I am trying to implement the exact solution to the Jeffery-Hamel flow problem according to White (1974) [Link]. The two equations of interest are here, with and α given.
- Boundary condition:
So first, I would like to determine C by using equation (2) using the following code:
Re = 100;
alpha = 15/360*2*pi;
bc = @(f, C) 1./(((1-f).*(2/3.*Re.*alpha.*(f.*f+f)+4.*alpha.*alpha.*f + C)).^(0.5));
bcInt = @(C) integral(@(f) bc(f, C), 0, rand(1));
bcEq = @(C) bcInt(C) - 1;
C_sol = fsolve(bcEq, rand)
However, I get the following error message:
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
<stopping criteria details>
Does anybody have an idea what I do wrong, or if I have to take a completely different path to solve this?
Thanks a lot!