Appendix A 647
p2=[1 -10 35 -50 24];
p3=[1 -7 17 -17 6];
y1=polyval(p1,x);
y2=polyval(p2,x);
y3=polyval(p3,x);
plot(x,y1,‘g’,x,y2,‘b’,x,y3,‘m’)
hold on
y = zeros(size(x));
plot(x,y,‘r’)
A.M.6
% Ordinary Differential Equations
%
% Given ODE: dh/dt = [6x10
-4
– 3x10
-4
xh
0.5
]/0.03
%
% Enter given ODE
%
dhdt=inline(‘(6*10^(-4) - 3*10^(-4)*(h^(0.5)))/0.03’,‘t’,‘h’);
%
% Choose step size and total time
%
dt=10;
tn=200*dt;
h0=0;
t=(0:dt:tn)’;

2
x/dt
2
= 9.8 – 0.05 (dx/dt)
648 Design and Optimization of Thermal Systems
% Replaced by two first order ODEs: dx/dt = y; dy/dt = 9.8 – 0.05 y
%
% Enter two first-order equations
%
dxdt=inline(‘y’,‘t’,‘x’,‘y’);
dydt=inline(‘9.8-0.05*y’,‘t’,‘x’,‘y’);
%
% Give step size, end point and starting conditions
%
dt=0.5;
tn=40*dt;
x0=0;
y0=0;
t=(0:dt:tn)’;
n=length(t);
x=x0*ones(n,1);
y=y0*ones(n,1);
%
% Euler’s Method
%
for j=2:n;
x(j)=x(j-1)+dt*dxdt(t(j-1),x(j-1),y(j-1));
y(j)=y(j-1)+dt*dydt(t(j-1),x(j-1),y(j-1));
end
plot(t,x,‘-b’,t,y,‘-g’)

C
C SPECIFY INITIAL PARAMETERS
C
CALL INPUT(A,B,C,F,N)
CALL TDMA(A,B,C,F,N,T)
C
C COMPUTE ACTUAL TEMPERATURES FROM THE TEMPERATURE DIFFERENCES T(I)
C
WRITE (6,7)
7 FORMAT(2X,’THE REQUIRED PHYSICAL TEMPERATURES IN CELSIUS ARE’/)
DO 8 I=1,N
TP=T(I)+20.0
WRITE (6,9)I,TP
8 CONTINUE
9 FORMAT(2X,’TP(‘,I2,’)=’,F10.4)
STOP
END
C*********************************************************************
C GET THE INPUT DATA
C*********************************************************************
SUBROUTINE INPUT(A,B,C,F,N)
PARAMETER (IN=30)
DIMENSION A(IN),B(IN),C(IN),F(IN)
PRINT *, ‘GIVE THE VALUE OF N’
READ *, N
G=50.41*(0.01**2)
C
C ‘FMTDM’ FORMS THE TRIDIAGONAL MATRIX AND THE RIGHT HAND SIDE
C COLUMN MATRIX
C

A(I)=-1.0
4 CONTINUE
RETURN
END
C**********************************************************************
C TRIDIAGONAL MATRIX ALGORITHM
C**********************************************************************
SUBROUTINE TDMA(A,B,C,F,N,T)
C
C N IS THE ORDER OF THE TRIDIAGONAL MATRIX
C A IS THE SUBDIAGONAL OF THE TRIDIAGONAL MATRIX
C B IS THE DIAGONAL OF THE TRIDIAGONAL MATRIX
C C IS THE SUPERDIAGONAL OF THE TRIDIAGONAL MATRIX
C F IS THE RIGHT HAND SIDE VECTOR
C T IS THE SOLUTION VECTOR
C
DIMENSION A(N),B(N),C(N),F(N),T(N)
NN=N-1
DO 5 I=2,N
D=A(I)/B(I-1)
B(I)=B(I)-C(I-1)*D
F(I)=F(I)-F(I-1)*D
5 CONTINUE
C
C APPLY BACK SUBSTITUTION
C
T(N)=F(N)/B(N)
DO 6 I=1,NN
J=N-I
T(J)=(F(J)-C(J)*T(J+1))/B(J)

