Why is my loop not working? "Index exceeds array bounds"

Function:

function [ row, cp, k] = apd (T)
if T > 318 & T < 320 
    row = 1.11
    cp = 1007
    k = 0.02781
else if T > 316 & T< 318
     row = 1.1135
     cp= 1007
     k = 0.027635
    else if T > 314 & T < 316
            row= 1.1205
            cp= 1007
            k= 0.02749
        else if T > 312 & T <314
                row= 1.1277
                cp = 1006.5
                k = 0.02734
            else if T >310 & T < 312
                    row = 1.1349
                    cp= 1006
                    k= 0.02719
                else if T >308 & T < 310 
                        row = 1.142
                        cp = 1006
                        k = 0.02704
                    else if T > 306 & T < 308
                            row= 1.14975
                            cp= 1006
                            k=0.0269
                        else if T > 304 & T < 306
                                row = 1.1573
                                cp = 1006
                                k= 0.02682
                            else if T >302 & T < 304 
                                    row = 1.16495
                                    cp = 1006
                                    k = 0.02666
                                else if T >297 & T < 302 
                                        row = 1.17865
                                        cp = 1006
                                        k = 0.026345

                                    end
                                end
                            end
                        end
                    end
                end
            end
        end
    end
end
end

This function supposedly generates 3 air properties for a range of temperatures.

now, for the upcoming code that monitors the change of temperature and the distance crossed as air enters a tube where heat transfer by convection occurs:

%%%%%% DEFINITIONS %%%%%%%
clear
Q_lpm=15;
Q(1) =(Q_lpm/1000)/60; %m3/s [INPUT]
diameter = 0.01; % m [INPUT]
t =0.01; % time step [INPUT]
viscosity = 1.95*10^-5; % N.s/m2
Pr = 0.702;
area = pi*(diameter)^2/4; %m2
xtraveled = 0
xtube = 1.5
xprev = 0
V(1) = Q(1)*t; 
x(1) = V(1)/area;
T(1) = 30 + 273;
Twall = 25+273;
 i = 0
%%%%% ITERATIONS %%%%%

while xtraveled < xtube
    xprev =xtraveled 
    
    i= i+1
    
    T = T(i)
 
    [row,cp,k]=apd(T) %% generates new row, cp and k every iteration
    
    mdot(i)= Q(i)*row; %% getting the mass flow rate at that specific row  
    velocity = Q(i) /  area;   
    Re(i) = (row*velocity*diameter)/(viscosity) % if Re> 2300 - turbulent (calculated at that row)   
    Nu(i) = 0.023*(Re(i)^0.8)*(Pr^0.4) %% nusselts number at that row  
    h1(i) =  Nu(i)*k /diameter %% Heat transfer coeefficient at each density 
    As(i) = pi*diameter*x(i) %% surface area at each distance crossed inside the tube   
    L(i) = (h1(i)*As(i)*(T(i)-Twall)*t)/(row*cp*V(i)) %% energy balance parameter   
    T(i+1) = - L(i) +T(i) %% the new temperature at the new control volume  
    Q(i+1) = mdot(i) /row %% the new flow with the new temperature (new density) 
    V (i+1) = Q(i+1) * t  %% the new control volume of the new flow 
    x (i+1) = V(i+1) / area %% the new distance crossed inside the tube 
    xtraveled = xprev + x(i+1) %% total distance travelled by the flow is the previous travelled one plus the new x at each iteration
    
end

whenever i run the code, it stops at L(i) showing an error of "Index exceeds array bounds"

[Dyuman Joshi]

You are overwriting the variable T in each iteration.

    T = T(i) %over-writing
    [row,cp,k]=apd(T)

change this to

    t = T(i)
    [row,cp,k]=apd(t)
    
    %or directly
    [row,cp,k]=apd(T(i))

and move "i=i+1;" line to below the apd function call line or at the bottom

Also, what would happen in the value of T is a boundary value.

For example - T = 302 / 304 / 306 ...

What will be the values of row, cp and k for these values?

