sol = bvp4c (OdeBVP, OdeBC, solinit, options);

ne the boundary conditions

function res = OdeBc (ya, yb, A, s, B, lambda)

global A s B lambda

res= [ya(1)-s;

ya(2)-lambda-A*ya(3);

ya(4)-1-B*ya(5);

yb(2);

yb(4)];

end

% setting the initial guess for first solution

function v = OdeInit1(x,A,s,lambda)

global A s lambda

v=[s+0.56

0

0

0

0];

end

% setting the initial guess for second solution

function v1 =OdeInit2(x, A, s)

global A s

v1 = [exp(-x)

exp(-x)

-exp(-x)

-exp(-x)

-exp(-x)];

end

end

[Torsten]

solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,s,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBC(ya, yb, A, s, B, lambda), solinit, options);

Same for your second call to bvp4c.

And define the parameters before calling bvp4c.

And remove the global statements inside the functions.

[KIRAN Sajjanshetty]

can u change directly in the code and send it here

i have tried for all possible ways but it is not running showing error

[Torsten]

Include the modified code (with all parameters you use) and the error message here.

[KIRAN Sajjanshetty]

Unrecognized function or variable 's'.

Error in slipflow>@(x)OdeInit1(x,A,s,lambda) (line 59)

solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,s,lambda));

Error in bvpinit (line 104)

w = feval(v,x(1),extraArgs{:});

Error in slipflow (line 59)

solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,s,lambda));

[Torsten]

Seems you didn't define "s" and gave it a value before calling bvpinit.

Answer 1

[Torsten]

function slipflow
format long g
%Define all parameters
% Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 15; %15, 10
stepsize1 = etaMax1;
stepsize2 = etaMax2;
% Input for the parameters
A=0.6;  %velocity slip
B=0.2;  %thermal slip
beta=0.02;  %heat gen/abs
S=2.4;  %suction(2.3,2.4,2.5)
Pr=6.2;     %prandtl number
lambda=-1;  %stretching shrinking
a=0.01; %phil-1st nanoparticle concentration
b=0.01; %(0.01,0.05)phi2-2nd nanoparticle concentration
c=a+b;  %phi-hnf concentration of hybrid nanoparticle 
%%%%%%%%%%% 1st nanoparticle properties (Al2O3)%%%%%%%%%%%%
C1=765;
P1=3970;
K1=40;
B1=0.85/((10)^5);
s1=35*(10)^6; %MHD
%%%%%%%%%%% 2nd nanoparticle properties (Cu)%%%%%%%%%%%%
C2=385; %specific heat
P2=8933; %density
K2=400; %thermal conductivity
B2=1.67/((10)^5);   %thermal expansion
s2=(59.6)*(10)^6; %MHD
%%%%%%%%%%% Base fluid properties %%%%%%%%%%%%
C3=4179; %specific heat
P3=997.1; %density
K3=0.613; %thermal conductivity
B3=21/((10)^5);   %thermal expansion
