# using ode45 to solve 3 ODEs with solar radiation

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Hasan Abbas on 23 Dec 2020
Commented: Jan on 27 Dec 2020
I am trying to solve 3 ODEs by using ode45. i dont know if im doing this right or not, I appreciate any small help.
my main problem is how to include the transient effect of solar radiation. I tried to solve it with constant solar radiation and it worked fine.
this is my code and when i run it i get this error.
Error using odearguments (line 95)
SOL returns a vector of length 17, but the length of initial conditions vector is 3. The vector returned by SOL and
the initial conditions vector must have the same number of elements.
Error in ode45 (line 115)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in test (line 51)
t1=8; %start time
t2=15; %end time
tspan=[0,(t2-t1)*3600];
IC=[38,40,37]; %initial temperatures
[time,temp]=ode45(@sol,tspan,IC);
function tdot =sol(t,T)
t1=8;
t2=15;
vol=4;
mair=vol*1.225;
cp=1005;
Qh=0;%220;
Tac=15;
mac=0.09;
Uinwall=4;
Uoutwall=4.5;
Uinmass=12;
Amass=3;
Tamb=45;
cpwall=600;
cpmass=1450;
mwall=900;
mmass=50;
emiss=0.9;
Tsky=22.6;
abswall=0.19;
absmass=1;
trans=0.8;
A=[2.479,0 %roof
0.864,0.864 %windsheild
0.787,0.787 %rear window
1.533+0.224+0.266,0.224+0.266 %right side
1.533+0.224+0.266,0.224+0.266]; %left side
Aw=A(:,1); %area of walls
Ag=A(:,2); % area of glass
Awall=sum(Aw,'all');
AHwall=Aw(1,:);
lat=33.3152; %latitude
long=44.3661; % longitude
gmt=3;
mint=0;
tiltang_w=[0 % tilt angle of the walls
60
45
90
90];
zs_w=[0 % zenith angle of the walls
0
180
90
270];
tiltang_g=[60 % tilt angle of the glass
45
90
90];
zs_g=[0 % zenith angle of the glass
180
90
270];
costhetaz=[]; % cosine of the zenith angle
costheta_w=[]; %incident angle of solar radiation on the walls
costheta_g=[]; %incident angle of solar radiation on the glass
for hour=t1:1:t2
lot=hour+mint/60;%local time of the city
dn=190; % day of the year
a=1160+75*sind((dn-275)*360/365); %constants of the equation
b=0.174+0.035*sind((dn-100)*360/365); %constants of the equation
c=0.095+0.04*sind((dn-100*360/365)); %constants of the equation
delta=23.45*sind((dn+284)*360/365); % Declination angle
bn=(dn-1)*360/365;
eot=2.2918*(0.0075+0.1686*cosd(bn)-...
3.2077*sind(bn)-1.4615*cosd(2*bn)-...
4.089*sind(2*bn)); % equation of time
lst=15*gmt; % local standard time
st=(lot+(eot/60)+(long-lst)/15); % solar time
omega=15*(12-st); % hour angle
costhetaz_i=cosd(delta).*cosd(lat).*cosd(omega)+...
sind(delta).*sind(lat); % cosine of the zenith angle
costheta_wi=sind(delta).*sind(lat).*cosd(tiltang_w)-...
sind(delta).*cosd(lat).*sind(tiltang_w).*cosd(zs_w)+...
cosd(delta).*cosd(lat).*cosd(tiltang_w).*cosd(omega)+...
cosd(delta).*sind(lat).*sind(tiltang_w).*cosd(zs_w).*cosd(omega)+...
cosd(delta).*sind(tiltang_w).*sind(zs_w).*sind(omega); %incident angle of solar radiation on the walls
costheta_gi=sind(delta).*sind(lat).*cosd(tiltang_g)-...
sind(delta).*cosd(lat).*sind(tiltang_g).*cosd(zs_g)+...
cosd(delta).*cosd(lat).*cosd(tiltang_g).*cosd(omega)+...
cosd(delta).*sind(lat).*sind(tiltang_g).*cosd(zs_g).*cosd(omega)+...
cosd(delta).*sind(tiltang_g).*sind(zs_g).*sind(omega);%incident angle of solar radiation on the glass
costhetaz=[costhetaz;costhetaz_i];
costheta_w=[costheta_w;costheta_wi];
costheta_g=[costheta_g;costheta_gi];
end
minLength = min(length(costhetaz), length(costheta_w)); % i wrote this line becasue i didnt get the same number of values for costheatz,costheta_w and costheta_g
costhetaz = costhetaz(1:minLength);
costheta_w = costheta_w(1:minLength);
costheta_g = costheta_g(1:minLength);
[idir]=a.*exp(-b./costhetaz); % direct solar radiation
costheta_w(costheta_w<0)=0; % this line to neglect the negative values of costheta_w and costheta_g
costheta_g(costheta_g<0)=0;
rad_w=idir.*costheta_w; % solar radiation on the walls
rad_g=idir.*costheta_g; % solar radiation on the glass
for i=1:1:5
end
for i=1:1:5
end
Q_ac=0;%(mac*cp*(Tac-T(1)));
Qin_w=(Uinwall*Awall*(T(1)-T(2)));
Qin_m=(Uinmass*Amass*(T(1)-T(3)));
Qout_w=(Uoutwall*Awall*(Tamb-T(2)));
tdot=[(Qh+Q_ac-Qin_w-Qin_m)/(mair*cp)
end
Jan on 27 Dec 2020
I do not have information about the purpose of your code. Therefore I cannot estimate, if the code is working as wanted or not. At least the variables Tac and mac are not used anywhere.
The expression "(T(3)+273)^4" seems to be very sensitive. What about using more digits like 273.15?
Qabssolar = interp1(Qabs_t, Qabssolar, t);
Qtranssolar = interp1(Qtrans_t, Qtranssolar, t);
Linear interpolations are not smooth. The stepsize control of ODE45 requires a smooth function. This can cause serious troubles, e.g. results, which are dominated by rounding errors. A stopping integration is possble also. Running a numerical integrator with not matching inputs is not a reliable method from a scientific point of view. If this is a part of a PhD thesis, I would reject it, if I am your professor.
The code does not allow to check the stability of the solution by varying the initial conditions and parameters. Did you validate the applied model?

