Index exceeds the number of array elements (101).

But i get this message below. (message in bold)

incorrectCheck the temperature vector with unknown time vector

Index exceeds the number of array elements (101).

Error in tutorial3 (line 42) t = time(i); % time in seconds Error in Test1

Could you help me with this?

function [T,aliveFlag] = heat_eqn(timeend,nt)
% Description: This file implements the Fourier Series solution to the heat equation.
%
% Input parameters:
% - timeend   - time of simulation in seconds
% - nt        - number of points in time vector
%
% Output parameters:
% - T         - temperature profile along persons head
% - aliveFlag - 1 if person is alive, 0 if the person is dead
L      = 0.12;                      % Size of the domain
rstart = 0;                         % Start of computational domain (m)
rend   = L;                         % End of computational domain (m)
nr     = 101;                       % Number of grid points along the radius vector
dr     = (rend-rstart)/(nr-1);      % Spatial step size, delta r (m)
r      = rstart:dr:rend;            % Vector of grid points in r


% Temporal (t) parameters 
timestart = 0;                      % Starting time (0 seconds)
dt        = (timeend-timestart)/(nr-1);  % Temporal step size, delta t (s)
time      = timestart:dt:timeend;        % Vector of times

% Phyiscal parameters
T1    = -41;                        % Temperature at r=0
T2    = 37;                         % Temperature at r=L
A     = T2-T1;                      % Amplitude of the saw tooth wave
k     = 0.527;                      % Thermal conductivity (W/m-K)
rho   = 1000;                       % Density (kg/m^3)
gamma = 3600;                       % Heat capacity (J/kg-K)
c     = sqrt(k/(rho*gamma));     % Heat equation constant   c^2=k/(rho*sigma)              


% Calculate B coefficients using a for loop
nfs = 1000;               % Number of fourier terms               
B = zeros(1,nfs);         % Initialise B vector   
lambda=zeros(1,nfs);      % Initialise lambda vector
for n = 1:nfs;           
    B(n)=(2*A)/(n*pi);                   % Calculate B coefficients
    lambda(n)=(n*pi*c)/L;
end


%% Solve for T using three for loops in time, space, and Fourier series

% Loop through time
for i = 1:nt               % For each time
    
    t = time(i);           % time in seconds
    
    % Vector of zeros to initialise the Fourier series solution.
    % This should be re-initialised at each new time step.
    T = zeros(1,nr); 
    
    % Loop through space
    for j = 1:nr;          % For each grid point        
        T(j) = (78*r(j))/L-41;         % Add the steady state solution
        
        % Loop through the Fourier series
        for n = 1:nfs;
            % Calculate series sum for T at r(j) and t
            p=(n*pi)/L;
            T(j)    = T(j)+(156/(n*pi))*sin(n*pi*r(j)/L)*exp(-1*p^2*c^2*t);              
        end
    end
    
   
end

aliveFlag= mean(T)>22;

end

[KSSV]

What input you have tried?

Answer 1

[KALYAN ACHARJYA]

I dont think there is any coding error. Please try in following way

function [T,aliveFlag] = heat_eqn(timeend,nt)
% Description: This file implements the Fourier Series solution to the heat equation.
% Input parameters:
% - timeend   - time of simulation in seconds
% - nt        - number of points in time vector
% Output parameters:
% - T         - temperature profile along persons head
% - aliveFlag - 1 if person is alive, 0 if the person is dead
L      = 0.12;                      % Size of the domain
rstart = 0;                         % Start of computational domain (m)
rend   = L;                         % End of computational domain (m)
nr     = 101;                       % Number of grid points along the radius vector
dr     = (rend-rstart)/(nr-1);      % Spatial step size, delta r (m)
r      = rstart:dr:rend;            % Vector of grid points in r
% Temporal (t) parameters 
timestart = 0;                      % Starting time (0 seconds)
dt        = (timeend-timestart)/(nr-1);  % Temporal step size, delta t (s)
time      = timestart:dt:timeend;        % Vector of times
% Phyiscal parameters
T1    = -41;                        % Temperature at r=0
T2    = 37;                         % Temperature at r=L
A     = T2-T1;                      % Amplitude of the saw tooth wave
k     = 0.527;                      % Thermal conductivity (W/m-K)
rho   = 1000;                       % Density (kg/m^3)
gamma = 3600;                       % Heat capacity (J/kg-K)
c     = sqrt(k/(rho*gamma));     % Heat equation constant   c^2=k/(rho*sigma)              
% Calculate B coefficients using a for loop
nfs = 1000;               % Number of fourier terms               
B = zeros(1,nfs);         % Initialise B vector   
lambda=zeros(1,nfs);      % Initialise lambda vector
for n = 1:nfs;           
    B(n)=(2*A)/(n*pi);                   % Calculate B coefficients
    lambda(n)=(n*pi*c)/L;
end
%% Solve for er series
% Loop thT using three for loops in time, space, and Fourirough time
for i = 1:nt               % For each time
    t = time(i);           % time in seconds
    % Vector of zeros to initialise the Fourier series solution.
    % This should be re-initialised at each new time step.
    T = zeros(1,nr);
    % Loop through space
    for j = 1:nr;          % For each grid point        
        T(j) = (78*r(j))/L-41;         % Add the steady state solution 
        % Loop through the Fourier series
        for n = 1:nfs;
            % Calculate series sum for T at r(j) and t
            p=(n*pi)/L;
            T(j)    = T(j)+(156/(n*pi))*sin(n*pi*r(j)/L)*exp(-1*p^2*c^2*t);              
        end
    end
end
aliveFlag=mean(T)>22;
end

Save the function as heat_eqn.m and call the function file in different script or from command window-

>>

[Temp_profile,Flag]=heat_eqn(10,5)
%............................^..^ choose the value as per your requirements 

Temp_profile =

Columns 1 through 13

-41.0000 36.9646 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 14 through 26

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 27 through 39

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 40 through 52

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 53 through 65

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 66 through 78

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 79 through 91

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Columns 92 through 101

37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000 37.0000

Flag =

1

From the last line of the code

aliveFlag=mean(T)>22;

AliveFlage is 1 if the Temp_profile mean is more than 22, which is seen from the Temp_profile vector, there from aliveFlag giving 1 as per description in your code.

[changsu namgung]

Thanks for your answer.

But i get this message below. (message in bold)

incorrectCheck the temperature vector with unknown time vector

Index exceeds the number of array elements (101).

Error in tutorial3 (line 42) t = time(i); % time in seconds Error in Test1

Could you help me with this as well?

[KALYAN ACHARJYA]

Can you show the pass values to the function heat_eqn(10,5)?

See my above example, its working.

[changsu namgung]

it's working on matlab 2015a that i have. but it keep saying that message on matlab grader which is a webpage for submitting homework.

[KALYAN ACHARJYA]

I have tried on 2015a, no issue. sorry I dont have any other version or Matlab grader .

[changsu namgung]

same...here. i guess nothing wrong with codes of course, and the matlab itself. But there is something that doesn't satisfy the program..thou. Anyway thanks for your efforts and help~