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)’;

n=length(t);
h=h0*ones(n,1);
%
%
Euler’s Method
%
for j=2:n;
h(j)=h(j-1)+dt*dhdt(t(j-1),h(j-1));
end
plot(t,h,‘-b’)
%
%
Heun’s Method
%
t=(0:dt:tn)’;
for j=2:n
h1=h(j-1)+dt*dhdt(t(j-1),h(j-1));
h(j)=h(j-1)+(dt/2)*(dhdt(t(j),h1) + dhdt(t(j-1),h(j-1)));
end
hold on
plot(t,h,‘-g’)
%
%
Using ode23
%
[t,h] = ode23(dhdt,2000,0)
%
Higher order ODE
%
% Second order ODE: d

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’)

%
%
Using ode45
%
% Define function
%
function dydt=rhs(t,y)
dydt=[y(2);9.8-0.05*y(2)];
%
% Solve ODE given by function ‘rhs’
%
y0=[0;0];
[t,y] = ode45(‘rhs’,20,y0)
%
% Then y(1) gives x and y(2) gives y
%
A.F.1
C GAUSSIAN ELIMINATION FOR A TRIDIAGONAL SYSTEM
C
C A(I), B(I) AND C(I) ARE THE THREE ELEMENTS IN EACH ROW OF
C THE GIVEN SYSTEM OF EQUATIONS, F(I) REPRESENTS THE CONSTANTS
C ON THE RIGHT-HAND SIDE OF THE EQUATIONS, T(I) ARE THE TEMPERATURE
C DIFFERENCES TO BE COMPUTED, G IS A PARAMETER DEFINED IN THE GIVEN
C PROBLEM, N IS THE NUMBER OF EQUATIONS AND TP REPRESENTS THE
C PHYSICAL TEMPERATURE, WHERE TP = T + 20. THE SYSTEM OF EQUATIONS
C TO BE SOLVED IS THE ONE GIVEN IN EXAMPLE 4.4.
Appendix A 649
C
PARAMETER (IN=30)
DIMENSION A(IN),B(IN),C(IN),T(IN),F(IN)

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

CALL FMTDM(G,N,A,B,C,F)
RETURN
END
C**********************************************************************
C THE FOLLOWING SUBROUTINE FORMS THE TRIDIAGONAL MATRIX OF THE FORM
C
C A*T(I-1) + B*T(I) + C*T(I+1) = R
C**********************************************************************
SUBROUTINE FMTDM(G,N,A,B,C,R)
DIMENSION A(N),B(N),C(N),R(N)
C
C ENTER THE CONSTANTS ON THE RIGHT-HAND SIDE OF THE EQUATIONS
C
R(1)=100.0
R(N)=100.0
NN=N-1
DO 1 I=2,NN
R(I)=0.0
1 CONTINUE
C
C ENTER THE MATRIX COEFFICIENTS
650 Design and Optimization of Thermal Systems
C
DO 2 I=1,N
B(I)=2.0+G
2 CONTINUE
DO 3 I=1,NN
C(I)=-1.0
3 CONTINUE
DO 4 I=2,N

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)

6 CONTINUE
RETURN
END
A.F.2
C GAUSS-SEIDEL METHOD FOR SOLVING A SYSTEM OF LINEAR EQUATIONS
C
C
C T(I) REPRESENTS THE TEMPERATURE DIFFERENCES FROM THE AMBIENT
C TEMPERATURE, TO(I) DENOTES THE TEMPERATURE DIFFERENCES AFTER
C THE PREVIOUS ITERATION, TP IS THE ACTUAL TEMPERATURE, S IS A
C CONSTANT DEFINED IN THE PROBLEM AND N IS THE NUMBER OF
C EQUATIONS. THE PROBLEM CONSIDERED IS THE ONE GIVEN IN
C EXAMPLE 4.4.
Appendix A 651
C
C
C ENTER VALUES OF RELEVANT PARAMETERS
C
PARAMETER (IN=30)
DIMENSION T(IN),TO(IN)
S=50.41*(0.01**2)+2.0
PRINT *, ‘GIVE THE NUMBER OF EQUATIONS : ’
READ (5,*) N
NN=N-1
EPS=0.1
C
C DIFFERENT CONVERGENCE PARAMETER EPS
C
DO 10 K=1,5
C