Mischa Kim on 24 Dec 2020
Hi Hasan,
based on the error message I suggest looking into tdot at the bottom of your ode function. Apparently, this is a 17x1 vector and by browsing through your code it seems that Qabssolar and Qtranssolar are also vectors, not scalars.
I suggest you set a breakpoint next to the last end command in your code above and run the code. The execution of the code will halt when the breakpoint is reached and you can hover over the variables to see value and size. Once you have confirmed that Qabssolar and Qtranssolar are indeed the cause of the issue you can work your way back up and isolate the source of the problem.
##### 1 CommentShowHide None
Hasan Abbas on 24 Dec 2020
Edited: Hasan Abbas on 24 Dec 2020
Thanks for your answer, i checked it and it is indeed a vector. but i have another problem, i will appreciateit if you can help me. I want the values of rad_w and rad_g to change by taking values from t1 to t2 and i want the ode45 to evaluate the 'sol' function at each time span corresponding to that time. so i have time span from t1 to t2 and i have for loop from t1 to t2.
Also, in that for loop i get vector of 8*1 for costhetaz but i get a vector of 40*1 for costheta_w and a vector of 32*1 for costheta_g because i have vectors of 5*1 for the walls and 4*1 for the glass, how can i make it all simultaneous so at each time span it take 1 value of costheaz and 5 values of costheta_w and 4 values of costheat_g?
if i have done this wrong, please explain it to me
thanks again

R2020b

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