How can I find the last alpha_k value?

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Aryo Aryanapour
Aryo Aryanapour on 27 Jan 2022
Commented: Jon on 28 Jan 2022
function main % Hauptfunktion
x0 = 200; % Startwert für die erste Iteration. Ermittelt anhand des Plots der Funktion
eps = 0.4; % Emissionsverhältnis
c_s = 5.67*10^(-8); % Strahlungskonstante
c12 = eps * c_s; %
alpha_k = 4; % Wärmeübergangskoeffizient bei ruhender Luft
s1 = 0.250; % Wanddicke der feruerfesten Stein
s2 = 0.015; % Wandddicke der äußeren Stahlwand
lamda1 = 0.35; % Wärmeleitfähigkeit der feuerfesten Stein
lamda2 = 22.7; % Wärmeleitfähigkeit der Stahlwand
Tw_1 = 1200; % Wandtemperatur der feuerfesten Stein
T_l = 10; % temperatur der Umgebungsluft
Pr = 0.7095;
lambda_L = 25.12;
betha = 3.543*10^(-3);
v = 144.0*10^(-7);
L = 7;
B = 15;
A = B * L;
g = 9.81;
Ra = @(x)Pr*(g*L^3*betha*(x-T_l))/v^2;
q1=0.825;
q2=0.387/((1+((0.492/Pr)^9/16))^(8/27));
q3=lambda_L/L;
alpha_k=@(x) ((q1+q2*(Ra(x)^(1/6)))^2)*q3;
%alpha_k = @(x)((0.825+(0.387*Ra(x)^1/6)/(1+(0.492/Pr)^9/16)^8/27)^2)*lambda_L/L;
func = @(x) eps * c_s * x^4 + (alpha_k(x) + 1/(s1/lamda1+s2/lamda2)) * x - ((1/(s1/lamda1+s2/lamda2)) * Tw_1 + alpha_k(x) * T_l); % Die Funktion
difft = @(x) (1713652349303737*x^3)/18889465931478580854784 - (138885763149071439966638298011785481*((6966792533989255*((2726811173664208678832570368*x)/66848762121410525 - 5453622347328417357665140736/13369752424282105)^(1/6))/18014398509481984 + 33/40))/(736008079697311707955200*((2726811173664208678832570368*x)/66848762121410525 - 5453622347328417357665140736/13369752424282105)^(5/6)) + (628*((6966792533989255*((2726811173664208678832570368*x)/66848762121410525 - 5453622347328417357665140736/13369752424282105)^(1/6))/18014398509481984 + 33/40)^2)/175 + (138885763149071439966638298011785481*x*((6966792533989255*((2726811173664208678832570368*x)/66848762121410525 - 5453622347328417357665140736/13369752424282105)^(1/6))/18014398509481984 + 33/40))/(7360080796973117079552000*((2726811173664208678832570368*x)/66848762121410525 - 5453622347328417357665140736/13369752424282105)^(5/6)) + 31780/22721;
xsol = newton_raphson(func, difft, x0)
wl = (1/(s1/lamda1+s2/lamda2))*(Tw_1-xsol) % Wärmestrom für Wärmeleitung
wsk = alpha_k(xsol) * (xsol-T_l) + (eps*c_s*xsol^4) % Wärmestrom für Konvektion + Strahlung
end
function xsol = newton_raphson(func, difft, x0)
x(1) = x0;
maxiter = 500; % maximale Anzahl an Iterationen
Abbr = 10^(-5); % Abbruchkriterium
eps = 0.4; % Emissionsverhältnis
c_s = 5.67*10^(-8); % Strahlungskonstante
c12 = eps * c_s; %
alpha_k = 4; % Wärmeübergangskoeffizient bei ruhender Luft
s1 = 0.250; % Wanddicke der feruerfesten Stein
s2 = 0.015; % Wandddicke der äußeren Stahlwand
lamda1 = 0.35; % Wärmeleitfähigkeit der feuerfesten Stein
lamda2 = 22.7; % Wärmeleitfähigkeit der Stahlwand
Tw_1 = 1200; % Wandtemperatur der feuerfesten Stein
T_l = 10; % temperatur der Umgebungsluft
H = 7; % Höhe
B = 15; % Breite
A = B * H; % Fläche
for i = 1:maxiter
if difft(x(i)) < Abbr % Ünerprüfung, ob die Ableitung von x Null ergibt. Falsches Startwert gewählt. Dadurch ergibt sich eine horizontale Tangente, welche die X-Achse nicht schneidet.Es kann keine weitere Nährungswert für die Nullstelle ausgeliefert weden.
fprintf('Die Ableitung von x ist Null, ein anderes Startwert wählen\n');
return;
end
x(i+1) = x(i) - func(x(i))/difft(x(i)); % Berechung mithilfe von Newton Verfahren (Hier befindet sich die Formel der Newton Verfahren)
abs_error(i+1) = abs((x(i+1)-x(i))/x(i+1))*100;
if abs(x(i+1) - x(i)) < Abbr
fprintf('Das Verfahren hat konvergiert bei x = %.10f\n', x(i+1));
else
fprintf('Iteration Nr: %d, aktuelle Schätzwert x = %.10f, error = %.5f, ', i, x(i+1), abs_error(i+1));
end
end
xsol = x(end); % Oberflächentemperatur der Außenwand
alpha_k; % therefore I get the value 4. But the alpha k value changes after the iteration and is calculated depending on x. I need this value
alpha_k = alpha_k(xsol); % I need this value
alpha_ges = alpha_k + eps *c_s*(xsol^4-(T_l+273.15)^4)/(xsol-(T_l+273.15)) % Wärmeübergangskoeffizient-Gesamt
Q_ges = (1/((s1/lamda1+s2/lamda2)+1/alpha_ges))*A*(Tw_1-T_l) % Wärmestrom-Gesamt
end
Array indices must be positive integers or logical values.
Error in Copy_of_ruhender_Luft_rev1>newton_raphson (line 75)
alpha_k = alpha_k(xsol);
Error in Copy_of_ruhender_Luft_rev1 (line 32)
xsol = newton_raphson(func, difft, x0)
1) Can someone please help me to see the last value for alpha k (xsol) ? I need the alpha value calculated depending on x.
2) I would also like to put this code in a live script. Unfortunately it does not work. I want to keep the code but change some parameters and then put both codes (original and parameter modified ) in one script. can someone please tell me how to do this? Thanks in advance
  5 Comments
Aryo Aryanapour
Aryo Aryanapour on 27 Jan 2022
Thank you so much Torsten. That's correct. The alpha_K = 4 was not used anywhere. This confused me a bit and I think this main function bothers me to run this code as a live script.

