Chapter 19: Furnace Calculations

Example 19.1 pgno:702

In [1]:
print"\t example 19.1 \t"
# For orientation purposes, one can make an estimate of the number of tubes required in the radiant section by assuming avg flux is 12000 Btu/(hr)*(ft**2)
# from Fig.19.14 it can be seen that with a tube temperature of 800DegF, an exit-gas temperature of l730DegF will be required to effect such a flux.
print"\t approxiate values are mentioned in the book \t"
Q=50000000; # Btu/hr
QF=(Q/0.75); # efficiency of tank is 75%
print"\t heat liberated by the fuel : Btu/hr \t",QF
w1=(QF/17130); # heating value of fuel is 17130Btu/lb
print"\t fuel quantity : lb/hr \t",w1
w2=(w1*17.44); # lb of fuel fired with 17.44lb of air
print"\t air required : lb/hr \t",w2
w3=(w1*0.3); # 0.3 lb of air is used for atomizing lb of fuel
print"\t steam for atomizing : lb/hr \t",w3
QA=(w2*82); # heating value at 400F is 82Btu/lb
print"\t QA is : Btu/hr \t",QA
print"\t QS is negligible \t"
QW=(0.02*QF);
print"\t QW is : Btu/hr \t",QW
Qnet=(QF+QA-QW);
print"\t Qnet is : Btu/hr \t",Qnet
#Heat out m gases at 1730DegF, 25 per cent excess air, 476 Btu/lb of flue gas
QG=(476*(w1+w2+w3));
print"\t QG is : Btu/hr \t",QG
Q1=(Qnet-QG);
print"\t Q1 is : Btu/hr \t",Q1 # calculation mistake in book
A=(3.14*38.5*(5./12.)); # area of tube
print"\t area of tube is : ft**2 \t",A
Nt=(Q1/(12000*A)); # 12000 is avg flux
print"\t estimated number of tubes : \t",Nt
# The layout of the cross section of the furnace may be as shown m Fig. 19.16.
# center to center distance is 8(1/2)in
Acp=(8.5*38.5/12);
print"\t cold plane surface per tube : ft**2 \t",Acp # calculation mistake in book
a=0.937; # a=alpha, from fig 19.11 as Ratio of center-to-center/OD is 1.7
Acp1=(Acp*a);
print"\t Acp1 is : ft**2 \t",Acp1
Acpt=(Acp1*Nt);
print"\t total cold plane surface is : ft**2 \t",Acpt
A1=(2*20.46*14.92); # from fig 19.16
print"\t surface of end walls : ft**2 \t",A1
A2=(38.5*14.92); # from fig 19.16
print"\t surface of side wall : ft**2 \t",A2
A3=(38.5*9.79); # from fig 19.16
print"\t surface of bridge walls : ft**2 \t",A3
A4=(2*20.46*38.5); # from fig 19.16
print"\t surface of floor and arch : ft**2 \t",A4
AT=(A1+A2+A3+A4);
print"\t AT is : ft**2 \t",AT
AR=(AT-Acpt);
print"\t AR is : ft**2 \t",AR
Ar=(AR/Acpt);
print"\t ratio of areas is : \t",Ar
print"\t dimension ratio is 3:2:1 \t"
L=((2/3)*(38.5*20.46*14.92)**(1/3));
print"\t length is : ft \t",L
print"\t gas emissivity \t"
# From the analysis of the fuel, the steam quantity, and the assumption that the humidity of the air is 50 per cent of saturation at 60F, the partial pressures of CO2 and H2O in the combustion gases with 25 per cent excess air are
pCO2=0.1084;
pH2O=0.1248
pCO2L=1.63; # pCO2L=(pCO2*L)
pH2OL=1.87;
P=((pCO2)/(pCO2+pH2O));
print"\t percentage correction at P : \t",P
Pt=pCO2L+pH2OL;
print"\t Pt is : \t",Pt
# %correction estimated to be 8%
eG=(((6500+14500)-(650+1950))/(39000-4400))*((100-8)/100); # values from fig 19.12 and 19.13, eq 19.5
print"\t eG is : \t",eG
f=0.635; # from fig 19.15 as (AR/Acpt)=1.09 and eG=0.496
print"\t overall exchange factor : \t",f
Z=(Q1/(Acpt*f));
print"\t Z is : \t",round(Z)
print"\t TG required (at Ts = 800F) = 1670F compared with 1730DegF assumed in heat balance) \t"
# end
	 example 19.1 	
	 approxiate values are mentioned in the book 	
	 heat liberated by the fuel : Btu/hr 	66666666.6667
	 fuel quantity : lb/hr 	3891.8077447
	 air required : lb/hr 	67873.1270675
	 steam for atomizing : lb/hr 	1167.54232341
	 QA is : Btu/hr 	5565596.41954
	 QS is negligible 	
	 QW is : Btu/hr 	1333333.33333
	 Qnet is : Btu/hr 	70898929.7529
	 QG is : Btu/hr 	34715859.1166
	 Q1 is : Btu/hr 	36183070.6363
	 area of tube is : ft**2 	50.3708333333
	 estimated number of tubes : 	59.8611475495
	 cold plane surface per tube : ft**2 	27.2708333333
	 Acp1 is : ft**2 	25.5527708333
	 total cold plane surface is : ft**2 	1529.61818515
	 surface of end walls : ft**2 	610.5264
	 surface of side wall : ft**2 	574.42
	 surface of bridge walls : ft**2 	376.915
	 surface of floor and arch : ft**2 	1575.42
	 AT is : ft**2 	3137.2814
	 AR is : ft**2 	1607.66321485
	 ratio of areas is : 	1.05102255612
	 dimension ratio is 3:2:1 	
	 length is : ft 	0.0
	 gas emissivity 	
	 percentage correction at P : 	0.464837049743
	 Pt is : 	3.5
	 eG is : 	0
	 overall exchange factor : 	0.635
	 Z is : 	37251.9195663
	 TG required (at Ts = 800F) = 1670F compared with 1730DegF assumed in heat balance) 	

