Analytic-numerical model of a convective boundary layer and heat transfer on a horizontal cone

An approximate analytical solution of a two dimensional problem for stationary Navier-Stokes, continuity and Fourier-Kirchhoff equations describing a free convective heat transfer from an isothermal cone is presented. The problem formulation is based on assumptions typical for natural convection: non-compressibility and the Boussinesq approximation. The solution is based on Frobenius expansions at the vicinities of two points: the initial point and the singular point of the boundary layer equation. Numerical matching of the expansions and Nusselt number evaluations are traced.