Unrecognized function or variable

Hi everyone,

I am having trouble with my code, in particular the variable 'T'. I always seem to get back to this error and was wondering where I am going wrong.

Thanks.

Unrecognized function or variable 'T'.

Error in Main_Script>dTdr (line 93)

dTdr_ = Z/(r*(k(T)+rho(T)*Cp(T)*epsilon_m_));

Error in Main_Script (line 21)

w1=h*dTdr(r(i),Z(i),Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));

% Parameters & Boundary Conditions
dTdz=30.12; Ri=0.05; Ro=0.075; Rm=0.0621; hcoeff=100;  To=300; Ti=0; Zo=0; Zi=1.3*Ri*hcoeff*(Ti-To); uRi=0; uRo=0; tawi=4.3465; tawo=3.792; npoints=1000;
h=(Ro-Ri)/npoints;
r=(Ri+h:h:Ro)';
uR= zeros(npoints,1);
T= zeros(npoints,1);
Z = zeros(npoints,1);
% 


% Call Runge Kutta Function Fourth Order

for i=1:1:(npoints-1)
     T(1)=Ti;
     Z(1)=Zi;
     uR(1)= uRi;
        
     if r(i)<Rm
         
         k1=h*dUdrI(r(i),tawi,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ri);
         w1=h*dTdr(r(i),Z(i),Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
         f1=h*dZdr(r(i),rho(T),Cp(T),uR,dTdz);
         
         k2=h*dUdrI((r(i)+h/2),tawi,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ri);
         w2=h*dTdr((r(i)+h/2),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
         f2=h*dZdr((r(i)+h/2),rho(T),Cp(T),uR,dTdz);
         
         k3=h*dUdrI((r(i)+h/2),tawi,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ri);
         w3=h*dTdr((r(i)+h/2),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
         f3=h*dZdr((r(i)+h/2),rho(T),Cp(T),uR,dTdz);
         
         k4=h*dUdrI((r(i)+h),tawi,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ri);
         w4=h*dTdr((r(i)+h),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
         f4=h*dZdr((r(i)+h),rho(T),Cp(T),uR,dTdz);
         
         uR(i+1) = uR(i) + (k1+2*k2+2*k3+k4)/6;
         T(i+1) = T(i) + (w1+2*w2+2*w3+w4)/6;
         Z(i+1) = Z(i) + (f1+2*f2+2*f3+f4)/6;
      end
      
end
 
 for i=(npoints-1):1:1
        T(1)=To;
        Z(1)=Zo;
        uR(1)=uRo;
        if r(i)>=Rm
            k1=h*dUdrO(r(i),tawo,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ro);
            w1=h*dTdr(r(i),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
            f1=h*dZdr(r(i),rho(T),Cp(T),uR,dTdz);
            
            k2=h*dUdrO((r(i)-h/2),tawo,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ro);
            w2=h*dTdr((r(i)-h/2),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
            f2=h*dZdr((r(i)-h/2),rho(T),Cp(T),uR,dTdz);
            
            k3=h*dUdrO((r(i)-h/2),tawo,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ro);
            w3=h*dTdr((r(i)-h/2),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
            f3=h*dZdr((r(i)-h/2),rho(T),Cp(T),uR,dTdz);
            
            k4=h*dUdrO((r(i)-h),tawo,mu(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo),Rm,Ro);
            w4=h*dTdr((r(i)-h),Z,Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));
            f4=h*dZdr((r(i)-h),rho(T),Cp(T),uR,dTdz);
            
            uR(i+1)=uR(i)+(k1+2*k2+2*k3+k4)/6;
            T(i+1)=T(i)+(w1+2*w2+2*w3+w4)/6;
            Z(i+1)=Z(i)+(f1+2*f2+2*f3+f4)/6;
            
        end
 end

 
figure, plot (r,uR)
xlabel('Radius')
ylabel('Velocity')
title('Velocity vs Radius')

figure, plot (r,T)
xlabel('Radius')
ylabel('Temperature')
title('Temperature vs Radius')

figure, plot (r,Z)
xlabel('Radius')
ylabel('Heat transfer per unit length')
title('Heat transfer per unit length vs Radius')

