Help with double for loop

Hi y'all

I have a problem in which I must use a double for loop for this equation:

roCpdT/dt=-vxroCpdT/dx-UA(T-Tv)

It's for a heat exchanger where :

• ro density of water
• Cp Heat capacity of water
• dT/dt Change of temperature as a function of time
• vx Flux velocity inside the inner tube of the heat exchanger
• dT/dx Change of temperature as a function of space
• U Global heat transfer coefficient
• A Trasnfer area
• T Temperature of a certain point in space at a certain time
• Tv Steam temperature

So, I must use a double ¨for¨ loop to graph the function between x = [0 40] meters and within a time of t = [0 : 100 : 2000] seconds. Please, How can I do it using the Euler method, and also, how can I plot the results (Preferebly 1 curve per time interval)? Thanks!

[darova]

Do you have a difference scheme?

[José Salazar]

Something like it:

dT/dx = (T(j+1) - T(j)) / deltax

dT/dt = (T(i+1) - T(i)) / deltat

and the third equation in which is combined both time and space variations of temperature. The variable that I need to find (solve for) it's T(i+1)(j+1). Please help me

Answer 1

[darova]

I'll give you a start

T= zeros(m,n);  % preallocation
T(1,:) = % initial condition
for i = 1:m-1
    for j = 1:n-1
        T(i+1,j+1) = T(i,j+1) + dt/dx*Vx*(T(i,j+1)-T(i,j)) - UA*(T(i,j+1)-Tv)
    end
end

note: dt/dx part should be small

[José Salazar]

Hi! I tried that but got some values with no logic at all. My temperature shouldn't be smaller than 25°C or above 100°C and yet I still got values outside of those limits. Can you please help me? Also I tried to plot the results because I want a curve for each time interval, but couldn't do it. Please hel me. This is what I got:

clc; clear; close all 
m = 1000; %Time domain
n = 40; %Lenght of HEX domain
T = zeros(m,n);
U = 3400;
Di = 0.03; %Diameter of tube
De = 0.065; %Diameter of shell
L = 40; %Max lenght of HEX
vz = 2; %Velocity of water in inner tube
Tv = 100; %Steam temperature
T(1,:) = 25; %Prealocación
Ts = 100; %Temperature of water leaving HEX
Tset = 100; %Set temperature
d = 977.5; %Density of water
Cp = 4181; %Cp of water
At = pi*Di*L; %Sectional area
deltat = 100; %segundos
deltaz = 1; %metros
t(1) = 0;
z(1) = 0;
for i = 1 : m-1
    for j = 1 : n-1
        T(i+1,j+1) = T(i,j+1) + ((vz * (T(i,j+1)-T(i,j))/deltaz)-((U*At)/(d*Cp))*(T(i,j+1)-Tv))*deltat;
        z(i+1) = z(i) + deltaz;
        t(i+1) = t(i) + deltat;
    end
end