Example 19.2 pgno:705

In [4]:
print"\t example 19.2 \n"
QF=50000000.;
G=22.36;
Acpt=1500.;
print"\t approxiate values are mentioned in the book "
Q=(QF/(1+(G/4200)*(QF/Acpt)**(1/2)))/2; # eq 19.15
print"\t Q is :  Btu/hr ",Q
print"\t The radiant-section average rate will be 8350 Btu/(hr) (ft2), and the exit-flue-gas temperature 1540DegF by heat balance. \n"
# end
	 example 19.2 

	 approxiate values are mentioned in the book 
	 Q is :  Btu/hr  24867609.5833
	 The radiant-section average rate will be 8350 Btu/(hr) (ft2), and the exit-flue-gas temperature 1540DegF by heat balance. 

Example 19.3 pgno:707

In [5]:
print"\t example 19.3 \n"
Qr=1.5; # Qr=(QF2/QF1)
Cr=1.5; # Cr=(CR2/CR1)
Gr=140/125; # Gr=(G2/G1)
Qr1=0.38; # Qr1=(Q1/QF1)
print"\t approxiate values are mentioned in the book \n"
a1=1.63; # a1=(G1*(CR1/27)^(1/2)), from eq 19.17
print"\t a1 is :  ",a1
a2=1.37*(a1); # a2=(G2*(CR2/27)^(1/2))
print"\t a2 is : ",a2
Qr2=(1/(1+a2)); # Qr2=(Q2/QF2),from eq 19.15
print"\t Qr2 is :  ",Qr2
Q21=(Qr2/Qr1)*(Qr); # Q21=(Q2/Q1)
print"\t ratio of heats is :  ",round(Q21,2)
print"\t Hence the radiant absorption will be increased only 22 per cent for an increase of 50 per cent in the heat liberated. \n"
# end
	 example 19.3 

	 approxiate values are mentioned in the book 

	 a1 is :   1.63
	 a2 is :  2.2331
	 Qr2 is :   0.309300671182
	 ratio of heats is :   1.22092370204
	 Hence the radiant absorption will be increased only 22 per cent for an increase of 50 per cent in the heat liberated. 