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

WRITE(6,6)EPS
6 FORMAT(//2X,‘EPS=’,F10.5)
WRITE(6,7)J
7 FORMAT(/2X,‘NUMBER OF ITERATIONS=’,I4/)
C
C COMPUTE ACTUAL TEMPERATURES
C
DO 8 I=1,N
652 Design and Optimization of Thermal Systems
TP=T(I)+20.0
WRITE(6,9)I,TP
8 CONTINUE
9 FORMAT(2X,‘TP(‘,I2,’)=’,F12.4)
EPS=EPS/10.0
10 CONTINUE
STOP
END
A.F.3
C ROOT SOLVING WITH THE SECANT METHOD
C X IS THE INDEPENDENT VARIABLE, FUN(X) IS THE GIVEN FUNCTION,
C X1 AND X2 ARE THE X VALUES FROM THE TWO PREVIOUS ITERATIONS,
C STARTING WITH THE TWO POINTS BOUNDING THE REGION, X3 IS THE
C APPROXIMATION TO THE ROOT, F1, F2 AND F3 ARE THE CORRESPONDING
C VALUES OF THE FUNCTION, AND EPS IS THE CONVERGENCE CRITERION
C THE FUNCTION USED IS THE ONE IN EXAMPLE 4.2.
C
EXTERNAL FUN
PRINT *, ‘ENTER THE TWO STARTING VALUES OF X’
READ (5,*) X1,X2
C

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,

$ ‘FUNCTION F(T)=’,F12.6//)
END IF
C
C VARY CONVERGENCE CRITERION
C
EPS=EPS/10
X1=X1I
X2=X2I
XOLD=X1
2 CONTINUE
STOP
END
C
C DEFINE THE FUNCTION
C
FUNCTION FUN(X)
FUN=(0.6*5.67*((850.0**4.0)-(X**4.0))/(10.0**8.0))-40.0*(X-350.0)
RETURN
END
A.F.4
C THIS PROGRAM FINDS THE REAL ROOTS OF AN EQUATION F(X)=0
C BY THE NEWTON-RAPHSON METHOD
C
C
C
C HERE X IS THE INDEPENDENT VARIABLE, Y1 THE VALUE OF THE
C FUNCTION AT X, Y2 THE FUNCTION AT X+0.001, YD THE DERIVATIVE,
C DX THE INCREMENT IN X FOR THE NEXT ITERATION, EPS THE
C CONVERGENCE CRITERION ON THE FUNCTION AND XMAX THE MAXIMUM
C VALUE OF X. THE FUNCTION USED IS THE ONE IN EXAMPLE 4.2.

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

IF (X .GE. XMAX) GO TO 20
GO TO 1
ELSE
5 WRITE(6,12) X,Y1
12 FORMAT(/2X,‘TEMPERATURE T =’,F8.4,4X,‘FUNCTION F(T)=’,F12.6)
10 FORMAT(2X,‘TEMPERATURE T =’,F8.4,4X,‘FUNCTION F(T)=’,F12.6)
END IF
20 STOP
END
C
C DEFINE THE FUNCTION
C
FUNCTION Y(X)
Y=(0.6*5.67*((850.0**4.0)-(X**4.0)))/(10.0**8.0) - 40.0*(X-350.0)
RETURN
END
A.F.5
C THIS PROGRAM SOLVES THE LAPLACE EQUATION BY EMPLOYING
C THE SUCCESSIVE OVER RELAXATION (SOR) ITERATION METHOD.
C
C WHEN THE PROGRAM IS RUN IT PROMPTS FOR THE INPUT VALUES REQUIRED.
C ENTER THE INPUT VALUES AND YOUR OUTPUT WILL BE IN A FILE CALLED
C ‘SOR.DAT’
C
C
C DESCRIPTION OF INPUT PARAMETERS:
C
C IL IS THE NUMBER OF GRID POINTS IN THE X DIRECTION.
C JL IS THE NUMBER OF GRID POINTS IN THE Y DIRECTION.
C DX IS THE GRID SIZE IN X DIRECTION.

