Free convection plume from the tip of a vertical needle (Q1122439)

Free convection from thin vertical needles of variable radius is of much interest since the governing boundary layer equations admit similarity solutions which are more revealing than the direct numerical integration of the partial differential equations. The possibility of self-similar solutions for needles was first studied by \textit{M. Van Dyke} [in: Problems of hydrodynamics and continuum mechanics. Nauk, Moskov (1969)]. The solutions for the free convection from a needle with constant surface temperature was given by \textit{T. Cebeci} and \textit{T. Y. Na} [Phys. Fluids 12, 463-465 (1969; Zbl 0182.594)]. The purpose of this paper is to study a problem which is quite different from previous literature, i.e. the similarity solution for an adiabatic needle with a concentrated heat source at the tip. This situation occurs in, for example, a stick burning at the bottom end.