Theoretical consideration of free convective heat transfer from a round isothermal plate slightly inclined from the vertical

A semi-analytical solution of simplified Navier-Stokes and Fourier-Kirchhoff equations describing free convective heat transfer from a round isothermal surface slightly inclined from the vertical is presented. The solution is based on the assumption, typical for natural convection, that the velocity component normal to the surface is negligibly small in comparison to the tangential one. Next we neglect the nonlinear inertia force term, but more real mass continuity is taken into account in control volume approach. This assumption do not permit to use stream function. The results for a vertical round plate in the form of the boundary layer thickness and mean Nusselt number are obtained in explicit form. They are in good agreement with literature solutions for vertical rectangular or square plates. The correction function to the Nusselt number for inclined plate is obtained in the analytical integral form that is calculated numerically and compared with the experimental values. Analysis of the results for the correction function is proportional to tan α, hence heat transfer intensifies for a positive inclination. The solution analysis also suggests extreme heat transfer at some angle for a given range of Rayleigh numbers.