(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