Boundary value problem using keller box method

Hi everyone, How to solve the given equation using Keller-Box method.

Equation:

Bcs:

for

[Torsten]

Before starting with an exotic solution method, I suggest to set up the problem first with the usual MATLAB tool "bvp4c".

This way, you can compare your results with a well-tested software.

[Chukwudi Andrew]

Modelling the system of boundary layer equations:

,

,

subject to boundary conditions:

,

where ′ denotes differentiation with respect to η, m is a constant and PR is the Prandtl number. Physical quantities of interest in this system are the skin friction coefficient and the local Nusselt number , which are defined as , .

By using an appropriate numerical method of a boundary value problem and computer application. Generate results of the velocity profiles of f′(η) vs η and the temperature profiles of θ(η) vs η. Let the value of parameters m and Pr become:

m = -0.0756, 0.000, 0.111, 0.333, 1.000

Pr = 0.05, 0.72, 1.0, 7.0, 100.

[Torsten]

Define

u1 = f, u2 = f', u3 = f'', u4 = theta, u5 = theta''

, set up the problem as

u1' = u2
u2' = u3
u3' = -0.5*(m+1)*u1*u3 - m*(1-u2^2)
u4' = u5
u5' = -0.5*Pr*(m+1)*u1*u5

and use "bvp4c" to solve.