% Heat Transfer per Unit Length
function [dZdr_] = dZdr (r,rho,Cp,uR,dTdz)
dZdr_ = -r*rho(T)*Cp(T)*uR*dTdz;
end
 % Temperature Profile
function [dTdr_] = dTdr (Z,r,k,rho,Cp,epsilon_m_)
dTdr_ = Z/(r*(k(T)+rho(T)*Cp(T)*epsilon_m_));
end 
% Velocity Profile
function [dUdrI_] = dUdrI (tawi,mu,rho,epsilon_m_,Rm,r,Ri)
dUdrI_= tawi./(mu+rho*epsilon_m_)*((Rm^2-r^2)/(Rm^2-Ri^2))*(Ri/r);
end

function [dUdrO_] = dUdrO (tawo,mu,rho,epsilon_m_,r,Rm,Ro)
dUdrO_= tawo./(mu+rho*epsilon_m_)*((r^2-Rm^2)/(Ro^2-Rm^2))*(Ro/r);
end

%eddy diffusivities of momentum
function [epsilon_m] = epsilon_m_ (r,T,Rm,Ri,Ro,tawi,tawo)
      if r<Rm
        radratio=(r-Ri)/(Rm-Ri);
        rEpsI=6.516e-4+3.9225e-1*radratio+(-6.0949e-1)*(radratio).^2+(2.3391e-1)*(radratio).^3+(1.410e-1)*(radratio).^4+(-9.6098e-2)*(radratio).^5;
        epsilon_m=rEpsI*sqrt(tawi./rho(T))*(Rm-Ri);
      else
        radratio=(Ro-r)/(Ro-Rm);
        rEpsO=6.516e-4+3.9225e-1*radratio+(-6.0949e-1)*(radratio).^2+(2.3391e-1)*(radratio).^3+(1.410e-1)*(radratio).^4+(-9.6098e-2)*(radratio).^5;
        epsilon_m=rEpsO*sqrt(tawo./rho(T))*(Ro-Rm);
      end
end
     
function [Cp_]=Cp(T)
Cp_=1010.4755 + 0.1151*(T) + 4.00e-5*(T).^2;
end

function [k_]=k(T)
k_=0.0243+(6.548e-5)*(T) - (1.65e-8)*(T).^2;
end

%Dynamic Viscosity
function [mu_]=mu(T)
mu_=1.747e-5 + 4.404e-8*(T) - 1.645e-11*((T).^2);
end

function [Pr_]=Pr(T)
Pr_=0.7057*10^(2.06e-5*(T));
end

function [rho_]=rho (T)
rho_ =1e5/(287*(T));
end

function [vis_]=vis(T)
vis_=1.380e-5 + (8.955e-8)*(T) - (1.018e-10)*(T)^2;
end

Answer 1

[Rik]

Inside of this function the variable T doesn't exist. You will have to pass it as a variable, or make this a nested function so it shares the variable with the outer function.

function [dTdr_] = dTdr (Z,r,k,rho,Cp,epsilon_m_)
dTdr_ = Z/(r*(k(T)+rho(T)*Cp(T)*epsilon_m_));
end

[Thomas Faulkner]

Thanks Rik!

What will I need to do to pass it as a variable?

I tried adding T to the brackets to call it as a variable but now I am getting a new error

Array indices must be positive integers or logical values.

Error in Main_Script>dTdr (line 93)

dTdr_ = Z/(r*(k(T)+rho(T)*Cp(T)*epsilon_m_));

Error in Main_Script (line 21)

w1=h*dTdr(r(i),Cp(T),k(T),rho(T),epsilon_m_(r,T,Rm,Ri,Ro,tawi,tawo));

Thanks for your help, I'm sure theres just a couple small mistakes I need to rectify.

>>

[Rik]

Apparently T contains non-integers and/or values smaller than 1.