C INPUT STARTING VALUES
C
J=0
DO 1 I=1,N
T(I)=0.0
1 CONTINUE
C
C STORE COMPUTED VALUES AFTER EACH ITERATION
C
2 DO 3 I=1,N
TO(I)=T(I)
3 CONTINUE
C
C COMPUTE THE END VALUES T(1) AND T(N)
C
T(1)=(T(2)+100.0)/S
T(N)=(100.0+T(N-1))/S
C
C COMPUTE INTERMEDIATE VALUES
C
DO 4 I=2,NN
T(I)=(T(I+1)+T(I-1))/S
4 CONTINUE
C
C CHECK FOR CONVERGENCE
C
J=J+1
DO 5 I=1,N
IF(ABS(TO(I)-T(I)) .GT. EPS) GO TO 2
5 CONTINUE

C STORE STARTING VALUES
X1I=X1
X2I=X2
XOLD=X1
WRITE(6,12) X1,X2
12 FORMAT(/10X,‘INITIAL X1=’,F7.2,10X,’INITIAL X2=’,F7.2//)
EPS=0.01
DO 2 I=1,4
1 F1=FUN(X1)
F2=FUN(X2)
C
C COMPUTE THE APPROXIMATION TO THE ROOT
C
X3=(X1*F2-X2*F1)/(F2-F1)
F3=FUN(X3)
XNEW=X3
C
C CHECK FOR CONVERGENCE
IF (ABS(XNEW-XOLD) .GT. EPS) THEN
X1=X2
X2=X3
XOLD=X3
WRITE(6,10)X3,F3
10 FORMAT(2X,‘TEMPERATURE T =’,F10.4,4X,‘FUNCTION F(T) =’,
$ F12.6)
GO TO 1
ELSE
Appendix A 653
11 WRITE(6,13)EPS,X3,F3
13 FORMAT(//2X,‘EPS=’,F9.6,4X,‘TEMPERATURE T =’,F10.4,4X,

C
C
C DEFINE FUNCTION AND SPECIFY INPUT PARAMETERS
C
EXTERNAL Y
EPS=0.001
WRITE(6,15)EPS
15 FORMAT(2X,‘EPS=’,F8.4/)
PRINT *, ‘ ENTER AN INITIAL GUESS FOR X’
READ (5,*) X
XMAX=850.0
1 Y1=Y(X)
WRITE(6,10) X,Y1
C
C CHECK FOR CONVERGENCE
C
IF (ABS(Y1) .GT. EPS) THEN
XN=X+0.001
Y2=Y(XN)
654 Design and Optimization of Thermal Systems
YD=(Y2-Y1)/0.001
C
C CHECK IF RESULTS DIVERGE
C
IF (YD .GE. (1.0/EPS)) GO TO 20
C
C COMPUTE NEW APPROXIMATION TO THE ROOT
C
DX=-Y1/YD
X=X+DX

C DY IS THE GRID SIZE IN Y DIRECTION.
C OMEGA IS THE RELAXATION PARAMETER
C PHIINT IS THE INITIAL GUESS FOR PHI TAKEN UNIFORM OVER THE
C WHOLE DOMAIN.
C ITMAX IS THE NUMBER OF MAXIMUM ITERATIONS BEFORE STOPPING.
C EPSI IS THE CONVERGENCE CRITERION.
C
C
C DESCRIPTION OF OTHER VARIABLES:
C
C PHI IS THE SOLUTION VARIABLE AT NTH TIME STEP.
Appendix A 655
C PHIOL IS THE SOLUTION VARIABLE AT N-1TH TIME STEP.
C
C
CHARACTER*2 XFILE(5)
CHARACTER*2 YFILE(5)
DIMENSION PHI(11,11),PHIOL(11,11)
PRINT*,‘ENTER INITIAL GUESS FOR PHI TAKEN UNIFORM OVER THE’
PRINT*,‘WHOLE DOMAIN’
READ(5,*)PHIINT
PRINT*,‘ENTER GRID SIZE DX=, DY=’
READ(5,*)DX,DY
PRINT *,‘ENTER NO. OF GRID POINTS IL= , JL= ’
PRINT*,‘ MAXIMUM POSSIBLE IS 11 FOR BOTH IL AND JL,’
PRINT*,‘UNLESS DIMENSION STATEMENTS ARE CHANGED.’
READ(5,*)IL,JL
PRINT *,‘ENTER THE RELAXATION PARAMETER’
READ(5,*)OMEGA
PRINT*,‘ENTER MAXIMUM NO. OF ITERATIONS ALLOWED BEFORE STOPPING’

