for loop in bvp4c i get circle in plotting not solid line why?

function sss

global Fr Pr f2 f1 shi2 shi3 lambda zeta Sk u Re Kf B A H1 H2 H3 C1 C2 C3 P1 P2 P3 K1 K2 K3 Kb n Z

Fr = 0.7;

Pr = 6.2 ;

B = 0.9;

for f2=0:0.05:0.15

f1 = 0.05 ;

lambda = 0.4;

zeta=5;

A= 0.4;

n=3.7;

Re=0.3;

C1=765;

P1=3970;

K1=40;

%%%%%%%%%%%%%%%%%%%%%%%

C2=385; % specific heat

P2=8933; % density

K2=400; % thermal conductivity

%%%%%%%%%%% %%%%%%%%%%%%

C3=4180; % specific heat

P3=997.1; % density

K3=0.6071; % thermal conductivity

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%

Z=zeta+B;

H1=P1*C1; % pho*cp nanoparticle 1

H2=P2*C2; % pho*cp nanoparticle 2

H3=P3*C3; % pho*cp base fluid

Kb = (K2 + (n - 1)*K3 - f2*(n - 1)*(K3 - K2))/(K2 + (n - 1)*K3 + f2*(K3 - K2)); % khnf/kbf

Kf=((K2 + (n - 1)*K3 - f2*(n - 1)*(K3 - K2))/(K2 + (n - 1)*K3 + f2*(K3 - K2)))*((K1 + (n - 1)*K3 - f1*(n - 1)*(K3 - K1))/(K1 + (n - 1)*K3 + f1*(K3 - K1)));

% khnf/kf

shi2=(((1 - f1)^2.5)*((1 - f2)^2.5))*(((1 - f1)*(1 - f2))+f1*(P1/P3)) + f2*(P2/P3) ;

% shi2 in velocity equation

shi3=(1 - f2)*((1 - f1) + f1*((H1)/(H3))) + f2*((H2)/(H3));

u=1/((1-f1)^2.5);

options = bvpset('RelTol',1e-6,'Stats','off') ;

solinit = bvpinit(linspace(0,5,10),[1; 0 ;0 ;0 ;0; 0]);

sol = bvp4c(@odes,@bcs,solinit,options);

Sk=u*1/((Re)^0.5)*(sol.y(3,1)-sol.y(2,1)/B);

hold on

plot(f2 ,Sk,'b-')

hold off

end

%--------------------------------------------------------------------------

function dydx = odes(~,y)

% global zeta Pr psi2 psi3 k B Fr A

dydx = zeros(6,1);

dydx(1) = y(2); % y(1)=f

dydx(2) = y(3);

dydx(3) = y(4);

dydx(4) = -(2/(zeta+B)*y(4))+(1/((zeta+B)^2)*y(3))-(1/((zeta+B)^3)*y(2))+2*lambda*(y(3)+(1/(zeta+B)*y(2)))+shi2*(-((B/(zeta+B)^2)*y(1)*y(3))-((B/(zeta+B)*y(1)*y(4)))+(B/((zeta+B)^3)*y(1)*y(2))+(3*B/((zeta+B)^2)*y(2)*y(2))+(3*B/((zeta+B)^2)*y(2)*y(3))+2*Fr*(2*y(2)*y(3)+((1/(zeta+B))*y(2)*y(2))));

dydx(5) = y(6); % y(5)=theta

dydx(6) = -(1/(zeta+B))*y(6)-((Pr*shi3*B)/(Kb*(zeta+B)))*(y(1)*y(6)-A*y(2)*y(5));% k=khnf/kbf

%--------------------------------------------------------------------------

end

function res = bcs(ya,yb)

res = [ya(1); ya(2)-1;ya(5)-1; yb(2); yb(3); yb(5)];

end

end

Answer 1

[Torsten]

sss()

F2 = 1×4

0 0.0500 0.1000 0.1500

function sss
global  Fr Pr f2 f1 shi2 shi3 lambda zeta  Sk u Re Kf B  A H1 H2 H3 C1 C2 C3 P1 P2 P3 K1 K2 K3  Kb n Z 


