Page 230 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 219

Zarea et al. (2014) applied a bees algorithm to optimize the design and
obtained the optimal design parameters as L h ¼0.995m, L c ¼0.995m,
1
h f ¼9.99mm, FPM¼405.69m , δ f ¼0.167mm, l s ¼9.998mm, and
N fl,h ¼10, which yield the minimum number of entropy generation units
of N s ¼0.052886.
Segundo et al. (2017) applied an adaptive differential evolution with
optional external archive and the Tsallis distribution to optimize the prob-
1
lem and got L h ¼0.996m, L c ¼0.994m, h f ¼9.99mm, FPM¼1000m ,
δ f ¼0.1mm, l s ¼8.82mm, and N fl,h ¼10. The minimum number of entropy
generation units reaches N s ¼0.046688.
Some researchers used other correlations of j and f factors for their design
tasks. For example, Yousefi et al. (2011) applied an imperialist competitive
algorithm to design a crossflow plate-fin heat exchanger, with the minimum
number of entropy generation units as the objective function. In their cal-
culation, the correlations of j and f factors of Manglik and Bergles (1995, see
Eqs. 3.266, 3.267) were used. Later, Yousefi et al. (2012) solved this design
task using a genetic algorithm hybrid with particle swarm optimization for
the minimum heat transfer area and the minimum relative total pressure
drop Δp h /Δp h,max +Δp c /Δp c,max , respectively. Hadidi (2015) carried out
the optimal design using a biogeography-based optimization algorithm with
the minimum heat transfer area as the optimization objective.
In fact, taking the number of entropy generation units as the objective
function of the optimization would not be a good choice for the design
of plate-fin heat exchangers. For a design task, the heat duty of the exchanger
is usually specified, that is, the outlet fluid temperatures are specified. As is
shown in Eq. (5.95), minimizing the number of entropy generation units is
equivalent to minimizing the pressure drops. Xie et al. (2008) suggested that
the objective function could be the total annual cost:

(5.97)
TAC ¼ C E + C U
C E ¼ C A A n A (5.98)
0 1
Δp h V Δp c V
C U ¼ C el τ @ h + c A (5.99)
η p,h η p,c

2
where, for example, the price per unit area C A ¼100 $/m , the area expo-
nent of nonlinear n A ¼0.6, the price of electrical energy C el ¼30 $/MWh,
the hours of operation per year τ¼6500h/yr, and the pump efficiency
η p ¼0.5.