General theory of a convective nucleus of a fluid in unsteady state and in nonlinear conditions (Q1117108)

A model of free convection in a fluid cylinder submitted to generic boundary conditions is developed. The fluid is subdivided into a boundary layer region and a nucleus moving with opposite velocities and the equations of Fourier, continuity and Navier-Stokes in the nucleus are solved exactly in terms of Fourier sums. The nucleus is linked to the boundary layer to provide the unknown function which solves completely this problem of convection. As an example the general solution is applied to the case of a temperature step which is found to travel undeformed through the nucleus (asymptotic solution).