fluid mechanics BVP problem with nonlinear PDE'S

May 2010
Given the second order non linear BVP

(ƒ')^n = 1 + γ θ …..……………………… 1

θ" + (λ +n+1/ 2n +1) ƒ θ' - n (2 λ +1/2n+ 1) * ƒ' θ = 0 ………… 2

Prime in the above eqn’s describe partial differentiation with respect to η

Boundary conditions are
ƒ (0) = 0, θ'(0) = -1
ƒ' (∞) = 0, θ(∞) = 0

where η is a function of x & y given by
Similarity variable, η = x ^ (λ-n/2n+1) * y
Θ is a dimensionless temperature
ƒ is a dimensionless stream function given by
Stream function, ψ = x ^ (λ+n+1/2n+1) * ƒ(η)

how to solve the above system of PD eqn’s
the above system of equations are related to mixed convection of non newtonian fluids

n is the viscosity index
I haven't confused with n's and η's anywhere
I think that equations are differentiable with respect to η and η is function of x and y
So the equations are PDE’s
Actually these equations are related to boundary layer mixed convection of non Newtonian fluids on vertical plate