MATLAB: Need help with matlab code

radiative cooling curve (rcc)

Need to numerically solve the differential equation below and plot T vs t which goes like radiative cooling curve.

dT/dt= -Q(T^4-T0^4)/3*L*T where T =1000K, T0=300K, Q=1.38e-23 and L=1e-4 m.

Thank you in advance!

Best Answer

Tv=1000; % K
T0=300; % K 
Q=1.38e-23; 
L=1e-4; % m.
syms T(t)
DE = diff(T) == -Q*(Tv^4-T0^4)/3*L*T;
DEs = dsolve(DE, T(0)==T0)
figure
fplot(DEs, [0 1E+16])
grid
xlabel('$t$',  'Interpreter','latex')
ylabel('$T(t)$',  'Interpreter','latex')
title(['$T(t) = ' latex(DEs) '$'], 'Interpreter','latex')

Or, use ode45.

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MATLAB: How to insert an if conditional in ode45

Try this:

x0=-70;
t0=0;
dt=0.1;
tmax=20;
% tvec=t0:dt:tmax;
tvec = [t0 tmax];
opts = odeset('Events',@depolEvents);
for k = 1:10
    [t{k},x{k}]=ode45(@test_ode, tvec, x0, opts);
    x0 = -65;
    tvec = [t{k}(end) t{k}(end)+tmax]
%     tvec = t{k}(end) : dt : t{k}(end)+tmax;
end
tv = cat(1,t{:});
xv = cat(1,x{:});
figure
plot (tv,xv)
grid
function [dydt]=test_ode(t,y)
         dydt=-1/10*y+13;     
end  
function [position,isterminal,direction] = depolEvents(t,y)
    position = y(1) + 50; % The value that we want to be zero
    isterminal = 1;  % Halt integration 
    direction = 1;   % The zero can be approached from either direction
end

This uses the techniques in ODE Event Location to stop the integration that is restartted in the next increment of the loop.

If it does not do what you want as written (since I may not have understood exactly what you want to do), experiment with it to get the result you want.

MATLAB: Adding underscore in xlabel latex interpreter

Are you looking for something like this

xlabel('$L_{{(ex)}_L}$','fontweight','bold','FontSize',20,'Interpreter','latex');

Best Answer

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MATLAB: How to insert an if conditional in ode45

MATLAB: Adding underscore in xlabel latex interpreter

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