Please help me to connect between three points with plot (draw line)

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I want to connect the three points (draw line) shown in the picture in the plot command.

 
function sol= proj
clc;clf;clear;
global lamda
%Relation of base fluid
rhof=1;
kf=0.613*10^5;
cpf=4179*10^4;
muf=10^-3*10;
sigf=0.05*10^-8;
alfaf=kf/(rhof*cpf);
%FE3O4
ph1=0.01;
rho1=5180*10^-3;
cp1=670*10^4;
k1=9.7*10^5;
sig1=0.74*10^-2;
%copper
ph2=0.01;
rho2=8933*10^-3;
cp2=385*10^4;
k2=401*10^5;
sig2=5.96*10^-1;
%Relation of hyprid
m=5.7;
kh=kf*((k1+(m-1)*kf-(m-1)*ph1*(kf-k1))/((k1+(m-1)*kf+ph1*(kf-k1))))*((k2+(m-1)*kf-(m-1)*ph2*(kf-k2))/((k2+(m-1)*kf+ph2*(kf-k2))));
muh= muf/((1-ph1)^2.5*(1-ph2)^2.5);
rhoh=rhof*(1-ph2)*((1-ph1)+ph1*(rho1/rhof))+ph2*rho2;
v1 =rhof*cpf*(1-ph2)*((1-ph1)+ph1*((rho1*cp1)/(rho2*cp2)))+ph2*(rho2*cp2);
sigh=sigf+(3*((ph1*sig1+ph2*sig2)-sigf*(ph1+ph2))/(((ph1*sig1+ph2*sig2)/(sigf*(ph1+ph2)))+2-((ph1*sig1+ph2*sig2)/sigf)+(ph1+ph2)));
alfah=kh/v1;
myLegend1 = {};
rr = [0.2 0.3 0.4];
for i =1:numel(rr)
    Nt = rr(i);s2=1;
     qq=[13 14 15];
     Prf=qq(i);
    an=0.1;Lb=1;Pe=0.1;
        p=-0.5;q=-0.5;M=1; L=(muf/rhof);L1=L^(p);L1=L^(p);
    delta=s2/(L1);
Nb=1; Nr=1;sc=0.45;gamma=pi/3;
a=25;b=0.1;v=1;u=1;
  s1=1;s2=1;
  s3=sqrt(a/(muf/rhof));
   Tw=273+50;Ti=273+27;deltaT=Tw-Ti;
   Lf=rhof*kf;
   y0 = [1,0,1,0,0,1,0,1,0,1,0];
options =bvpset('stats','on','RelTol',1e-4);
    m = linspace(0,1.5);
   solinit = bvpinit(m,y0);
      sol= bvp4c(@projfun,@projbc,solinit,options);
      figure(1)
    plot(qq(i),-(sol.y(11,1)),'s')
    grid on,hold on
    myLegend1{i}=['Nt = ',num2str(rr(i))];
    grid on,hold on
    i=i+1;
end
figure(1)
legend(myLegend1)
hold on
    function dy= projfun(~,y)
        dy= zeros(11,1);
%         alignComments
        E  = y(1);
        dE = y(2);
        F  = y(3);
        dF= y(4);
        W = y(5);
        t = y(6);
        dt  = y(7);
        phi = y(8);
        dphi  = y(9);
         z=y(10);
         dz=y(11);
    dy(1) = dE;        
          dy(2) = (rhoh/muh)*((((a*u)/L1^(2)))*E^2+(1/L1)*W*dE+((sigh/sigf)/(rhoh/rhof))*(1/L1^2)*M*E*sin(gamma)*sin(gamma));
         dy(3) = dF;
          dy(4) = (rhoh/muh)*((((b*v)/L1^(2)))*F^2+(1/L1)*W*dF+((sigh/sigf)/(rhoh/rhof))*(1/L1^2)*M*F*sin(gamma)*sin(gamma));
         dy(5) = -(1/L1)*(u*a*E+b*v*F);
        dy(6) = dt;
dy(7) =(Prf*(rhof/muf))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2);
        dy(8)= dphi;
dy(9)=(sc/L^(p+1))*W*dphi-(s1/s2)*(Nt/Nb)*(((Prf*(rhof/muf)))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2));
    dy(10)=dz;
    dy(11)=(Lb/((muf/rhof)*L1))*W*dz+Pe*delta*dz*dphi+(Pe*delta*z+((Pe*delta*an)/(s3*(muf/rhof)^q)))*((sc/L^(p+1))*W*dphi-(s1/s2)*(Nt/Nb)*(((Prf*(rhof/muf)))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2)));
   
    
    end
end
function res= projbc(ya,yb)
res= [ya(1)-1;
    ya(3)-1; 
    ya(5)-0;
    ya(6)-1;
    ya(8)-1;ya(10)-1;
    yb(1);
    yb(3);
    yb(6);
    yb(8);
    yb(10)];
end

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Answer 1

Voss on 10 Feb 2023

Open in MATLAB Online

1 vote

Inside the loop, store the values necessary to plot the line after the loop. See the y_store variable below.

proj

The solution was obtained on a mesh of 282 points. The maximum residual is 7.317e-05. There were 19109 calls to the ODE function. There were 253 calls to the BC function. The solution was obtained on a mesh of 283 points. The maximum residual is 7.783e-05. There were 19152 calls to the ODE function. There were 253 calls to the BC function. The solution was obtained on a mesh of 282 points. The maximum residual is 8.303e-05. There were 19108 calls to the ODE function. There were 253 calls to the BC function.

