I do not understand the error I am obtaining. When I do not use the values of x,y,and z i get an answer, but when i use them i get an error.

I do not understand the error I am obtaining. When I do not use the values of x,y,and z i get an answer, but when i use them i get an error.

syms x y z f g
%%%%%Variable Values%%%%%%%%%
n=0;
m=0;
k = (0.6569);
h = 11;
alpha = 2.57*10^(-7);
t=0;
L=(.051);
W=(.01);
H=(.005);
% x=(.051/4);
% y=(.01/2);
% z=(.005/4);
beta = ((n+0.5)*pi);
eta = ((m/.01)*pi);
mew = (117);
lamda = (((n+0.5)*pi))^2+(117)^2+(((m/.01)*pi))^2;
%%%%%%%%DETERMINATION OF CONSTANT C%%%%%%%%%%%%%%%%
f(z,y,x) = cos(beta*z)*sin(mew*y)*cos(eta*x)*sin(eta*x);
C_nmp_numerator = int(int(int(f,z,[0 (H/2)]),y,[0 W]),x,[0 (L/2)]);

g(z,y,x) = (cos(beta*z))^2*(sin(mew*y))^2*((((-k*mew)/h)*(cos(mew*x))^2*sin(mew*x))+((sin(mew*x))^2*cos(mew*x)));
C_nmp_denominator = int(int(int(g,z,[0 (H/2)]),y,[0 W]),x,[0 (L/2)]);


C_nmp = C_nmp_numerator/C_nmp_denominator;
%%%%%%%%DETERMINATION DEMENTIONLESS TEMP THETA%%%%%%%%%%%%%%%%

theta = (C_nmp * cos(beta*z)*sin(eta*y)*((-k*mew)/h)*cos(mew*x)+sin(mew*x))*exp(-(lamda*lamda)*alpha*t)

Answer 1

[Walter Roberson]

syms x y z f g

x y z are symbolic

% x=(.051/4);
% y=(.01/2);
% z=(.005/4);

If those had the comment marks removed, the resulting x y z would be numeric and not integers

f(z,y,x) = cos(beta*z)*sin(mew*y)*cos(eta*x)*sin(eta*x);

When x, y, z are symbolic, that statement defines a symbolic function that relates symbolic names x, y, z to a formula.

When x, y, z are numeric, that statement calculates a specific numeric value on the right hand side, and tries to assign to to array f indexed at locations 0.00125, 0.005, 0.01275 . But those are not positive integers, so the indexing fails.

C_nmp_numerator = int(int(int(f,z,[0 (H/2)]),y,[0 W]),x,[0 (L/2)]);

If you had managed to fix the above f(z,y,x) definition so that f became a numeric scalar, then you would not be able to int() a numeric scalar.

[Walter Roberson]

So what can you do? This:

syms x y z f g
%%%%%Variable Values%%%%%%%%%
n=0;
m=0;
k = (0.6569);
h = 11;
alpha = 2.57*10^(-7);
t=0;
L=(.051);
W=(.01);
H=(.005);
X=(.051/4);
Y=(.01/2);
Z=(.005/4);
beta = ((n+0.5)*pi);
eta = ((m/.01)*pi);
mew = (117);
lamda = (((n+0.5)*pi))^2+(117)^2+(((m/.01)*pi))^2;
%%%%%%%%DETERMINATION OF CONSTANT C%%%%%%%%%%%%%%%%
f(z,y,x) = cos(beta*z)*sin(mew*y)*cos(eta*x)*sin(eta*x);
C_nmp_numerator = int(int(int(f,z,[0 (H/2)]),y,[0 W]),x,[0 (L/2)]);

g(z,y,x) = (cos(beta*z))^2*(sin(mew*y))^2*((((-k*mew)/h)*(cos(mew*x))^2*sin(mew*x))+((sin(mew*x))^2*cos(mew*x)));
C_nmp_denominator = int(int(int(g,z,[0 (H/2)]),y,[0 W]),x,[0 (L/2)]);


C_nmp = C_nmp_numerator/C_nmp_denominator;
%%%%%%%%DETERMINATION DEMENTIONLESS TEMP THETA%%%%%%%%%%%%%%%%

theta = (C_nmp * cos(beta*z)*sin(eta*y)*((-k*mew)/h)*cos(mew*x)+sin(mew*x))*exp(-(lamda*lamda)*alpha*t)

theta = 

vpa(subs(theta, {x, y, z}, {X, Y, Z}))

ans = 

0.99687746550155485732270131796321