Answer 1

[VBBV]

%%%%%% DEFINITIONS %%%%%%%
clear
Q_lpm=15;
Q(1) =(Q_lpm/1000)/60; %m3/s [INPUT]
diameter = 0.01; % m [INPUT]
t =0.01; % time step [INPUT]
viscosity = 1.95*10^-5; % N.s/m2
Pr = 0.702;
area = pi*(diameter)^2/4; %m2
xtraveled = 0

xtraveled = 0

xtube = 1.5

xtube = 1.5000

xprev = 0

xprev = 0

V(1) = Q(1)*t; 
x(1) = V(1)/area;
T(1) = 30 + 273;
Twall = 25+273;
 i = 0

i = 0

%%%%% ITERATIONS %%%%%

while (xtraveled <  xtube) 
    xprev =xtraveled ;
    
    i= i+1;
    
%     T = T(i)
 
    [row,cp,k]=apd(T(i)); %% generates new row, cp and k every iteration
    
    mdot(i)= Q(i)*row; %% getting the mass flow rate at that specific row  
    velocity(i) = Q(i) /  area;   
    Re(i) = (row*velocity(i)*diameter)/(viscosity); % if Re> 2300 - turbulent (calculated at that row)   
    Nu(i) = 0.023*(Re(i)^0.8)*(Pr^0.4) ;%% nusselts number at that row  
    h1(i) =  Nu(i)*k /diameter; %% Heat transfer coeefficient at each density 
    As(i) = pi*diameter*x(i); %% surface area at each distance crossed inside the tube   
    L(i) = (h1(i)*As(i)*(T(i)-Twall)*t)/(row*cp*V(i)); %% energy balance parameter   
    T(i+1) = - L(i) +T(i); %% the new temperature at the new control volume  
    Q(i+1) = mdot(i) /row; %% the new flow with the new temperature (new density) 
    V (i+1) = Q(i+1) * t;  %% the new control volume of the new flow 
    x (i+1) = V(i+1) / area; %% the new distance crossed inside the tube 
    xtraveled = xprev + x(i+1); %% total distance travelled by the flow is the previous travelled one plus the new x at each iteration
    
end

subplot(211); plot(T); subplot(212);plot(Re)

function [row, cp, k] = apd (T)
if T > 318 & T < 320 
    row = 1.11;
    cp = 1007;
    k = 0.02781;
else if T > 316 & T< 318
     row = 1.1135;
     cp= 1007;
     k = 0.027635;
    else if T > 314 & T < 316
            row= 1.1205;
            cp= 1007;
            k= 0.02749;
        else if T > 312 & T <314
                row= 1.1277;
                cp = 1006.5;
                k = 0.02734;
            else if T >310 & T < 312
                    row = 1.1349;
                    cp= 1006;
                    k= 0.02719;  
                else if T >308 & T < 310 
                        row = 1.142;
                        cp = 1006;
                        k = 0.02704;
                    else if T > 306 & T < 308
                            row= 1.14975;
                            cp= 1006;
                            k=0.0269;
                        else if T > 304 & T < 306
                                row = 1.1573;
                                cp = 1006;
                                k= 0.02682;
                            else if T >302 & T < 304 
                                    row = 1.16495;
                                    cp = 1006;
                                    k = 0.02666; 
                                else if T >297 & T < 302 
                                        row = 1.17865;
                                        cp = 1006;
                                        k = 0.026345;
                                else 
                                    return

                                    end
                                end
                            end
                        end
                    end
                end
            end
        end
    end
end
 
end

[VBBV]

T = T(i)  % this is first or initial term to be used out of loop

During increments in while loop, you are changing the size of vector variabl;e T every time by assigning as above

You are passing vector of values for temperature T into function, in the while loop. Use this instead

[row,cp,k]=apd(T(i));

If none of conditions inside the funcion are true then its required to return since its being called inside while loop.

[smith]

Thank you very much, this has helped, but the whole point of the function isnt working, which is, at each iteration i want to change the values of row,cp and k for the corresponding temperature of the iteration.

[VBBV]

The row, cp and k values change for corresponding termperature (iteration) using the below line

[row,cp,k]=apd(T(i)); % the function here returns a different row, cp and k value