Page 238 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 227

ð
Q ¼ _m h c p,h t h,in t h,out Þ ¼ 0:8962 1045 513 333:4Þ
ð
3
¼ 172:06 10 W
(5) Optimization of the design
The optimal design is modeled as follows:
!
Δp h _m h Δp c _m c
min TAC ¼ C E + C U ¼ C A A h + A c Þ + C el τ +
n A
ð
ρ
η p,h h,in η ρ
p,c c,in
s:t:
Q Q max 0
N fl,h N fl,h,max 0
N fl,h,min N fl,h 0
L h L h,max 0
L h,min L h 0
L c L c,max 0
L c,min L c 0
h f,h h f,h,max 0
h f,h,min h f,h 0
h f,c h f,c,max 0
h f,c,min h f,c 0
δ f,h δ f,h,max 0
δ f,h,min δ f,h 0
δ f,c δ f,c,max 0
δ f,c,min δ f,c 0
l s,h l s,h,max 0
l s,h,min l s,h 0
l s,c l s,c,max 0
l s,c,min l s,c 0
FPM h FPM h,max 0
FPM h,min FPM h 0
FPM c FPM c,max 0
FPM c,min FPM c 0
2
with the price per unit area C A ¼100 $/m , the area exponent of nonlinear
n A ¼0.6, the price of electrical energy C el ¼30 $/MWh, the hours of
operation per year τ¼6500h/yr, the pump efficiency η p ¼0.5, and the
specified heat duty of exchanger Q min ¼160kW.
Carrying out the optimization, we obtain the design parameters as
1
L h ¼0.600m, L c ¼0.880m, h f,h ¼h f,c ¼10mm, FPM h ¼508.5m ,