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’

READ(5,*)ITMAX
PRINT *,‘ENTER CONVERGENCE CRITERION’
READ(5,*)EPSI
PRINT*,‘THE INPUT VALUES ARE:’
PRINT*,‘INITIAL GUESS FOR PHI=’,PHIINT
PRINT*,‘DX=’,DX,‘DY=’,DY
PRINT*,‘IL=’,IL,‘JL=’,JL
PRINT*,‘MAX NO. OF ITERATIONS=’,ITMAX
PRINT*,‘CONVERGENCE CRITERION=’,EPSI
ITERATION=0
C
C OPEN THE DATA FILES FOR GRAPHING
C
XFILE(1)=‘X1’
XFILE(2)=‘X2’
XFILE(3)=‘X3’
XFILE(4)=‘X4’
XFILE(5)=‘X5’
YFILE(1)=‘Y1’
YFILE(2)=‘Y2’
YFILE(3)=‘Y3’
YFILE(4)=‘Y4’
YFILE(5)=‘Y5’
C
C SET INITIAL DISTRIBUTION OF PHI
C
DO 51 I=1,IL
DO 5 J=1,JL
PHI(I,J)=PHIINT
5 CONTINUE

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)

C
C CHECK FOR CONVERGENCE
C
DO 351 I=1,IL
DO 35 J=1,JL
IF(ABS(PHI(I,J)-PHIOL(I,J)).GE.EPSI)GO TO 15
35 CONTINUE
351 CONTINUE
GO TO 50
40 PRINT*,‘SOLN. DOES NOT CONVERGE IN’,ITMAX,‘ITERATIONS’
50 OPEN(UNIT=10,FILE=‘SOR.DAT’)
WRITE(10,110)EPSI
110 FORMAT(1X,‘CONVERGENCE CRITERION =’1X,E9.1)
WRITE(10,115)OMEGA
115 FORMAT(//,1X,‘W=’,F5.2)
WRITE(10,120)ITERATION
120 FORMAT(//,1X,‘NO. OF ITERATIONS TO CONVERGE=’,1X,I4,//)
WRITE(10,130)
130 FORMAT(1X,‘PHI DISTRIBUTION IS:’,//)
WRITE(10,140)(I,I=1,IL)
140 FORMAT(1X,‘I=’,8X,11(I2,8X))
DO 60 J=1,JL
WRITE(10,100)J,(PHI(I,J),I=1,IL)
60 CONTINUE
100 FORMAT(1X,‘J=’,I2,3X,11(F8.5,2X))
C
C OUTPUT FOR GRAPHICS
C
II=1
Appendix A 657

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

END
C*******************************************************
SUBROUTINE BCOND(PHI,IL,JL)
C
C THIS SUBROUTINE IMPLEMENTS APPROPRIATE BOUNDARY CONDITIONS.
C
DIMENSION PHI(11,11)
C SET THE CONDITIONS ON I=1 AND I=IL SURFACES.
C
DO 25 J=1,JL
PHI(1,J)=0.
PHI(IL,J)=0.
25 CONTINUE
C
C SET THE CONDITIONS ON J=1 AND J=JL SURFACES
C
DO 30 I=1,IL
PHI(I,1)=0.
PHI(I,JL)=1.
30 CONTINUE
RETURN
END
658 Design and Optimization of Thermal Systems
A.F.6
C THE SUCCESSIVE SUBSTITUTION METHOD FOR NONLINEAR EQUATIONS
C
C
C HERE F1 IS THE FLOW RATE OF ARGON IN MOLES/S, F2 IS THE FLOW
C RATE OF NITROGEN, C IS THE TOTAL FLOW RATE, B AND P ARE THE
C PARAMETERS DEFINED IN THE PROBLEM (EXAMPLE 4.6), D IS THE

