Outputting arrays from function in for loop

Hello, I am not really sure the best way to describe this problem... Essentially what I want to do is solve a function that outputs an array, while in a for loop. If you look at the code, lines 45 through 48 are the parts in question. Rather than solving dT three separate times, I would like to solve it within a for loop that will output something like T(i), then call an entire column and plot it.

clc;
clear all;
close all;

%%Solution Outline
%%Assumptions
%%Paranmeters
% nio for niobium

nio.d    = 0.01;             % [m]          Diameter of the sphere
nio.Ti   = 900 + 273;        % [K]          Initial Temperature
nio.Tf   = 300 + 273;        % [K]          Final Temperature
nio.rho  = 8600;             % [kg/m^3]     Density
nio.c    = 290;              % [J/kg K]     Specific Heat
nio.k    = 63;               % [W/m K]      Thermal Conductivity
nio.Tinf = 25 + 273;         % [K]          Assumed Room Temperature 

nio.A    = 4*pi*(nio.d/2)^2; % [m^2]        Surface Area of the Sphere
nio.V    = 4/3*pi*(nio.d/2)^3;%[m^3]        Volume of Sphere
nio.eps  = 0.6;              %              Emissivity

h   = [10,200,500];     % [W/m^2 K]    Convection Coefficient 

sigma     = 5.67e-8;       % Stefan Boltzmann constant

%%Calculations

% The first step is to create a plot with the various h values
% How can I do the following in a for loop?
[t1,T1] = dT(nio,h(1)); 
[t2,T2] = dT(nio,h(2));
[t3,T3] = dT(nio,h(3));

plot(t1,T1,t2,T2,t3,T3);

%%Sub Function

function [t,T] = dT (nio,h)
dT = @(t,T) ( -h*nio.A*(T-nio.Tinf) - nio.A*sigma*nio.eps*(T^4 - ...
     nio.Tinf^4)) / (nio.rho*nio.V*nio.c);
[t,T] = ode45 (dT, [0,60] , [nio.Ti]);
end
end

Answer 1

[OCDER]

Going to use nio.sigma instead of sigma, since sigma is a matlab function and NOT a constant that you want in your function dT.

nio.sigma     = 5.67e-8;     % Stefan Boltzmann constant

To fix the plotting, do something like this:

Data = cell(2, 3); %row1 = t1,t2,t3, row2 = T1,T2,T3
for j = 1:3
    [Data{1, j}, Data{2, j}] = dT(nio,h(j));
end
plot(Data{:})

Found some issues with your function, see comments. Make sure this is the same equation though!

function [t,T] = dT(nio,h)

%RECHECK CHANGES to make they are the same eqn!
%dT = @(t,T) ( -h*nio.A*(T-nio.Tinf) - nio.A*sigma*nio.eps*(T^4 - nio.Tinf^4)) / (nio.rho*nio.V*nio.c);
%- dont' name dT function handle same as your dT function name. It gets confusing.
%  > using aT instead
%- sigma is matlab function, so you can't use that as a variable.
%  > using nio.sigma instead

aT = @(t,T) ( -h*nio.A.*(T-nio.Tinf) - nio.A*nio.sigma*nio.eps*(T.^4 - nio.Tinf^4)) / (nio.rho*nio.V*nio.c);
[t, T] = ode45(aT, [0,60] , [nio.Ti]);

[Michael Ennis]

Thank you!