s3=0.05; %MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%multiplier%%%%%%%%%%%%%%%%%%%
H1=P1*C1;       %pho*cp nanoparticle 1
H2=P2*C2;       %pho*cp nanoparticle 2
H3=P3*C3;       %pho*cp base fluid
H4=a*H1+b*H2+(1-c)*H3; %pho*cp hybrid nanofluid
H5=a*P1+b*P2+(1-c)*P3;  %pho hybrid nanofluid
H6=1/((1-c)^2.5);   % mu hybrid nanofluid / mu base fluid
H7=a*(P1*B1)+b*(P2*B2)+(1-c)*(P3*B3);   % thermal expansion of hybrid nanofluid
%Kn=K3*(K1+2*K3-2*a*(K3-K1))/(K1+2*K3+a*(K3-K1));     %thermal conductivity of nanofluid
Kh=(((a*K1+b*K2)/c)+2*K3+2*(a*K1+b*K2)-2*c*K3)/(((a*K1+b*K2)/c)+2*K3-(a*K1+b*K2)-2*c*K3); %khnf/kf
H8=(((a*s1+b*s2)/c)+2*s3+2*(a*s1+b*s2)-2*c*s3)/(((a*s1+b*s2)/c)+2*s3-(a*s1+b*s2)-2*c*s3); % \sigma hnf/ \sigma f
D1=(H5/P3)/H6;
D3=(H7/(P3*B3))/(H5/P3);                % multiplier of boundary parameter
D2= Pr*((H4/H3)/Kh);
D4=H8/(H5/P3);  %multiplier MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBC(ya, yb, A, S, B, lambda), solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y= deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'-')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'-')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for first solution
descris =[sol.x; sol.y];
save 'sliphybrid_upper.txt' descris -ascii
% Displaying the output for first solution
fprintf('\n First solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% second solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2),@(x)OdeInit2(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBC(ya, yb, A, S, B, lambda), solinit, options);
eta= linspace (etaMin, etaMax2, stepsize2);
y = deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'--')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'--')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for second solution
descris=[sol.x; sol.y];
save 'sliphybrid_lower.txt'descris -ascii
% Displaying the output for first solution
fprintf('\nSecond solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
% Define the ODE function
function f = OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta)
f =[y(2);y(3);D1*(2*(y(2)*y(2))-y(1)*y(3));y(5);(Pr/Kh)*((-H4/H3)*(y(1)*y(5)-y(2)*y(4))-beta*y(4))];
end
% Define the boundary conditions
function res = OdeBc (ya, yb, A, S, B, lambda)
res= [ya(1)-S;ya(2)-lambda-A*ya(3);ya(4)-1-B*ya(5);yb(2);yb(4)];
end
% setting the initial guess for first solution
function v = OdeInit1(x,A,S,lambda)
v=[S+0.56;0;0;0;0];
end
% setting the initial guess for second solution
function v1 =OdeInit2(x, A, S,lambda)
v1 = [exp(-x);exp(-x);-exp(-x);-exp(-x);-exp(-x)];
end