ans = struct with fields:

solver: 'bvp4c' x: [0 0.0076 0.0152 0.0303 0.0455 0.0530 0.0606 0.0682 0.0758 0.0833 0.0909 0.0985 0.1061 0.1136 0.1212 0.1288 0.1364 0.1439 0.1515 0.1591 0.1667 0.1742 0.1818 0.1894 0.1970 0.2045 0.2121 0.2172 0.2222 0.2273 0.2323 0.2374 0.2424 0.2475 … ] y: [11×282 double] yp: [11×282 double] stats: [1×1 struct]

function sol= proj

clc;clf;clear;

global lamda

%Relation of base fluid

rhof=1;

kf=0.613*10^5;

cpf=4179*10^4;

muf=10^-3*10;

sigf=0.05*10^-8;

alfaf=kf/(rhof*cpf);

%FE3O4

ph1=0.01;

rho1=5180*10^-3;

cp1=670*10^4;

k1=9.7*10^5;

sig1=0.74*10^-2;

%copper

ph2=0.01;

rho2=8933*10^-3;

cp2=385*10^4;

k2=401*10^5;

sig2=5.96*10^-1;

%Relation of hyprid

m=5.7;

kh=kf*((k1+(m-1)*kf-(m-1)*ph1*(kf-k1))/((k1+(m-1)*kf+ph1*(kf-k1))))*((k2+(m-1)*kf-(m-1)*ph2*(kf-k2))/((k2+(m-1)*kf+ph2*(kf-k2))));

muh= muf/((1-ph1)^2.5*(1-ph2)^2.5);

rhoh=rhof*(1-ph2)*((1-ph1)+ph1*(rho1/rhof))+ph2*rho2;

v1 =rhof*cpf*(1-ph2)*((1-ph1)+ph1*((rho1*cp1)/(rho2*cp2)))+ph2*(rho2*cp2);

sigh=sigf+(3*((ph1*sig1+ph2*sig2)-sigf*(ph1+ph2))/(((ph1*sig1+ph2*sig2)/(sigf*(ph1+ph2)))+2-((ph1*sig1+ph2*sig2)/sigf)+(ph1+ph2)));

alfah=kh/v1;

myLegend1 = {};

rr = [0.2 0.3 0.4];

y_store = zeros(1,numel(rr));

for i =1:numel(rr)

Nt = rr(i);s2=1;

qq=[13 14 15];

Prf=qq(i);

an=0.1;Lb=1;Pe=0.1;

p=-0.5;q=-0.5;M=1; L=(muf/rhof);L1=L^(p);L1=L^(p);

delta=s2/(L1);

Nb=1; Nr=1;sc=0.45;gamma=pi/3;

a=25;b=0.1;v=1;u=1;

s1=1;s2=1;

s3=sqrt(a/(muf/rhof));

Tw=273+50;Ti=273+27;deltaT=Tw-Ti;

Lf=rhof*kf;

y0 = [1,0,1,0,0,1,0,1,0,1,0];

options =bvpset('stats','on','RelTol',1e-4);

m = linspace(0,1.5);

solinit = bvpinit(m,y0);

sol= bvp4c(@projfun,@projbc,solinit,options);

figure(1)

y_store(i) = -(sol.y(11,1));

plot(qq(i),-(sol.y(11,1)),'s')

grid on,hold on

myLegend1{i}=['Nt = ',num2str(rr(i))];

grid on,hold on

i=i+1;

end

figure(1)

plot(qq,y_store,'k')

legend(myLegend1)

hold on

function dy= projfun(~,y)

dy= zeros(11,1);

% alignComments

E = y(1);

dE = y(2);

F = y(3);

dF= y(4);

W = y(5);

t = y(6);

dt = y(7);

phi = y(8);

dphi = y(9);

z=y(10);

dz=y(11);

dy(1) = dE;

dy(2) = (rhoh/muh)*((((a*u)/L1^(2)))*E^2+(1/L1)*W*dE+((sigh/sigf)/(rhoh/rhof))*(1/L1^2)*M*E*sin(gamma)*sin(gamma));

dy(3) = dF;

dy(4) = (rhoh/muh)*((((b*v)/L1^(2)))*F^2+(1/L1)*W*dF+((sigh/sigf)/(rhoh/rhof))*(1/L1^2)*M*F*sin(gamma)*sin(gamma));

dy(5) = -(1/L1)*(u*a*E+b*v*F);

dy(6) = dt;

dy(7) =(Prf*(rhof/muf))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2);

dy(8)= dphi;

dy(9)=(sc/L^(p+1))*W*dphi-(s1/s2)*(Nt/Nb)*(((Prf*(rhof/muf)))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2));

dy(10)=dz;

dy(11)=(Lb/((muf/rhof)*L1))*W*dz+Pe*delta*dz*dphi+(Pe*delta*z+((Pe*delta*an)/(s3*(muf/rhof)^q)))*((sc/L^(p+1))*W*dphi-(s1/s2)*(Nt/Nb)*(((Prf*(rhof/muf)))*(1/(Nr+(kh/kf)))*(((v1)/(rhof*cpf))*(1/L1)*W*dt-(muh/(rhof*cpf))*(L1/s1)*(1/deltaT)*(-(1/L1)*(u*a*E+b*v*F))^2)));

end

function res= projbc(ya,yb)

res= [ya(1)-1;

ya(3)-1;

ya(5)-0;

ya(6)-1;

ya(8)-1;ya(10)-1;

yb(1);

yb(3);

yb(6);

yb(8);

yb(10)];

end

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T K on 11 Feb 2023

Already done, thank you very much. Finally, I would like to draw two lines at two values of Nt, as shown in the image.

Voss on 11 Feb 2023

You're welcome!

Where do the x- and y-coordinates of the points defining those two lines come from?

Once you have the coordinates, you can plot the lines.

https://www.mathworks.com/help/matlab/ref/plot.html

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Please help me to connect between three points with plot (draw line)

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Please help me to connect between three points with plot (draw line)

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