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,

$ ‘AMMONIA:’,F12.5)
ELSE
GO TO 1
END IF
STOP
END
659
Appendix B
Material Properties
B.1: Properties of dry air at atmospheric pressure—SI units
B.2: Property values of gases at atmospheric pressure
B.3: Properties of saturated water
B.4: Properties of common liquids—SI units
B.5: Thermalpropertiesofmetalsandalloys
B.6: Properties of other materials
B.7: Emissivities E
n
oftheradiationinthedirectionofthenormaltothesur-
face and E of the total hemispherical radiation for various materials for
the temperature T
A NOTE ON MATERIAL PROPERTIES
Thesetablesonthepropertiesofcommonmaterialsareprovidedforquickrefer-
ence and convenience. However, for detailed design and optimization of practical
systems, the various handbooks, encyclopedias, and references cited in the text
should be used instead, for the most appropriate and accurate property data.
TABLE B.1
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
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

/c
v
M k Pr ha
215 –58.15 –73 1.646 1.006 1.4050 14.12 19.36 0.734 214.8 293.9
220 –53.15 –64 1.607 1.006 1.4048 14.40 19.78 0.732 219.8 297.4
225 –48.15 –55 1.572 1.006 1.4046 14.67 20.20 0.731 224.8 300.8
230 –43.15 –46 1.537 1.006 1.4044 14.94 20.62 0.729 229.8 304.1
235 –38.15 –37 1.505 1.006 1.4042 15.20 21.04 0.727 234.9 307.4
240 –33.15 –28 1.473 1.005 1.4040 15.47 21.45 0.725 239.9 310.6
245 –28.15 –19 1.443 1.005 1.4038 15.73 21.86 0.724 244.9 313.8
250 –23.15 –10 1.413 1.005 1.4036 15.99 22.27 0.722 250.0 317.1
255 –18.15 –1 1.386 1.005 1.4034 16.25 22.68 0.721 255.0 320.2
260 –13.15 8 1.359 1.005 1.4032 16.50 23.08 0.719 260.0 323.4
265 –8.15 17 1.333 1.005 1.4030 16.75 23.48 0.717 265.0 326.5
270 –3.15 26 1.308 1.006 1.4029 17.00 23.88 0.716 270.1 329.6
275 –1.85 35 1.235 1.006 1.4026 17.26 24.28 0.715 275.1 332.6
280 6.85 44 1.261 1.006 1.4024 17.50 24.67 0.713 280.1 335.6
285 11.85 53 1.240 1.006 1.4022 17.74 25.06 0.711 285.1 338.5
290 16.85 62 1.218 1.006 1.4020 17.98 25.47 0.710 290.2 341.5
295 21.85 71 1.197 1.006 1.4018 18.22 25.85 0.709 295.2 344.4
300 26.85 80 1.177 1.006 1.4017 18.46 26.24 0.708 300.2 347.3
305 31.85 89 1.158 1.006 1.4015 18.70 26.63 0.707 305.3 350.2
310 36.85 98 1.139 1.007 1.4013 18.93 27.01 0.705 310.3 353.1
315 41.85 107 1.121 1.007 1.4010 19.15 27.40 0.704 315.3 355.8
320 46.85 116 1.103 1.007 1.4008 19.39 27.78 0.703 320.4 358.7
325 51.85 125 1.086 1.008 1.4006 19.63 28.15 0.702 325.4 361.4
330 56.85 134 1.070 1.008 1.4004 19.85 28.53 0.701 330.4 364.2
335 61.85 143 1.054 1.008 1.4001 20.08 28.90 0.700 335.5 366.9
340 66.85 152 1.038 1.008 1.3999 20.30 29.28 0.699 340.5 369.6
345 71.85 161 1.023 1.009 1.3996 20.52 29.64 0.698 345.6 372.3