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Accepted Answer

Jon
Jon on 27 Jan 2022
I was just going through your code and made a corrected version. I see now that Torsten has also given you a comment that echos what I have put in the attached file.
Your main problem is that you are reusing the same name alpha_k for a variable, which you assign the value of 4, and also as a function handle. I didn't actually see any place that you used the value of 4 assigned to alpha_k as a variable so I just commented that out.
I also added alpha_k as an argument to your function newton_raphson so that it would know what the definition of this function was.
Finally as I had told you in your earlier post on this same topic https://www.mathworks.com/matlabcentral/answers/1630740-why-doesn-t-newton-s-method-calculate-the-correct-temperature?s_tid=srchtitle you don't need to have the function main surrounding the start of the script. So I removed that. That might have been related to why this wasn't running as a live script. Since you defined the function main, you have to have a script or command line that calls main. You can't run a function with the run command. Anyhow I just copied and pasted my modified script into the live editor and it now runs fine. Also attached.
  6 Comments
Jon
Jon on 28 Jan 2022
Just don't use omicron :)

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More Answers (1)

Benjamin Thompson
Benjamin Thompson on 27 Jan 2022
See the article "Anonymous Functions" in the MATLAB help. You must pass all parameters to the anonymous function as inputs, so maybe
Ra = @(x,Pr,g,L,betha,T_1,v) Pr*(g*L^3*betha*(x-T_l))/v^2;
Unless you want to declare all the parameters as globals.
Also, do not overwrite your function handle for alpha_k. Try:
alpha_k_output = alpha_k(xsol);
alpha_k will also need all those parameters that Ra needs unless you want them to be global. Try a smaller example to debug how you are using alpha_k and Ra first before trying to use them in the newton_raphson local function.
  1 Comment
Aryo Aryanapour
Aryo Aryanapour on 27 Jan 2022
Mr Thompson,
Many thanks for your help.

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