How can i solve these systems of ODE
2 views (last 30 days)
Show older comments
samuel okeleye on 21 Jan 2015
Commented: Zoltán Csáti on 1 Apr 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
Zoltán Csáti on 22 Jan 2015
These are typical boundary layer equations. There are several strategies to tackle it. The two main solution methods: truncate it to some finite [0 L] interval or solve it on the semi-implicit domain. I recommend you the chebfun library because it is very easy to use. You can also use the built-in bvp4c function which is based on this article. There is also an example for the Falkner-Skan problem in it on page 16.
More Answers (1)
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.
Zoltán Csáti on 1 Apr 2015
I recommend you the Department of Fluid and Heat Engineering , because of your specialization. I suggest you to gather information about the university and the research area here and if you take it seriously, I can ask the department if they need a researcher or not.
Find more on Programming in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!Start Hunting!