51 CONTINUE
C
C START SOLVING FOR PHI.
C
15 ITERATION=ITERATION+1
IF(ITERATION.GE.ITMAX)GO TO 40
656 Design and Optimization of Thermal Systems
C
C SAVE THE FIELD AT PREVIOUS TIME STEP.
C
DO 101 I=1,IL
DO 10 J=1,JL
PHIOL(I,J)=PHI(I,J)
10 CONTINUE
101 CONTINUE
C
C DO SOR ITERATIONS ON PHI ON INTERIOR POINTS.
C
DO 201 J=2,JL-1
DO 20 I=2,IL-1
PHIGS=(PHI(I+1,J)+PHI(I-1,J))/DX**2+
$ (PHI(I,J+1)+PHI(I,J-1))/DY**2
PHIGS=PHIGS/(2./DX**2+2./DY**2)
PHI(I,J)=OMEGA*PHIGS+(1 OMEGA)*PHIOL(I,J)
20 CONTINUE
201 CONTINUE
C
C IMPOSE THE BOUNDARY CONDITIONS
C
CALL BCOND(PHI,IL,JL)

DO 70 I=1,5
II=II+1
OPEN (UNIT=12,FILE=XFILE(I))
DO 66 J=1,JL
WRITE(12,*)PHI(II,J)
66 CONTINUE
CLOSE(UNIT=12)
70 CONTINUE
JJ=1
DO 71 J=1,4
JJ=JJ+2
OPEN(UNIT=12,FILE=YFILE(J))
DO 72 I=1,IL
WRITE(12,*)PHI(I,JJ)
72 CONTINUE
CLOSE(UNIT=12)
71 CONTINUE
OPEN(UNIT=12,FILE=‘XX’)
DO 73 I=1,IL
XX=FLOAT(I-1)*DX
WRITE(12,*)XX
73 CONTINUE
CLOSE(UNIT=12)
OPEN(UNIT=12,FILE=‘YY’)
DO 74 J=1,JL
YY=FLOAT(J-1)*DY
WRITE(12,*)YY
74 CONTINUE
CLOSE(UNIT=12)
STOP

C AMOUNT OF AMMONIA COLLECTED IN MOLES/S, CO IS THE VALUE OF C
C AFTER THE PREVIOUS ITERATION AND EPS IS THE CONVERGENCE
C CRITERION APPLIED TO THE TOTAL FLOW RATE C
C
C
C INPUT OF STARTING VALUES
C
EPS=0.0001
B=0.1
C=180.0
1 CO=C
C
C COMPUTATION OF UNKNOWN QUANTITIES
C
F1=0.9/(1.0-B)
P=1.0-0.57*EXP(-0.0155*F1)
F2=90.0/(1.0-B*P)
B=1.0-23.5/(4.0*F2*P+F1)
C=F1+4.0*F2
D=0.57*EXP(-0.0155*F1)*2.0*F2
WRITE (6,2)F1,C,D
2 FORMAT(2X,‘ARGON:’,F12.5,4X,‘FLOW:’,F12.5,4X,‘NH3:’, F12.5)
C
C CONVERGENCE CHECK
C
IF (ABS(C-CO) .LE. EPS) THEN
PRINT*,‘THE SOLUTION HAS CONVERGED’
PRINT*,‘THE SOLUTION IS:’
WRITE (6,3)F1,C,D
3 FORMAT(/2X,‘ARGON:’,F12.5,4X,‘TOTAL FLOW:’,F12.5,4X,

