How to draw the Graph of Ns for different values of M?

function Entropy

clc

M=0.0;

Pr=1.0; %Prandtl

Ec=0.5;

Bi=0.5;

Omega=1.0;

Re=5.0;

Br=1.0;

% Initial values

sol = bvpinit(linspace(0,8,30),[1 0 0 0 0 ]);

% solution in structure form

sol1 = bvp4c(@bvpexam2, @bcexam2, sol);

% x values

x1 = sol1.x;

% y values in row form (y, y', y'', theta, theta');

y1 = sol1.y;

figure (1)

plot(x1, y1(4, :),'-R','linewidth',1,'Linesmoothing','on');

hold on

grid on

% Here I define residual of boundary conditions

function res = bcexam2(y0, yinf)

res = [y0(1); y0(2)-1; y0(5)+Bi*(1-y0(4)); yinf(2); yinf(4)];

end

% First order ODEs are define here

function ysol = bvpexam2(x,y)

yy1=-2*y(1)*y(3)+y(2)*y(2)+M*y(2);

yy2=-2*Pr*y(1)*y(5)-Pr*Ec*y(3)*y(3)-M*Pr*Ec*y(2)*y(2);

Ns=Re*y(5)*y(5)+Re*(Br/Omega)*y(3)*y(3)+Re*(Br/Omega)*M*y(2)*y(2);

Be=Re*y(5)*y(5)/(Re*y(5)*y(5)+Re*(Br/Omega)*y(3)*y(3)+Re*(Br/Omega)*M*y(2)*y(2));

ysol = [y(2);y(3);yy1; y(5);yy2];

end

end

Answer 1

[Mark Sherstan]

Try this (change the ii to satisfy whatever range of N you would like to observe):

for ii = 0:0.1:1
    Entropy(ii)
end

Where I modified your function to take an input:

function [] = Entropy(M) 
clc
%M=0.0;
Pr=1.0;  %Prandtl
Ec=0.5;
Bi=0.5;
Omega=1.0;
Re=5.0;
Br=1.0;
   
% Initial values  
sol = bvpinit(linspace(0,8,30),[1 0 0 0 0 ]);
%  solution in structure form
sol1 = bvp4c(@bvpexam2, @bcexam2, sol);
% x values
x1 = sol1.x;
% y values in row form (y, y', y'', theta, theta');
 y1 = sol1.y;
 
        figure (1)
         plot(x1, y1(4, :),'-R','linewidth',1,'Linesmoothing','on');
        hold on
        grid on
% Here I define residual of boundary conditions
    function res = bcexam2(y0, yinf)
        
 
   res  = [y0(1); y0(2)-1; y0(5)+Bi*(1-y0(4)); yinf(2);  yinf(4)]; 
  
    end
% First order ODEs are define here
    function ysol = bvpexam2(x,y)
  yy1=-2*y(1)*y(3)+y(2)*y(2)+M*y(2);
  yy2=-2*Pr*y(1)*y(5)-Pr*Ec*y(3)*y(3)-M*Pr*Ec*y(2)*y(2);
  Ns=Re*y(5)*y(5)+Re*(Br/Omega)*y(3)*y(3)+Re*(Br/Omega)*M*y(2)*y(2);
 Be=Re*y(5)*y(5)/(Re*y(5)*y(5)+Re*(Br/Omega)*y(3)*y(3)+Re*(Br/Omega)*M*y(2)*y(2));
       
ysol  = [y(2);y(3);yy1; y(5);yy2];
 
 
    end
end

[Aamir Hamid]

This answer did not resolve my problem.