,
many studies have been made. A review of new developments in dynamic
analysis of heat exchangers was made by Roetzel (1996), in which the axial
dispersion model is developed to predict the dynamic behavior of heat
exchangers considering the flow maldistribution in heat exchangers. Sys-
tematic description of the dynamic behavior of heat exchangers (except
the plate-fin heat exchangers) was provided by Roetzel and Xuan (1999).
Dynamic behavior of multistream plate-fin heat exchangers was first
studied numerically by Pingaud et al. (1989). In their mathematical model,
the dynamics of fins were neglected, and the steady-state fin efficiency and
bypass efficiency were used to take the fin effect into account. As has been
pointed out by Luo and Roetzel (2000a, 2001), this treatment would not be
acceptable for the fins with high fin Biot number (low fin efficiency).
Du et al. (1996b), Du (1996), Li et al. (2002), and Roetzel et al. (2002)
applied the lumped parameter model to the plate-fin heat exchangers, which
offered the dynamic behavior of the apparatus without dealing with detailed
temperature distributions. All of these researches neglect the effect of the fin
dynamics on the temperature responses.
Luo and Roetzel (2000a, 2001) studied the dynamic behavior of plate-fin
surface for single-blow test technique, in which the fin dynamics was
included in their model. Their researches confirmed that for plate-fin heat
exchangers, the effect of the lateral heat conduction resistance of fins cannot
be neglected if the Biot number of the fin is large enough, namely, as the fin
efficiency is not high. Later, Guan et al. (2001) and Zhu et al. (2004) devel-
oped their dynamic model for the parallel channel plate-fin heat exchangers
including the fin dynamics and solved the problem by the use of the Laplace
transform and numerical inverse transform algorithm. The analytical solu-
tion of the dynamic temperature responses of multistream parallel channel
plate-fin heat exchangers was proposed by Roetzel and Luo (2003). Using
finite-difference method with moving grid algorithm, Luo and Roetzel
(2000b) numerically solved a more realistic model in which the fin dynam-
ics, longitudinal heat conduction in separating plates, and longitudinal heat
dispersion in fluids are considered. With the numerical method, their model
can be applied to more general cases including variable properties and phase
change.