For Loop through Matrix
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Ts is changing over time. I need to get Ts to change in matrix T. How do I get it to change with each iteration within the matrix T?
clear all;clc
%Given
x=0:0.25:1; %thickness [m]
rho=2300; %density [kg/m^3]
k=1.4; %Thermal conductivity [W/mK]
c=880; %thermal coeff [J/kgK]
t=[2 11 45]*3600; %time [s]
%let
deltax=1/4;
deltat=1;
a=k/deltax;
b=(rho*deltax*c)/deltat;
%Initial conditions
Tx=300+400.*(x./2)-400*(x./2).^2;
%Solve for T'
for k=1:length(x)
for i=1:length(t)
if i<=10*3600
Ts=300+10/3600*i;
elseif i>10*3600 && i<=25*3600
Ts=400-5/3600*(i-10*3600);
else
Ts=325;
end
%Create matrices
A=1/b*[(-2*a+b) a 0 0;
a (-2*a+b) a 0;
0 a (-2*a+b) a;
0 0 a (-2*a+b)];
T=[Tx(1); Tx(2); Tx(3); Ts];
% Solve for B
B=A*T;
end
end
4 Comments
Torsten
on 2 May 2022
Your T vector has only 4 elements, but your x vector has 5.
Further, T is the vector of unknown - thus B = A*T does not make sense.
What is the differential equation together with the boundary conditions you are trying to solve ?
Accepted Answer
Torsten
on 2 May 2022
Edited: Torsten
on 3 May 2022
rho=2300; %density [kg/m^3]
k=1.4; %Thermal conductivity [W/mK]
c=880; %thermal coeff [J/kgK]
xstart = 0.0;
xend = 1.0;
nx = 100;
dx = (xend-xstart)/(nx-1);
x = xstart:dx:xend;
tstart = 0.0;
tend = 45*3600;
dt = 0.5*dx^2*rho*c/k;
nt = ceil((tend-tstart)/dt);
t = linspace(tstart,tend,nt);
T0 = Tinit(x);
T = zeros(nt,nx);
T(1,:) = T0;
for j = 1:nt-1
Ts = Texternal(t(j+1)/3600);
T(j+1,1) = Ts;
T(j+1,2:nx-1) = T(j,2:nx-1) + dt*k/(rho*c)*(T(j,3:nx)-2*T(j,2:nx-1)+T(j,1:nx-2))/dx^2;
Tnxp1 = T(j,nx-1);
T(j+1,nx) = T(j,nx) + dt*k/(rho*c)*(T(j,nx-1)-2*T(j,nx)+Tnxp1)/dx^2;
end
to = [2 11 45]*3600;
it = arrayfun(@(tout)find(t-tout>=0,1,'first'),to);
plot(x,[T(it(1),:);T(it(2),:);T(it(3),:)])
function Ts = Texternal(t)
if t <= 10
Ts = 300 + 10*t;
elseif t > 10 && t <= 25
Ts = 400 - 5*(t-10);
else
Ts = 325;
end
end
function T0 = Tinit(x)
T0 = 300 + 400.*(x./2) - 400*(x./2).^2;
end
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