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.

% 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.

Answer 1

[Ashutosh Singh Baghel]

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'.