c
p
c
p
/c
v
M
k Pr ha
100 –173.15 –280 3.598 1.028 6.929 9.248 0.770 98.42 198.4
110 –163.15 –262 3.256 1.022 1.4202 7.633 10.15 0.768 108.7 208.7
120 –153.15 –244 2.975 1.017 1.4166 8.319 11.05 0.766 118.8 218.4
130 –143.15 –226 2.740 1.014 1.4139 8.990 11.94 0.763 129.0 227.6
140 –133.15 –208 2.540 1.012 1.4119 9.646 12.84 0.761 139.1 236.4
150 –123.15 –190 2.367 1.010 1.4102 10.28 13.73 0.758 149.2 245.0
160 –113.15 –172 2.217 1.009 1.4089 10.91 14.61 0.754 159.4 253.2
170 –103.15 –154 2.085 1.008 1.4079 11.52 15.49 0.750 169.4 261.0
180 –93.15 –136 1.968 1.007 1.4071 12.12 16.37 0.746 179.5 268.7
190 –83.15 –118 1.863 1.007 1.4064 12.71 17.23 0.743 189.6 276.2
200 –73.15 –100 1.769 1.006 1.4057 13.28 18.09 0.739 199.7 283.4
205 –68.15 –91 1.726 1.006 1.4055 13.56 18.52 0.738 204.7 286.9
210 –63.15 –82 1.684 1.006 1.4053 13.85 18.94 0.736 209.7 290.5
(Continued)
660 Design and Optimization of Thermal Systems
TABLE B.1 (CONTINUED)
Properties of Dry Air at Atmospheric Pressure—SI Units
Temperature Properties
K nC nF R c
p
c
p

350 76.85 170 1.008 1.009 1.3993 20.75 30.03 0.697 350.6 375.0
355 81.85 179 0.9945 1.010 1.3990 20.97 30.39 0.696 355.7 377.6
360 86.85 188 0.9805 1.010 1.3987 21.18 30.78 0.695 360.7 380.2
365 91.85 197 0.9672 1.010 1.3984 21.38 31.14 0.694 365.8 382.8
370 96.85 206 0.9539 1.011 1.3981 21.60 31.50 0.693 370.8 385.4
375 101.85 215 0.9413 1.011 1.3978 21.81 31.86 0.692 375.9 388.0
380 106.85 224 0.9288 1.012 1.3975 22.02 32.23 0.691 380.9 390.5
385 111.85 233 0.9169 1.012 1.3971 22.24 32.59 0.690 386.0 393.0
390 116.85 242 0.9050 1.013 1.3968 22.44 32.95 0.690 391.0 395.5
395 121.85 251 0.8936 1.014 1.3964 22.65 33.31 0.689 396.1 398.0
400 126.85 260 0.8822 1.014 1.3961 22.86 33.65 0.689 401.2 400.4
410 136.85 278 0.8608 1.015 1.3953 23.27 34.35 0.688 411.3 405.3
420 146.85 296 0.8402 1.017 1.3946 23.66 35.05 0.687 421.5 410.2
Appendix B 661
TABLE B.1 (CONTINUED)
Properties of Dry Air at Atmospheric Pressure—SI Units
Temperature Properties
K
nC nF R
c
p
c
p
/c
v
M
k Pr ha
430 156.85 314 0.8207 1.018 1.3938 24.06 35.75 0.686 431.7 414.9
440 166.85 332 0.8021 1.020 1.3929 24.45 36.43 0.684 441.9 419.6
450 176.85 350 0.7342 1.021 1.3920 24.85 37.10 0.684 452.1 424.2

1200 926.85 1700 0.2941 1.179 1.322 46.26 1279 675.2
1300 1026.85 1580 0.2714 1.197 1.316 48.46 1398 701.0
1400 1126.85 2060 0.2521 1.214 1.310 50.57 1518 725.9
1500 1226.85 2240 0.2353 1.231 1.304 52.61 1640 749.4
1600 1326.85 2420 0.2206 1.249 1.299 54.57 1764 772.6
1800 1526.85 2780 0.1960 1.288 1.288 58.29 2018 815.7
(Continued)
662 Design and Optimization of Thermal Systems
TABLE B.1 (CONTINUED)
Properties of Dry Air at Atmospheric Pressure—SI Units
Temperature Properties
K
nC nF R
c
p
c
p
/c
v
M
k Pr ha
2000 1726.85 3140 0.1764 1.338 1.274 2280 855.5
2400 2126.85 3860 0.1467 1.574 1.238 2853 924.4
2800 2526.85 4580 0.1245 2.259 1.196 3599 983.1
Symbols and units: K, absolute temperature, kelvins; nC, temperature, degrees Celsius; nF, tempera-
ture, degree Fahrenheit; R, density, kg/m
3
; c
p
, specic heat capacity, kJ/kgK; c

