having trouble with ode45

I have a 2nd order diff eq that I am solving using using the shooting method. When I run the code I get the error Error using pin_fin>nest Too many input arguments. I have no idea why I am getting this error so any help would be greatly appreciated. Thanks.

code
function BC_at_L = pin_fin(T0)
  L = 0.1;    %length of the pin in meters
  R = 0.005;  %radius of the pin in meters
  k = 250;    %thermal conductivity of the pin with units of Watts per 
              %meter per Kelvin (W/(m*K))
  epsilon = 1;    %emissivity 
  sigma = 5.67 * 10^-8;   %Stefan-Boltzmann constant with units of Watts
                          %per meter squared per Kelvin to the fourth
                          %power (W/(m^2*K^4))
  Qdot = 25;  %rate of heat dissipation with units of Watts
  A = pi*R^2;     %cross sectional area of the pin with units of meters
                  %squared
  Qb = Qdot/A;  %heat flux at the base of the pin
  U0 = -Qb/k;
  [dTdx] = nest;
  BC_at_L = ode45(@nest,[0 L], [T0 U0]);
  function [dTdx] = nest
      dTdx = zeros(2,1);
      dTdx(1) = (2/(k*R))*epsilon*sigma*(T0^4);
      dTdx(2) = U0;
  end
end

Answer 1

[Star Strider]

Your ODE function ‘nest’ has to take at least two input arguments where the first is the independent variable and the second is the variable of integration. Your ‘nest’ function takes no input arguments, and that is throwing the error. See the ode45 documentation Examples section for details. (I don’t understand your ‘nest’ function, so I can’t offer any specific solutions.)

[Kelly Grissom]

The 'nest' function is a nested function inside the function pin_fin. I thought that a nested function should be able to use the variables already established in the main function (pin_fin). However, I did add the variables T0 and U0 to lines 11 and 13 and now I am getting a different error message. It says: In an assignment A(I) = B, the number of elements in B and I must be the same. I ran through the code using the debugger and once it goes into 'nest' for some reason it assigns T0 a value of 0 and U0 the values of T0 and U0 so indeed they are not the same size. I don't know why all of a sudden U0 has taken on both the value of itself and T0 and T0 now has a value of 0.

[Star Strider]

You are passing ‘nest’ to ode45, so it has to correspond to what the ODE solvers require. It has to have the inputs I described. I don’t know what the variable-of-integration is in ‘nest’, or what differential equation it represents, so unfortunately I can’t help you get it to work.

[Kelly Grissom]

I am still getting an error message, but I do understand what was going wrong initially thanks to your answer so you did answer that question.

[Star Strider]

My pleasure.

What error are you getting? What ODE does ‘nest’ represent? If I understand what you’re doing (at least to some extent), we can probably get your code to work.