Plane convective plume in liquid glass from localized heat source

By processing and analyzing experimental data available in the literature, the range of applicability of the Gebhart–Mollendorf power law equation of state Δρ∝ΔTγ and the range of physical values of its exponent γ have been extended. In the boundary layer approximation, a solution is obtained for the problem of a convective plume from a linear heat source in a fluid with a power law dependence of density on temperature over a wide range of parameter values. For this purpose, the method of numerical continuation of exact solutions is adapted to the problem under consideration. The structures of flow regimes are classified over a wide range of Prandtl numbers Pr and the exponent γ. The hidden integral of motion associated with convective momentum rate and convective mass rate is discovered, and its behavior is investigated.