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Question Details:
The flow of a fluid over a flat plate, aligned with the flow, is governed by the equation:
( )2
F '''+ FF ''+ beta[ 1- (F')^2] = 0
where primes denote differentiation with respect to the independent variable n(eta) , that is
F'' = d'' F / d n
The dimensionless quantity F is termed as stream function. The boundary
conditions for this problem are as follows:
at n(eta) = 0, F(0) = F' (0) = 0 (1)
at " = infinty, F' (infinity) = 1 (2)
Employing the fourth order Runge-Kutta method along with the shooting method, solve
this boundary-value problem. For the application of the second boundary condition, take
n(eta) = 8 as being large enough to represent infinity. Take step size dn = 0.1 and a convergence criterion of 0.00001.
Solve the above problem for beta = 0 and submit your project in the following format:
1. Briefly describe the numerical scheme employed to solve the above problem.
2. Plot F' (n) vs. n and find n where F' (n) = 0.9999 .
3. Tabulate and plot '' F, F', F vs. n(eta) .
4. Submit a copy of the code.
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