Need help with matlab code
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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!
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Star Strider
2021-2-2
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')
6 个评论
Emma K.
2021-2-2
Walter Roberson
2021-2-2
If T0 and Tv are the same then Tv^4 - T0^4 would be 0, and the right hand side of the differential equation would be 0, which implies a linear equation.
Emma K.
2021-2-2
Star Strider
2021-2-2
‘... T and Tv are the same ...’
Not really. Here, ‘T’ is the function and ‘Tv’ is one value (as is ‘T0’).
When plotted, it appears linear over relatively short intervals for ‘t’, while over longer intervals (such as I use here, and the answer to your other question about it), it has the expected exponential decay.
To do a true numerical integration, you will likely want to use ode45. This code demonstrates a symbolic integration, and what the correct plot looks like.
Emma K.
2021-2-4
Star Strider
2021-2-4
My pleasure!
If my Answer helped you solve your problem, please Accept it!
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