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

460 186.85 368 0.7677 1.023 1.3911 25.22 37.78 0.683 462.3 428.7
470 196.85 386 0.7509 1.024 1.3901 25.58 38.46 0.682 472.5 433.2
480 206.85 404 0.7351 1.026 1.3892 25.96 39.11 0.680 482.8 437.6
490 216.85 422 0.7201 1.028 1.3881 26.32 39.76 0.680 493.0 442.0
500 226.85 440 0.7057 1.030 1.3871 26.70 40.41 0.680 503.3 446.4
510 236.85 458 0.6919 1.032 1.3861 27.06 41.06 0.680 513.6 450.6
520 246.85 476 0.6786 1.034 1.3851 27.42 41.69 0.680 524.0 454.9
530 256.85 494 0.6658 1.036 1.3840 27.78 42.32 0.680 534.3 459.0
540 266.85 512 0.6535 1.038 1.3829 28.14 42.94 0.680 544.7 463.2
550 276.85 530 0.6416 1.040 1.3818 28.48 43.57 0.680 555.1 467.3
560 286.85 548 0.6301 1.042 1.3806 28.83 44.20 0.680 565.5 471.3
570 296.85 566 0.6190 1.044 1.3795 29.17 44.80 0.680 575.9 475.3
580 306.85 584 0.6084 1.047 1.3783 29.52 45.41 0.680 586.4 479.2
590 316.85 602 0.5980 1.049 1.3772 29.84 46.01 0.680 596.9 483.2
600 326.85 620 0.5881 1.051 1.3760 30.17 46.61 0.680 607.4 486.9
620 346.85 656 0.5691 1.056 1.3737 30.82 47.80 0.681 628.4 494.5
640 366.85 692 0.5514 1.061 1.3714 31.47 48.69 0.682 649.6 502.1
660 386.85 728 0.5347 1.065 1.3691 32.09 50.12 0.682 670.9 509.4
680 406.85 764 0.5189 1.070 1.3668 32.71 51.25 0.683 692.2 516.7
700 426.85 800 0.5040 1.075 1.3646 33.32 52.36 0.684 713.7 523.7
720 446.85 836 0.4901 1.080 1.3623 33.92 53.45 0.685 735.2 531.0
740 466.85 872 0.4769 1.085 1.3601 34.52 54.53 0.686 756.9 537.6
760 486.85 903 0.4643 1.089 1.3580 35.11 55.62 0.687 778.6 544.6
780 506.85 944 0.4524 1.094 1.3559 35.69 56.68 0.688 800.5 551.2
800 526.85 950 0.4410 1.099 1.354 36.24 57.74 0.689 822.4 557.8
850 576.85 1070 0.4152 1.110 1.349 37.63 60.30 0.693 877.5 574.1
900 626.85 1160 0.3920 1.121 1.345 38.97 62.76 0.696 933.4 589.6
950 676.85 1250 0.3714 1.132 1.340 40.26 65.20 0.699 989.7 604.9
1000 726.85 1340 0.3529 1.142 1.336 41.53 67.54 0.702 1046 619.5
1100 826.85 1520 0.3208 1.161 1.329 43.96 1162 648.0

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

p
/c
v
, specic heat
capacity ratio, dimensionless; M, viscosity [for Ns/m
2
(= kg/ms) multiply tabulated values by 10
−6
];
k, thermal conductivity, mW/mK; Pr, Prandtl number, dimensionless; h, enthalpy,. KJ/kg; a, sound
velocity, m/s.
Source: Reprinted with permission from R. C. Weast, ed., Handbook of Tables for Applied Engineer-
ing Scioence. Copyright ¡ 1970, CRC Press, Inc., Boca Raton, FL.
TABLE B.2
Property Values of Gases at Atmospheric Pressure
Helium
T, K
R,
kg/m
3
c
p
,
Ws/kg  K M, kg/ms N, m
2
/s k, W/m  K A, m
2
/s Pr
3 5.200 × 10
3

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

300 0.08185 14.314 8.963 109.5 0.182 1.554 0.706
350 0.07016 14.436 9.954 141.9 0.206 2.031 0.697
1.895 × 10
−6
Appendix B 663
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
2
/s Pr
400 0.06135 14.491 10.864 177.1 0.228 2.568 0.690
450 0.05462 14.499 11.779 215.6 0.251 3.164 0.682
500 0.04918 14.507 12.636 257.0 0.272 3.817 0.675
550 0.04469 14.532 13.475 301.6 0.292 4.516 0.668
600 0.04085 14.537 14.285 349.7 0.315 5.306 0.664
700 0.03492 14.574 15.89 455.1 0.351 6.903 0.659
800 0.03060 14.675 17.40 569 0.384 8.563 0.664
900 0.02723 14.821 18.78 690 0.412 10.217 0.676
1000 0.02451 14.968 20.16 822 0.440 11.997 0.686
1100 0.02227 15.165 21.46 965 0.464 13.726 0.703
1200 0.02050 15.366 22.75 1107 0.488 15.484 0.715

