For Loop through Matrix

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

[Jan]

In your code t has 3 elements. Then the loop:

for i=1:length(t)    

runs for i=1, i=2, i=3. In all these cases, the first branch of the IF-condition is met:

   if i<=10*3600       

I assume, you want something else, maybe:

   if t(i) <= 36000      

I do not understand the actual problem - what does this mean: "I need to get Ts to change in matrix T".

[Brittany Burns]

Ts is a boundary condition that changes over time. I need it in order to solve for Ts in matrix T.

[Torsten]

@Brittany Burns

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 ?

[Brittany Burns]

I'm trying to solve for T' on the RHS

Answer 1

[Torsten]

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

[Brittany Burns]

Thanks!