Asked by samuel okeleye
on 21 Jan 2015

(d^3 f)/(dη^3 )=-1/2.f(η).(d^2 f)/(dη^2 )-Grθ(η)…….. (1)

(d^2 θ)/(dη^2 )=-Pr.f(η). dθ/dη…………………….. (2)

(d^2 ϕ)/(dη^2 )=-1/2 Sc.f(η). dϕ/dη……….………… (3)

Gr, Sc and Pr are constants.

Domain is η from zero to infinity and I want the iteration to stop the moment the difference is 〖 10〗^(-6)

Boundary conditions f'(0)=0,θ(0)=1 and ϕ(0)=1 f'(∞)=1,θ(∞)=0 and ϕ(∞)=0

Answer by Zoltán Csáti
on 22 Jan 2015

Accepted Answer

samuel okeleye
on 23 Jan 2015

Zoltán Csáti
on 23 Jan 2015

Well, I recommend you the following.

- Download chebfun
- Install it
- Open it's GUI
- Type the equations
- Solve it

If you need any help, feel free to write.

samuel okeleye
on 20 Feb 2015

i had to read a lot to be able to solve the problem with bvp4c but i have been able to solve it now. Thank God and thank you. My problem now is to be able to have a plot of y(4) and y(6) at various values of Gr_nf,Sc_nf and Pr_nf in just one plot. Below is my code

function [yprime]=myblayerode1(eta,y)

%Gr_nf,Pr_nf and Sc_nf are the grashof number, Prantl number and Schmidt

%number of the concerned fluid respectively.

%yprime is a vector of all the first order ODEs on the left hand side

%having turned all 2nd and 3rd order ODEs to 1st order. y(1)to y(7) are the

%variables on the right hanside of the resulting 1st order

%ODE.f=y(1),f'=y(2),f''=y(3),theta=y(4),theta'=y(5),phi=y(6),phi'=y(7) and

%yprime is a column vector

%df/deta,df'/deta,df''/deta,dtheta/deta,dtheta'/deta,dphi/deta and

%dphi'/deta.

Gr_nf=11.297;

Pr_nf=17.716;

Sc_nf=100;

yprime=[y(2,:);y(3,:);-0.5.*y(1,:).*y(3,:)-Gr_nf.*y(4,:);y(5,:);-0.5.*Pr_nf*y(1,:).*y(5,:);y(7,:);-0.5.*Sc_nf.*y(1,:).*y(7,:)];

function res= bvpbc(ya,yb)

Bi=1;

%BC: Evaluates the residue of the boundary condition

res1=[ya(1,:);ya(2,:);yb(2,:)-1];

res2=[(ya(5,:)+Bi.*(1-ya(4,:)));yb(4,:)];

res3=[ya(6,:)-1;yb(6,:)];

res=[res1;res2;res3;];

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

options =bvpset('RelTol',1e-06,'AbsTol',1e-06,'stats','on');

sol = bvp4c(@myblayerode1,@bvpbc,solinit,options);

eta=0:0.5:10;

y=deval(sol,eta);

sol.eta=eta;

sol.y=y;

hold off

plot(eta,y(7,:),'r:s');

print plot;

so instead of having one number for Gr_nf,Pr_nf and Sc_nf i want to have like 5 numbers and i want the result to be displayed as numbers and on a graph, just like the velocity profile for power law fluid in your work with gabriella bognar where you varied n from 1.0 to 1.5. Thanks in anticipation of your assistance.

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Answer by Zoltán Csáti
on 31 Mar 2015

Well, you have to solve the system of BVPs several times for each different values of Gr, Pr and Sc. Then you can plot the data in one figure (see plot command) and can also add a legend. You may also put an arrow representing the effect of the different parameter values on the boundary layer. These can either be done programatically or by using the interactive tools.

Sorry for not answering earlier, but the comments - in contrast to the answers - are not sent to my e-mail address.

samuel okeleye
on 1 Apr 2015

Zoltán Csáti
on 1 Apr 2015

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