[Torsten]

Rename the function

OdeBc

in

OdeBC

For MATLAB, small and capital letters define different things.

Same with the letter "s" you used in your original code. I hope you always meant your "S" - I replaced it where it was needed.

Answer 2

[Farooq Aamir]

This working now.

slipflow()

 First solution:
f"(0)=0.954395347
-theta(0)=3.658786212
Cfx=1.003836827
Nux=3.881552117

Second solution:
f"(0)=0.075669302
-theta(0)=3.617987101
Cfx=0.079589273
Nux=3.838268944

function slipflow
format long g
%Define all parameters
% Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 15; %15, 10
stepsize1 = etaMax1;
stepsize2 = etaMax2;
% Input for the parameters
A=0.6;  %velocity slip
B=0.2;  %thermal slip
beta=0.02;  %heat gen/abs
S=2.4;  %suction(2.3,2.4,2.5)
Pr=6.2;     %prandtl number
lambda=-1;  %stretching shrinking
a=0.01; %phil-1st nanoparticle concentration
b=0.01; %(0.01,0.05)phi2-2nd nanoparticle concentration
c=a+b;  %phi-hnf concentration of hybrid nanoparticle 
%%%%%%%%%%% 1st nanoparticle properties (Al2O3)%%%%%%%%%%%%
C1=765;
P1=3970;
K1=40;
B1=0.85/((10)^5);
s1=35*(10)^6; %MHD
%%%%%%%%%%% 2nd nanoparticle properties (Cu)%%%%%%%%%%%%
C2=385; %specific heat
P2=8933; %density
K2=400; %thermal conductivity
B2=1.67/((10)^5);   %thermal expansion
s2=(59.6)*(10)^6; %MHD
%%%%%%%%%%% Base fluid properties %%%%%%%%%%%%
C3=4179; %specific heat
P3=997.1; %density
K3=0.613; %thermal conductivity
B3=21/((10)^5);   %thermal expansion
s3=0.05; %MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%multiplier%%%%%%%%%%%%%%%%%%%
H1=P1*C1;       %pho*cp nanoparticle 1
H2=P2*C2;       %pho*cp nanoparticle 2
H3=P3*C3;       %pho*cp base fluid
H4=a*H1+b*H2+(1-c)*H3; %pho*cp hybrid nanofluid
H5=a*P1+b*P2+(1-c)*P3;  %pho hybrid nanofluid
H6=1/((1-c)^2.5);   % mu hybrid nanofluid / mu base fluid
H7=a*(P1*B1)+b*(P2*B2)+(1-c)*(P3*B3);   % thermal expansion of hybrid nanofluid
%Kn=K3*(K1+2*K3-2*a*(K3-K1))/(K1+2*K3+a*(K3-K1));     %thermal conductivity of nanofluid
Kh=(((a*K1+b*K2)/c)+2*K3+2*(a*K1+b*K2)-2*c*K3)/(((a*K1+b*K2)/c)+2*K3-(a*K1+b*K2)-2*c*K3); %khnf/kf
H8=(((a*s1+b*s2)/c)+2*s3+2*(a*s1+b*s2)-2*c*s3)/(((a*s1+b*s2)/c)+2*s3-(a*s1+b*s2)-2*c*s3); % \sigma hnf/ \sigma f
D1=(H5/P3)/H6;
D3=(H7/(P3*B3))/(H5/P3);                % multiplier of boundary parameter
D2= Pr*((H4/H3)/Kh);
D4=H8/(H5/P3);  %multiplier MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBc(ya, yb, A, S, B, lambda), solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y= deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'-')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'-')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for first solution
descris =[sol.x; sol.y];
%save 'sliphybrid_upper.txt' descris -ascii
% Displaying the output for first solution
fprintf('\n First solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% second solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2),@(x)OdeInit2(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBc(ya, yb, A, S, B, lambda), solinit, options);
eta= linspace (etaMin, etaMax2, stepsize2);
y = deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'--')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'--')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for second solution
descris=[sol.x; sol.y];
%save 'sliphybrid_lower.txt'descris -ascii
% Displaying the output for first solution
fprintf('\nSecond solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
% Define the ODE function
function f = OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta)
f =[y(2);y(3);D1*(2*(y(2)*y(2))-y(1)*y(3));y(5);(Pr/Kh)*((-H4/H3)*(y(1)*y(5)-y(2)*y(4))-beta*y(4))];
end
% Define the boundary conditions
function res = OdeBc(ya, yb, A, S, B, lambda)
res= [ya(1)-S;ya(2)-lambda-A*ya(3);ya(4)-1-B*ya(5);yb(2);yb(4)];
end
% setting the initial guess for first solution
function v = OdeInit1(x,A,S,lambda)
v=[S+0.56;0;0;0;0];
end
% setting the initial guess for second solution
function v1 =OdeInit2(x, A, S,lambda)
v1 = [exp(-x);exp(-x);-exp(-x);-exp(-x);-exp(-x)];
end

[Nurain]

why i try to run this coding but still error at line 56

[Torsten]

Which MATLAB version do you use ?

What is line 56 ?

[khuram Rafique]

sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBC(ya, yb, A, S, B, lambda), solinit, options);

[khuram Rafique]

still eror in line 56 which mentioned above

[Farooq Aamir]

Your error please?

[Farooq Aamir]

sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,beta), @(ya,yb)OdeBc(ya, yb, A, S, B, lambda), solinit, options); Use this it will work, kindly check your fuction name while calling it.

[khuram Rafique]

Thanks Farooq Aamir sir, its working now

[Ramanuja]

Thanks Farooq Aamir sir,

Thanks Farooq Aamir sir,

Thanks Farooq Aamir sir,