Hello, I have a code for determining a temperatur after a distance form a start temperature. In the code, there is a K value which is at 1. I want ti interpoliate T(z) of K.

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Ammar Anayi
Ammar Anayi on 14 Oct 2021
% Uppgift 2A.1
%a)
a = 0.01; b = 0.02; % enheten meter
Ti = 723; % Dirichlet, enheten K
Te = 293; % Neumann, enheten K
K = 315;
N = 400; % antal delintervall
h = (b-a)/N; % nätstorlek
r = a:h:b; % punkter xj, b+h är spökpunkt;
u_exact = 0; % exakt lösning
% Matrisen A
A = zeros(N+2,N+2); %inkludera rad för spökpunkten
for i = 2:N+1
A(i,i-1)=((1/h.^2)-1/(2.*h.*r(i)));
A(i,i) = -2/h.^2;
A(i,i+1)=((1/h.^2)+(1/(2.*h.*r(i))));
end
A(1,1) = 1; % För Dirichlet RV
A(N+2, N) = -1/(2*h);
A(N+2,N+1) = K;
A(N+2,N+2) = 1/(2*h);
f = [0]';
f(1) = Ti;
f(N+2)=K*Te;
ftrans = f';
T = A\ftrans;
plot( r(1:N+1) , T(1:N+1) ); %plotta inte spökpunkten!
z = find(r==0.02);
T(z)
%% b)
% K100 ska finnas för att yttertemp skall ej nå 100 grader celsius (373 K)
% u(0.02) ska vara en funktion av K, då K ändras kommer u(0.02) att ändras
% tills att vi når ett värde som är mindre än 373K.
K1 = 1;
K2 = 10;
K3 = 20;
K4 = 30;
T1 = 717.1204;
T2 = 670.6470;
T3 = 629.6585;
T4 = 596.6963;
T5 = 373;
KI = [K1 K2 K3 K4 ];
TI = [T1 T2 T3 T4 T5];
Points = [1 2 3 4 5];
I = interp1(KI,TI,Points, 'cubic')
% I calculated by hand and the interpoliation is not linear, så i try cubic but do not know. I want to
% find a K where the final temp och T(z) is less than 373 kelvin.

Answers (1)

Ashutosh Singh Baghel
Ashutosh Singh Baghel on 21 Oct 2021
Hi Ammar,
Please find proper values for 'query points' as defined by the variable "Points" here.
Also, provide a Value for variable "KI" as it should be of the same length as the variable "TI."
Below is an example of doing so.
%% b)
% K100 must be present so that the outside temperature does not reach 100 degrees Celsius (373 K)
% u (0.02) must be a function of K, then change K,
% u (0.02) change until we reach a value less than 373K
KI = [1 10 20 30 40];
TI = [717.1204 670.6470 629.6585 596.6963 373];
Points = [1:0.1:40];
I = interp1(KI,TI,Points,'spline');
plot(I)
Please refer to the MATLAB Documentation page on 'interp1'.

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