Why does "Temperature" rises instantly in this solution with ode45? Also, I could not figure out why integration time interval "t_interval" gives no solution i started at "0"?

Question

Talha 2023-2-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1912760-why-does-temperature-rises-instantly-in-this-solution-with-ode45-also-i-could-not-figure-out-why

回答： Oguz Kaan Hancioglu 2023-2-15

采纳的回答： Oguz Kaan Hancioglu

XSteam.m

在 MATLAB Online 中打开

%% Clean the Workspace

clc

clear all

%% Variables

global mS Ts_in

Vceo = 102.687; % m3

Ts_in = 104.8; % C, inlet steam temp

mS = 85.3; % kg/sec

T0 = 57.2; % Initial temp

t_interval = [0.01 10]; % Time interval

IC = T0; % Initial Condition

%% Solve the DE

[t,Tsol] = ode45(@(t,T) cfunc(t,T) , t_interval , IC);

%% From Tsat to Psat

for i=1:size(Tsol)

Psol(i) = XSteam('psat_T',Tsol(i));

i = i + 1;

end

%% Plotting

figure;

subplot(1,2,1)

plot(t,Tsol)

xlabel('Time (s)')

ylabel('Temperature (C)')

subplot(1,2,2)

plot(t,Psol)

xlabel('Time (s)')

ylabel('Pressure (bar)')

function dTdt = cfunc(t,T)

global mS Ts_in

A = 3300; % m2, heat transfer area

U = 9.9616; % kW/m2.K, heat transfer coefficient

T_hi = 104.8;

T_ho = T;

T_ci = 52.2;

T_co = 97.8;

LMTD = (abs(T_hi-T_co)-abs(T_ho-T_ci))/(log(abs(T_hi-T_co)/abs(T_ho-T_ci)));

Q = LMTD*U*A;

deltaHcond = (XSteam('hL_T',T) - XSteam('hV_T',T));

cvS = XSteam('CvV_T',T);

cpW = XSteam('CpL_T',T);

mCond = abs(Q/deltaHcond);

dTdt = ((Ts_in*XSteam('CpV_T',Ts_in)*mS-mCond*deltaHcond-mCond*T*cpW) / (cvS*(abs(mS-mCond))) - T)/t ;

end

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Answer 1

Oguz Kaan Hancioglu 2023-2-15

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1912760-why-does-temperature-rises-instantly-in-this-solution-with-ode45-also-i-could-not-figure-out-why#answer_1171935

If you change the format to long you can see that t and Tsol values change. The differential equation settles the last value in 0.001 seconds. The ode45 function seems working correctly. However, if you think the output of the ode45 is not correct, you can check your dTdt = cfunc(t,T) function.

t_interval is the time step of the ode45. Since it solves differential equations, the interval should be bigger than 0. In your function, you are dividing your calculation by t_interval. When you entered 0 time interval the output of the Tsol equals NaN. That's why you see an empty plot.