Newton's Law of Cooling Euler's method, don't understand how it works in matlab

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Anastasia Zistatsis 2021-1-17

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评论： Anastasia Zistatsis 2021-1-17

Hello!

My professor has only given one example on Euler's method, so I'm really working from scratch here and would like guidance on starting Euler's method for this problem:

I apologize for asking a question with none of my own coding given. A starter or pseudocode for the Euler's would be immensely helpful!

You are working as a crime scene investigator and must predict the temperature of a homicide victim over a 5 hour period . You know that the room where the victim was found was at 10 ∘ C when the body was discovered.

Use Newton's law of cooling and Euler's method to compute the victim's body temperature for the 5 hour period using values of k = 0.12/hr and Δ t = 0.5 h r. Assume that the victim's body temperature at the time of death was 37 ∘ C , and that the room temperature was at a constant value of 10 ∘ C over the 5 hour period.

dT/dt = -k(T-T_a)

Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature)

This is what I have so far:

for i=1:12

T(i+1,2)= T(i,2)+0.5*k*(T(i+1,1)-T_f);

end

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Answer 1

KALYAN ACHARJYA 2021-1-17

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https://ww2.mathworks.cn/matlabcentral/answers/718995-newton-s-law-of-cooling-euler-s-method-don-t-understand-how-it-works-in-matlab#answer_599685

在 MATLAB Online 中打开

As you have tried, so sufficient Hint here

dt=0.5;
T_amb=10;
t=0:dt:5; % Check
T=zeros(1,length(t));
T(1)=37;
k=0.12;
for i=1:length(t)-1
    dTdt=-k*(T(i)-T_amb);
    T(i+1)= T(i)+0.5*dTdt;
end 
plot(t,T);
grid on;