Setya Wijayanta NPM: 1006788555 Soal 5.14 To ventilate ventilate a factory factory building, building, 5 kg/s of factory factory air at a temperat temperature ure of 27 is e!"austed, e!"austed, and an identica identicall flo# rate rate of outdoor outdoor air at at a temperature temperature of $12 is introduced introduced to to take its its place. To recover some of t"e "eat of t"e e!"aust air, "eat e!c"angers are placed in t"e e!"aust and t"e ventilation air ducts as s"o#n in %ig. 5$25, and 2 kg/s of #ater is pumped bet#e bet#een en t"e t#o "eat "eat e!c" e!c"ang anger ers. s. T"e &' valu value e of bot" bot" of t"ese t"ese coun counter ter flo# "eat "eat e!c"angers is (.)) k*/+. *"at is t"e temperature of air entering t"e factory
'ir $12 5 kg/s cp 1 k/0kg+ k/0kg+
2 kg/s #ater
&' (.)) k*/+
cp 4.1 k/
'ir 27
0kg+
5 kg/s
t
Solusi-
besaran yang diketahui: Wair = = c p air
= 1 k!"#kg$% 5 kg"s = 5 kW"$
W&ater = = c p &ater
= '(1) k!"#kg$% * kg"s = 8+,8 kW"$
-. = 6+,, kW"$ /eberapa persaaan untuk enyeesaikan s2a: Persaaan di heat e3changer 4entiati2n # 1" sebeah kiri%: = Wair #t #tair+i1 tair+21% = 5 kW" kW"$ $ #91* #91* 9 tair+21% = W&ater #t #t&ater+21 t&ater+i1% = 8+,8 kW"$ #t &ater+21 t&ater+i1 % niai di persaaan diatas adaah saa+ aka: 5 kW" kW"$ $ #91* #91* 9 tair+21% = 8+,8 8+,8 kW"$ kW"$ #t&ater+21 t&ater+i1 %
960 9 5 t air+21 = 8(,8t &ater+21 8(,8t&ater+i1 9 5 tair+21 9 8(,8t &ater+21 ; 8(,8t&ater+i1 = 60 Persaaan ain adaah:
#1%
tair+21 = tair+i1 #tair+i1 9 t&ater+i1 %
dengan < = -. #
% = 6(,, kW"$ #
= 6(,,0(08067 = 0(5106,
dengan easukkan niai t air+i1=91* dan < = 0(5106,+ aka
tair+21 = 91* #91* 9 t &ater+i1 %
tair+21 = 91* #91* 9 t &ater+i1 % tair+21 = 91* #91* 9 t &ater+i1 %0(6**) tair+21 = 91* ; 7('75* ; 0(6**) t &ater+i1 tair+21 9 0(6**) t &ater+i1 = '(5*'8
#*%
Persaaan di heat e3changer e3haust # *" sebeah kanan%: = Wair #tair+i* tair+2*% = 5 kW"$ #*7 9 tair+2* % = W&ater #t&ater+2* t&ater+i*% = 8+,8 kW"$ #t &ater+2* t&ater+i* % niai di persaaan diatas adaah saa+ aka: 5 kW"$ #*7 9 t air+2*% = 8+,8 kW"$ #t&ater+2* t&ater+i* % 1,5 9 5 t air+2* = 8(,8t&ater+2* 8(,8t&ater+i* 9 5 tair+2* 9 8(,8t &ater+2* ; 8(,8t&ater+i* =91,5
dengan < = -. #
% = 6(,, kW"$ #
0(5106, dengan easukkan niai t air+i*=*7 dan < = 0(5106,+ aka
tair+2* = *7 #*7 9 t &ater+i*%
= 6(,,0(08067 =
tair+2* = *7 #*7 9 t &ater+i*% tair+2* = *7 #*7 9 t &ater+i*%0(6**) tair+2* = *7 16(81)* ; 0(6**) t &ater+i* tair+2* 9 0(6**) t &ater+i* = 10(1808 dengan ensubstitusikan t&ater+i* = t&ater+21 + aka: tair+2* 9 0(6**) t &ater+21 = 10(1808 #'% !adi terdapat ' 4ariabe yang tidak diketahui niainya dengan ' persaaan inear( -ntuk eudahkan ' persaaan diatas dapat dituiskan dengan engganti abang t air+21 = a+ t air+2* = b+ t&ater+i1 = c+ t&ater+21 = d( aka keepat persaaan diatas enjadi: 9 5 a ; 8(,8 c 9 8(,8 d = 60 #1% a 9 0(6**) c = '(5*'8 #*% 9 5 b 9 8(,8t c ; 8(,8 d =91,5 #,% b 9 0(6**) d = 10(1808 #'% daa bentuk atrik bisa kita tuis:
/esaran yang kita cari enurut s2a adaah t air+21 = a+ dengan enggunakan eiinasi gauss: A=[-5 0 8.38 -8.38;1 0 -0.6229 0;0 -5 -8.38 8.38;0 1 0 -0.6229] B=[60;-4.5248;-135;10.1808] a=A\B
.= 95(0000 0 8(,800 98(,800 1(0000 0 90(6**) 0 0 95(0000 98(,800 8(,800 0 1(0000 0 90(6**) /= 60(0000 9'(5*'8 91,5(0000 10(1808 a= *()1)7 1*(080, 11()51' ,(0')' !adi tair+21 = *+)