8.42 × 10
−7
0.0106
33 1.4657 5.200 50.2 3.42 × 10
−6
0.0353 0.04625 × 10
−4
0.74
144 3.3799 5.200 125.5 37.11 0.0928 0.5275 0.70
200 0.2435 5.200 156.6 64.38 0.1177 0.9288 0.694
255 0.1906 5.200 181.7 95.50 0.1357 1.3675 0.70
366 0.13280 5.200 230.5 173.6 0.1691 2.449 0.71
477 0.10204 5.200 275.0 269.3 0.197 3.716 0.72
589 0.08282 5.200 311.3 375.8 0.225 5.125 0.72
700 0.07032 5.200 347.5 494.2 0.251 6.661 0.72
800 0.06023 5.200 381.7 634.1 0.275 8.774 0.72
900 0.05286 5.200 413.6 781.3 0.298 10.834 0.72
Hydrogen
30 0.84722 10.840 × 10
3
1.606 × 10
−6
0.0228 0.02493 × 10
−4
0.759
50 0.50955 10.501 2.516 4.880 0.0362 0.0676 0.721
100 0.24572 11.229 4.212 17.14 0.0665 0.2408 0.712
150 0.16371 12.602 5.595 34.18 0.0981 0.475 0.718
200 0.12270 13.540 6.813 55.53 0.1282 0.772 0.719
250 0.09819 14.059 7.919 80.64 0.1561 1.130 0.713

1300 0.01890 15.575 24.08 1273 0.512 17.394 0.733
1333 0.01842 15.638 24.44 1328 0.519 18.013 0.736
Oxygen
100 3.9918 0.9479 × 10
3
7.768 × 10
−6
1.946 × 10
−6
0.00903 0.023876 × 10
−4
0.815
150 2.6190 0.9178 11.490 4.387 0.01367 0.05688 0.773
200 1.9559 0.9131 14.850 7.593 0.01824 0.10214 0.745
250 1.5618 0.9157 17.87 11.45 0.02259 0.15794 0.725
300 1.3007 0.9203 20.63 15.86 0.02676 0.22353 0.709
350 1.1133 0.9291 23.16 20.80 0.03070 0.2968 0.702
400 0.9755 0.9420 25.54 26.18 0.03461 0.3768 0.695
450 0.8682 0.9567 27.77 31.99 0.03828 0.4609 0.694
500 0.7801 0.9722 29.91 38.34 0.04173 0.5502 0.697
550 0.7096 0.9881 31.97 45.05 0.04517 0.6441 0.700
600
0.6504 1.0044 33.92 52.15 0.04832 0.7399 0.704
Nitrogen
100 3.4808 1.0722 × 10
3
6.862 × 10
−6
1.971 × 10
−6

Carbon Dioxide
220
2.4733 0.783 × 10
3
11.105 × 10
−6
4.490 × 10
−6
0.010805 0.05920 × 10
−4
0.818
250 2.1657 0.804 12.590 5.813 0.012884 0.07401 0.793
300 1.7973 0.871 14.958 8.321 0.016572 0.10588 0.770
350 1.5362 0.900 17.205 11.19 0.02047 0.14808 0.755
400 1.3424 0.942 19.32 14.39 0.02461 0.19463 0.738
450 1.1918 0.980 21.34 17.90 0.02897 0.24813 0.721
500 1.0732 1.013 23.26 21.67 0.03352 0.3084 0.702
550 0.9739 1.047 25.08 25.74 0.03821 0.3750 0.685
600 0.8938 1.076 26.83 30.02 0.04311 0.4483 0.668
Carbon Monoxide
220
1.55363 1.0429 × 10
3
13.832 × 10
−6
8.903 × 10
−6
0.01906 0.11760 × 10
−4
0.758