Example 19.4 pgno:708

In [6]:
print"\t example 19.4 \t"
eS=0.9; # assumed
TG=1500;
TS=650;
pCO2=0.1084;
pH2O=0.1248;
print"\t approxiate values are mentioned in the book \t"
L=(0.4*8.5)-(0.567*5);  # table 19.1
print"\t L is :  ft \t",L
pH2OL=0.1248*L;
pCO2L=0.1084*L;
print"\t pH2OL is :  atm-ft \t",pH2OL
print"\t pCO2L is :  atm-ft \t",pCO2L
qH2O=1050; # at TG, from fig 19.12 ana 19.13
qCO2=1700; # at TG, from fig 19.12 ana 19.13
qTG=(qH2O+qCO2);
print"\t qTG is :  \t",qTG
qsH2O=165; # at TS, from fig 19.12 ana 19.13
qsCO2=160; # at TS, from fig 19.12 ana 19.13
qTS=(qsH2O+qsCO2);
print"\t qTG is :  \t",qTS
q=(0.9*(qTG-qTS)); # q=(QRC/A)
print"\t q is :  \t",q
P=((pCO2)/(pCO2+pH2O));
print"\t percentage correction at P :\t",P
Pt=pCO2L+pH2OL;
print"\t Pt is :  \t",Pt
# %correction estimated to be 2%
q1=(q*0.98); # # q1=(QRC/A)
print"\t q1 is :  \t",q1
hr=(q1/(TG-TS));
print"\t radiation coefficient is :  Btu/(hr)*(ft^2)*(F) \t",round(hr,2)
#end
	 example 19.4 	
	 approxiate values are mentioned in the book 	
	 L is :  ft 	0.565
	 pH2OL is :  atm-ft 	0.070512
	 pCO2L is :  atm-ft 	0.061246
	 qTG is :  	2750
	 qTG is :  	325
	 q is :  	2182.5
	 percentage correction at P : %.3f 	0.464837049743
	 Pt is :  	0.131758
	 q1 is :  	2138.85
	 radiation coefficient is :  Btu/(hr)*(ft^2)*(F) 	2.51629411765

Example 19.5 pgno:709

In [10]:
print"\t example 19.5 \t"
Q=500000;
print"\t approxiate values are mentioned in the book \t"
a=(3.5+(3.14*4*(120/360)))/(1); # a=(alpha*Acp) from fig 19.17
AR=(3+3.6+3);
print"\t a is :  ft**2/ft \t",a
print"\t AR is :  ft**2/ft \t",AR
# Arbitrarily neglecting end wa.lls and also .the side wall refractory over 3'0" above the floor
R=(AR/a);
print"\t ratio of two areas is :  \t",R
eG=0.265;
TG=1174; # F
TS=500; # F
f=0.56; # from fig 19.15 as (AR/Acpt)=2.49 and eG=0.265
q=15300; # at TG and TS,q=(Q/(a*f))
# However, the convection coefficient is small, 1.0 +or- Btu/(hr)(ft2)("F), and AR/a is not 2.0 as in the assumptions for the Lobo and Evans equation.
q1=(q)-(7*(TG-TS)); # q1=(Q/(a*f))
print"\t q1 is :  Btu/(hr)*(ft**2) \t",q1
q2=(q1*f); # q2=(Q/(a))
print"\t q2 is :  Btu/(hr)*(ft**2) \t",q2
print"\t convection rate basis \t"
q3=(1*(TG-TS)*(4.2/a)); # q2=(Q/(a))
print"\t q3 is :  Btu/(hr)*(ft**2) \t",q3 # calculation mistake in book
qt=(q2+q3); # qt=(Q/(a))
print"\t qt is :  Btu/(hr)*(ft**2) \t",qt
ar=(Q/qt);
print"\t required a is :  ft**2 \t",ar
L=(ar/a)-2;
print"\t length required is :  ft \t",round(L,1)
# end
	 example 19.5 	
	 approxiate values are mentioned in the book 	
	 a is :  ft**2/ft 	3.5
	 AR is :  ft**2/ft 	9.6
	 ratio of two areas is :  	2.74285714286
	 q1 is :  Btu/(hr)*(ft**2) 	10582
	 q2 is :  Btu/(hr)*(ft**2) 	5925.92
	 convection rate basis 	
	 q3 is :  Btu/(hr)*(ft**2) 	808.8
	 qt is :  Btu/(hr)*(ft**2) 	6734.72
	 required a is :  ft**2 	74.2421362729
	 length required is :  ft 	19.2