Fr = 0.7;  
Pr = 6.2 ; 
B = 0.9;  
F2 = 0:0.05:0.15
for i=1:numel(F2) 
f2 = F2(i);
    f1 = 0.05 ; 
    lambda = 0.4; 
    zeta=5; 
    A= 0.4;  
    n=3.7;  
    Re=0.3; 
    
    
    C1=765;
    P1=3970;
    K1=40;
    %%%%%%%%%%%%%%%%%%%%%%%
    C2=385; % specific heat
    P2=8933; % density
    K2=400; % thermal conductivity
    
    %%%%%%%%%%% %%%%%%%%%%%%
    C3=4180; % specific heat
    P3=997.1; % density
    K3=0.6071; % thermal conductivity
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%
    Z=zeta+B;
    H1=P1*C1;       % pho*cp nanoparticle 1
    H2=P2*C2;       % pho*cp nanoparticle 2
    H3=P3*C3;       % pho*cp base fluid
    
    Kb = (K2 + (n - 1)*K3 - f2*(n - 1)*(K3 - K2))/(K2 + (n - 1)*K3 + f2*(K3 - K2)); % khnf/kbf
    
    Kf=((K2 + (n - 1)*K3 - f2*(n - 1)*(K3 - K2))/(K2 + (n - 1)*K3 + f2*(K3 - K2)))*((K1 + (n - 1)*K3 - f1*(n - 1)*(K3 - K1))/(K1 + (n - 1)*K3 + f1*(K3 - K1)));
    % khnf/kf
    
    shi2=(((1 - f1)^2.5)*((1 - f2)^2.5))*(((1 - f1)*(1 - f2))+f1*(P1/P3)) + f2*(P2/P3)  ;  
    % shi2 in  velocity equation
    
    
    shi3=(1 - f2)*((1 - f1) + f1*((H1)/(H3))) + f2*((H2)/(H3)); 
    
    u=1/((1-f1)^2.5);
    
    
    options = bvpset('RelTol',1e-6,'Stats','off') ;  
    solinit = bvpinit(linspace(0,5,10),[1; 0 ;0 ;0 ;0; 0]);
    sol = bvp4c(@odes,@bcs,solinit,options);
    Sk(i)=u*1/((Re)^0.5)*(sol.y(3,1)-sol.y(2,1)/B);
    

end
plot(F2,Sk)
%--------------------------------------------------------------------------
    function dydx = odes(~,y)
        % global zeta Pr psi2 psi3 k B  Fr A
        dydx = zeros(6,1);
        dydx(1) = y(2); % y(1)=f
        dydx(2) = y(3);
        dydx(3) = y(4);
        dydx(4) = -(2/(zeta+B)*y(4))+(1/((zeta+B)^2)*y(3))-(1/((zeta+B)^3)*y(2))+2*lambda*(y(3)+(1/(zeta+B)*y(2)))+shi2*(-((B/(zeta+B)^2)*y(1)*y(3))-((B/(zeta+B)*y(1)*y(4)))+(B/((zeta+B)^3)*y(1)*y(2))+(3*B/((zeta+B)^2)*y(2)*y(2))+(3*B/((zeta+B)^2)*y(2)*y(3))+2*Fr*(2*y(2)*y(3)+((1/(zeta+B))*y(2)*y(2))));
        dydx(5) = y(6); % y(5)=theta
        dydx(6) = -(1/(zeta+B))*y(6)-((Pr*shi3*B)/(Kb*(zeta+B)))*(y(1)*y(6)-A*y(2)*y(5));% k=khnf/kbf
        %--------------------------------------------------------------------------
    end
    function res = bcs(ya,yb)
        res = [ya(1); ya(2)-1;ya(5)-1; yb(2); yb(3); yb(5)];
    end
end

[farooq omer]

thank you so much but this code is not working on my R2018 software of matlab sir...what to do .ive acces to R2018 only in my lab

[farooq omer]

how to draw lines for A=0.4,0.6,0.8 using a loop in this code

[Torsten]

Make sss a script instead of a function. Make odes and bcs usual functions instead of nested functions. Add the necessary global variables in the functions. Save all functions in separate files with their respective names (bcs.m, odes.m). Load the script (sss.m) into your MATLAB editor. Press the RUN button.

[Torsten]

how to draw lines for A=0.4,0.6,0.8 using a loop in this code

In the same way as you used a loop for f2.