380
0.5863 2.060 × 10
3
12.71 × 10
−6
2.16 × 10
−5
0.0246 0.2036 × 10
−4
1.060
400 0.5542 2.014 13.44 2.42 0.0261 0.2338 1.040
450 0.4902 1.980 15.25 3.11 0.0299 0.307 1.010
500 0.4405 1.985 17.04 3.86 0.0339 0.387 0.996
550 0.4005 1.997 18.84 4.70 0.0379 0.475 0.991
600 0.3652 2.026 20.67 5.66 0.0422 0.573 0.986
650 0.3380 2.056 22.47 6.64 0.0464 0.666 0.995
700 0.3140 2.085 24.26 7.72 0.0505 0.772 1.000
Appendix B 665
TABLE B.2 (CONTINUED)
Property Values of Gases at Atmospheric Pressure
T, K
R,
kg/m
3
c
p
,
Ws/kg  K M, kg/ms N, m
2
/s k, W/m  K A, m

7
(m
2
/s)
Br 10
3
(1/K) Pr
0 4.218 99.8 1.791 1.792 0.5619 1.332 −0.0853 13.45
5 4.203 1000.0 1.520 1.520 0.5723 1.362 0.0052 11.16
10 4.193 999.8 1.308 1.308 0.5820 1.389 0.0821 9.42
15 4.187 999.2 1.139 1.140 0.5911 1.413 0.148 8.07
20 4.182 998.3 1.003 1.004 0.5996 1.436 0.207 6.99
25 4.180 997.1 0.8908 0.8933 0.6076 1.458 0.259 6.13
30 4.180 995.7 0.7978 0.8012 0.6150 1.478 0.306 5.42
35 4.179 994.1 0.7196 0.7238 0.6221 1.497 0.349 4.83
40 4.179 992.3 0.6531 0.6582 0.6286 1.516 0.389 4.34
45 4.182 990.2 0.5962 0.6021 0.6347 1.533 0.427 3.93
50 4.182 998.0 0.5471 0.5537 0.6405 1.550 0.462 3.57
55 4.184 985.7 0.5043 0.5116 0.6458 1.566 0.496 3.27
60 4.186 983.1 0.4668 0.4748 0.6507 1.581 0.529 3.00
65 4.187 980.5 0.4338 0.4424 0.6553 1.596 0.560 2.77
70 4.191 977.7 0.4044 0.4137 0.6594 1.609 0.590 2.57
75 4.191 974.7 0.3783 0.3881 0.6633 1.624 0.619 2.39
80 4.195 971.6 0.3550 0.3653 0.6668 1.636 0.647 2.23
85 4.201 968.4 0.3339 0.3448 0.6699 1.647 0.675 2.09
90 4.203 965.1 0.3150 0.3264 0.6727 1.659 0.702 1.97
95 4.210 961.7 0.2978 0.3097 0.6753 1.668 0.728 1.86
100 4.215 958.1 0.2822 0.2945 0.6775 1.677 0.755 1.76
120 4.246 942.8 0.2321 0.2461 0.6833 1.707 0.859 1.44
140 4.282 925.9 0.1961 0.2118 0.6845 1.727 0.966 1.23

(1/K) Pr
160 4.339 907.3 0.1695 0.1869 0.6815 1.731 1.084 1.08
180 4.411 886.9 0.1494 0.1684 0.6745 1.724 1.216 0.98
200 4.498 864.7 0.1336 0.1545 0.6634 1.706 1.372 0.91
220 4.608 840.4 0.1210 0.1439 0.6483 1.674 1.563 0.86
240 4.770 813.6 0.1105 0.1358 0.6292 1.622 1.806 0.84
260 4.991 783.9 0.1015 0.1295 0.6059 1.549 2.130 0.84
280 5.294 750.5 0.0934 0.1245 0.5780 1.455 2.589 0.86
300 5.758 712.2 0.0858 0.1205 0.5450 1.329 3.293 0.91
320 6.566 666.9 0.0783 0.1174 0.5063 1.156 4.511 1.02
340 8.234 610.2 0.0702 0.1151 0.4611 0.918 7.170 1.25
360 16.138 526.2 0.0600 0.1139 0.4115 0.485 21.28 2.35
Source: A. J. Chapman, Heat Transfer, 4th ed., Macmillan, New York, 1984. Reprinted with permis-
sion of Simon & Schuster, copyright ¡ 1984.
Appendix B 667
TABLE B.4
Properties of Common Liquids—SI Units
a
Common Name
Density,
kg/m
3
Specific
Heat,
kJ/kg  K
Viscosity,
N  s/m
2
Thermal
Conductivity,