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

0.009450 0.025319 × 10
−4
0.786
200 1.7108 1.0429 12.947 7.568 0.01824 0.10224 0.747
300 1.1421 1.0408 17.84 15.63 0.02620 0.22044 0.713
400 0.8538 1.0459 21.98 25.74 0.03335 0.3734 0.619
500 0.6824 1.0555 25.70 37.66 0.03984 0.5530 0.684
600 0.5687 1.0756 29.11 51.19 0.04580 0.7486 0.686
700 0.4934 1.0969 32.13 65.13 0.05123 0.9466 0.691
800 0.4277 1.1225 34.84 81.46 0.05609 1.1685 0.700
900 0.3796 1.1464 37.49 91.06 0.06070 1.3946 0.711
1000 0.3412 1.1677 40.00 117.2 0.06475 1.6250 0.724
1100 0.3108 1.1857 42.28 136.0 0.06850 1.8591 0.736
1200 0.2851 1.2037 44.50 156.1 0.07184 2.0932 0.748
(Continued)
664 Design and Optimization of Thermal Systems
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
2
/s Pr

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

250 0.8410 1.0425 15.40 11.28 0.02144 0.15063 0.750
300 1.13876 1.0421 17.843 15.67 0.02525 0.21280 0.737
350 0.97425 1.0434 20.09 20.62 0.02883 0.2836 0.728
400
0.85363 1.0484 22.19 25.99 0.03226 0.3605 0.722
450
0.75848 1.0551 24.18 31.88 0.0436 0.4439 0.718
500 0.68223 1.0635 26.06 38.19 0.03863 0.5324 0.718
550
0.62024 1.0756 27.89 44.97 0.04162 0.6240 0.721
600 0.56850 1.0877 29.60 52.06 0.04446 0.7190 0.724
Ammonia, NH
3
220 0.3828 2.198 × 10
3
7.255 × 10
−6
1.90 × 10
−5
0.0171 0.2054 × 10
−4
0.93
273 0.7929 2.177 9.353 1.18 0.0220 0.1308 0.90
323 0.6487 2.177 11.035 1.70 0.0270 0.1920 0.88
373 0.5590 2.236 12.886 2.30 0.0327 0.2619 0.87
423 0.4934 2.315 14.672 2.97 0.0391 0.3432 0.87
473 0.4405 2.395 16.49 3.74 0.0467 0.4421 0.84
Steam (H
2
O vapor)

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

2
/s Pr
750
0.2931 2.119 26.04 8.88 0.0549 0.883 1.005
800 0.2739 2.152 27.86 10.20 0.0592 1.001 1.010
850 0.2579 2.186 29.69 11.52 0.0637 1.130 1.019
Source: Eckert, E.R.G. and Drake, R.M. (1972) Analysis of Heat and Mass Transfer, McGraw-Hill,
New York.
TABLE B.3
Properties of Saturated Water
T
(nC)
c
p
(kJ/kg nC)
R
(kg/m
3
)
Mr 10
3
(kg/m  s)
Nr 10
6
(m
2
/s)
k
(W/m nC)
Ar 10

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

(Continued)
666 Design and Optimization of Thermal Systems
TABLE B.3 (CONTINUED)
Properties of Saturated Water
T
(nC)
c
p
(kJ/kg nC)
R
(kg/m
3
)
Mr 10
3
(kg/m  s)
Nr 10
6
(m
2
/s)
k
(W/m nC)
Ar 10
7
(m
2
/s)
Br 10
3

