ode45 for Thwaites Method

I am trying to use the ode45 solver to solve boundar layer momentum thickness using Thwaites Method for a flat plate

The equation I am trying to put into ode45 is with the initial given condition for theta being which is from the analytical blasius solution. and are known for each point along the flat plate and I want to input them into ode45. I am however at a loss at how to translate this into Matlab.

My attempt:

[xode theta] = ode45(@(x,theta) thwaites(x,Ve,dVedx,v,theta) ,[0 1],Theta0)


function dthetadx = thwaites(x,Ve,dVedx,v,theta)
sym theta
dthetadx = .225 .* v./(Ve .* theta) - (3 .* theta)./Ve .* dVed
end

Answer 1

[Pravin Jagtap]

Hello Zachary,

Refer to the following documentation link of ‘ode45’ function. This will give your better insights into how to use ‘ode45’ function and its suitability for your problem along with examples:

https://www.mathworks.com/help/matlab/ref/ode45.html#bu04u19-1

Hope this will help you.