Dodecane 754.6 2.21 0.001374 0.140 247.18 216 489.4 256
Ether 713.5 2.21 0.000223 0.130 157 96.2 307.7 372 0.0016
Ethylene glycol 1097 2.36 0.0162 0.258 260.2 181 470 800
Fluorine refrigerant
R-11 1476 0.870
b
0.00042 0.093
b
162 297.0 180
c
Fluorine refrigerant
R-12 1311 0.971
b
0.071
b
115
34.4 243.4 165
c
(Continued
)
668 Design and Optimization of Thermal Systems
TABLE B.4 (CONTINUED)
Properties of Common Liquids—SI Units
a
Common Name
Density,
kg/m
3
Specific
Heat,

Hexane 654.8 2.26 0.000297 0.124 178.0 152 341.84 365
Iodine 2.15 386.6 62.2 457.5 164
Kerosene 820.1 2.09 0.00164 0.145 251
Linseed oil 929.1 1.84 0.0331 253 560
Mercury 0.139 0.00153 234.3 11.6 630 295 0.00018
Octane 698.6 2.15 0.00051 0.131 216.4 181 398 298 0.00072
Phenol 1072 1.43 0.0080 0.190 316.2 121 455 0.00090
Propane 493.5 2.41
b
0.00011 85.5 79.9 231.08 428
c
Propylene 514.4 2.85 0.00009 87.9 71.4 225.45 342
Propylene glycol 965.3 2.50 0.042 213 460 914
Sea water 1025 3.76–4.10 270.6
Toluene 862.3 1.72 0.000550 0.133 178 71.8 383.6 363
Turpentine 868.2 1.78 0.001375 0.121 214 433 293 0.00099
Water 997.1 4.18 0.00089 0.609 273 333 373 2260 0.00020
a
At
1.0 atm pressure (0.101325 MN/m
2
), 300
K, except as noted.
b
At
297 K, liquid.
c
At
0.101325 MN/m
2

Al–Si (Silumin copper
bearing) 86.5 Al,
12.5 Si,
1 Cu 2,659 0.867 137 5.933 119 137 144 152 161
Al–Si (Alusil)
78–80
Al,
20–22 Si 2,627 0.854 161 7.172 144 157 168 175 178
Al–Mg–Si, 97 Al, 1 Mg,
1 Si, 1 Mn 2,707 0.892 177 7.311 175 189 204
(Continued)
670 Design and Optimization of Thermal Systems
TABLE B.5 (CONTINUED)
Thermal Properties of Metals and Alloys
Properties at 20nC Thermal Conductivity, k (W/m nC)
Metal
R
(kg/m
3
)
c
p
(kJ/
kg nC)
k
(W/m nC)
Ar 10
5
(m
2

10% 7,785 0.46 31 0.867 31 31 31 29 29 28 28 29
20% 7,689 0.46 22 0.635 22 22 22 22 24 24 26 29
30% 7,625 0.46 19 0.542
Cr–Ni (chrome-nickel);
15 Cr, 10 Ni 7,865 0.46 19 0.526
18 Cr, 8 Ni (V2A) 7,817 0.46 16.3 0.444 16.3 17 17 19 19 22 26 31
20 Cr, 15 Ni 7,833 0.46 15.1 0.415
25 Cr, 20 Ni 7,865 0.46 12.8 0.361
Ni–Cr (nickel-chrome);
80 Ni, 15 Cr 8,522 0.46 17 0.444
60 Ni, 15 Cr 8,266 0.46 12.8 0.333
40 Ni, 15 Cr 8,073 0.46 11.6 0.305
20 Ni, 15 Cr 7,865 0.46 14.0 0.390 14.0 15.1 15.1 16.3 17 19 22
(Continued)