(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,

W/m  K
Freezing
Point, K
Latent
Heat of
Fusion, kJ/kg
Boiling
Point, K
Latent Heat
of Evaporation,
kJ/kg
Coefficient
of Cubical
Expansion, K
−1
Acetic acid 1049 2.18 0.001155 0.171 290 181 391 402 0.0011
Acetone 784.6 2.15 0.000316 0.161 179.0 98.3 329 518 0.0015
Alcohol,
ethyl 785.1 2.44 0.001095 0.171 158.6 108 351.46 846 0.0011
Alcohol, methyl 786.5 2.54 0.00056 0.202 175.5 98.8 337.8 1100 0.0014
Alcohol, propyl 800.0 2.37 0.00192 0.161 146 86.5 371 779
Ammonia
(aqua) 823.5 4.38 0.353
Benzene 873.8 1.73 0.000601 0.144 278.68 126 353.3 390 0.0013
Bromine 0.473 0.00095 245.84 66.7 331.6 193 0.0012
Carbon disulde 1261 0.992 0.00036 0.161 161.2 57.6 319.40 351 0.0013
Carbon tetrachloride 1584 0.866 0.00091 0.104 250.35 174 349.6 194 0.0013
Castor oil 956.1 1.97 0.650 0.180 263.2
Chloroform 1465 1.05 0.00053 0.118 209.6 77.0 334.4 247 0.0013
Decane 726.3 2.21 0.000859 0.147 243.5 201 447.2 263

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,

kJ/kg  K
Viscosity,
N  s/m
2
Thermal
Conductivity,
W/m  K
Freezing
Point, K
Latent
Heat of
Fusion, kJ/kg
Boiling
Point, K
Latent Heat
of Evaporation,
kJ/kg
Coefficient
of Cubical
Expansion, K
−1
Fluorine refrigerant
R-22 1194 1.26
b
0.086
b
113 183 232.4 232
c
Glycerine 1259 2.62 0.950 0.287 264.8 200 563.4 974 0.00054
Heptane 679.5 2.24 0.000376 0.128 182.54 140 371.5 318

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

, saturation
temperature.
Source: Reprinted with permission from R. C. Weast, ed., Handbook of Tables for Applied Engineering science. Copyright ¡ 1970, CRC Press, Inc., Boca Raton, FL.
Appendix B 669
TABLE B.5
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
/s) 100nC0nC 100nC 200nC 300nC 400nC 600nC 800nC 1000nC 1200nC
Aluminum
Pure 2,707 0.896 204 8.418 215 202 206 215 228 249
Al–Cu (Duralumin) 94–96
AL 3–5 Cu, trace Mg 2,787 0.883 164 6.676 126 159 182 194
Al–Mg (Hydronalium) 91–95
Al, 5–9 Mg 2,611 0.904 112 4.764 93 109 125 142
Al–Si (Silumin) 87 Al, 13 Si 2,659 0.871 164 7.099 149 163 175 185

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

/s) 100nC0nC 100nC 200nC 300nC 400nC 600nC 800nC 1000nC 1200nC
Lead 11,373 0.130 35 2.343 36.9 35.1 33.4 31.5 29.8
Iron
Pure 7,897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36
Wrought iron (C < 0.5%) 7,849 0.46 59 1.626 59 57 52 48 45 36 33 33 33
Cast iron (C ≈
4%) 7,272 0.42 52 1.703
Steel (Cmax. ≈ 1.5%)
Carbon Steel, C ≈ 0.5% 7,833 0.465 54 1.474 55 52 48 45 42 35 31 29 31
1.0% 7,801 0.473 43 1.172 43 43 42 40 36 33 29 28 29
1.5% 7,753 0.486 36 0.970 36 36 36 35 33 31 28 28 29
Iron
Steel
Nickel steel, Ni ≈ 0% 7.897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36
10% 7,945 0.46 26 0.720
20% 7,993 0.46 19 0.526
30% 8,073 0.46 12 0.325
40% 8,169 0.46 10 0.279
50% 8,266 0.46 14 0.361
60% 8,378 0.46 19 0.493
70% 8,506 0.46 26 0.666
80% 8,618 0.46 35 0.872
Appendix B 671
90% 8,762 0.46 47 1.156
100% 8,906 0.448 90 2.276
Invar, Ni = 36% 8,137 0.46 10.7 0.286
Chrome steel, Cr = 0% 7,897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36
1% 7,865 0.46 61 1.665 62 55 52 47 42 36 33 33
2% 7,865 0.46 52 1.443 54 48 45 42 38 33 31 31
5% 7,833 0.46 40 1.110 40 38 36 36 33 29 29 29

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)