# Plot of nested for loop for thickness variable

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Commented: G A on 1 Jul 2021
Hi MATLAB Community,
I am struggling to get my plot to include several different thicknesses in my plot. Any advice would be greatly appreciated. Like in the plot below, but with the thickness: 0.04 0.045 0.05 and one with 0.05 0.65 0.1 0.12.
clc
clearvars
close all
%--------------------------------------------------------------------------
k=55; %steel thermal conductivity (W/m/K)
dens=8000; %steel density (kg/m^3)
cp=500; % steel specific heat capacity (J/kg/K)
h_n=200;%Liquid Nitrogen convective heat transfer coefficient (W/m^2/K)
t_n=-150; %Nitrogen temperature (C)
t_a=20; % air temperature (C)
h_a=20; % not accurate (W/m^2/K)
t_i=t_a; % initial temperature (C)
t_target=-25; % (C)
%--------------------------------------------------------------------------
ck = 0;
b=.1; % full contact length
for thick=.04:.005:.05; %thickness
%--------------------------------------------------------------------------
del=.005;
dt=.4;
t_t=3000;
%--------------------------------------------------------------------------
results=[];
for len=.2:.2:2
l_LN=b/2;
l_a=(len-b)/2;
n1=round(l_LN/del+1);
n=round((l_LN+l_a)/del)+1;
m=round(thick/del)+1;
nt=round(t_t/dt)+1;
jb=sort([1,2:n1,n1+1:n-1,n,n+1:n:(m-2)*n+1,(m-1)*n+1,m*n,2*n:n:(m-1)*n,(m-1)*n+2:m*n-1]);
alfa=k/dens/cp;
t=alfa*dt/del^2;
%--------------------------------------------------------------------------
max_time_step=del^2/4/alfa/(1+h_n*del/k);
if dt>=max_time_step
disp(['Unstable! time step = ',num2str(dt), ' > max permissible time step =', num2str(max_time_step)])
return
end
t2t_target=t_t;
u=ones(nt,m*n)*t_i;
for i=1:nt-1
tinf=t_n;hlk=h_n*del/k;
u(i+1,1)=(1-4*t-2*t*hlk)*u(i,1)+2*t*(u(i,2)+u(i,n+1)+hlk*tinf);
for j=2:n1
u(i+1,j)=(1-4*t-2*t*hlk)*u(i,j)+t*(u(i,j-1)+u(i,j+1)+2*u(i,j+n)+2*hlk*tinf);
end
tinf=t_a;hlk=h_a*del/k;
for j=n1+1:n-1
u(i+1,j)=(1-4*t-2*t*hlk)*u(i,j)+t*(u(i,j-1)+u(i,j+1)+2*u(i,j+n)+2*hlk*tinf);
end
u(i+1,n)=(1-4*t-4*t*hlk)*u(i,n)+2*t*(u(i,n-1)+u(i,2*n)+2*hlk*tinf);
for j=n+1:n:(m-2)*n+1
u(i+1,j)=(1-4*t)*u(i,j)+t*(u(i,j-n)+2*u(i,j+1)+u(i,j+n));
end
j=(m-1)*n+1;
u(i+1,j)=(1-4*t-2*t*hlk)*u(i,j)+2*t*(u(i,j+1)+u(i,j-n)+hlk*tinf);
u(i+1,m*n)=(1-4*t-4*t*hlk)*u(i,m*n)+2*t*(u(i,m*n-1)+u(i,(m-1)*n)+2*hlk*tinf);
for j=2*n:n:(m-1)*n
u(i+1,j)=(1-4*t-2*t*hlk)*u(i,j)+t*(u(i,j-n)+u(i,j+n)+2*u(i,j-1)+2*hlk*tinf);
end
for j=(m-1)*n+2:m*n-1
u(i+1,j)=(1-4*t-2*t*hlk)*u(i,j)+t*(u(i,j-1)+u(i,j+1)+2*u(i,j-n)+2*hlk*tinf);
end
for j=1:m*n
if ~ismember(j,jb)
u(i+1,j)=(1-4*t)*u(i,j)+t*(u(i,j-1)+u(i,j+1)+u(i,j-n)+u(i,j+n));
end
end
if u(i+1,(m-1)*n+1)<=t_target
disp(['Time to reach @ T = ', num2str(t_target), ' C = ' num2str((i+1)*dt), 's'])
u(i+2:nt,:)=[];
break
end
end
results=[results;len,(i+1)*dt]
end
figure
plot(results(:,1),results(:,2))
hold on
plot(results(:,1),results(:,2))
title('Time to Reach vs. thickness')
ck = ck+1;
legend_string{ck} = ['b = ',num2str(b),' m; t = ',num2str(thick),' m' ];
legend(legend_string')
xlabel('b (m)')
ylabel('Time to T_{target} (s)')
grid minor
end
hold off

G A on 1 Jul 2021
Place figure(1) with a number before for-loop and use plot(results(:,1),results(:,2)) only once.
If you use figure() without any number, then three different figures will be created
figure(1)
clf
hold on
for thick=.04:.005:.05; %thickness
...
for len=.2:.2:2
...
end
plot(results(:,1),results(:,2))
title('Time to Reach vs. thickness')
...
end
hold off
G A on 1 Jul 2021
Happy to help!

R2020a

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