Stefan problem coupled with natural convection: An application to dissolution process

Abstract

This paper investigates the process of dissolution of a solute in a solvent placed in an horizontal concentric cylinder. The theoretical investigation solves a Stefan problem with phase transition due to natural convective flow. To realize the objective, the governing equation for the concentration distribution, stream function–vorticity form of the Navier–Stokes equation for the flow field, and a Stefan condition for calculating the timescale evolution of the front are coupled together with different parameters. These non-linear equations are solved using a stable and second-order accurate boundary-fitted alternating direction implicit scheme with first-order upwind difference approximation for convective terms. The numerical scheme is validated initially by applying it to solve a natural convection problem with no phase transition, for which benchmark solutions are available. The validated scheme is then applied to the chosen problem followed by a refinement study to obtain a reliable solution. The obtained results are used to analyze the effect of physical parameters such as the Stefan number (Ste), geometric aspect ratio of solute to fluid, the Rayleigh number (Ra) and the Schmidt (Sc) number on dissolution rates as well as the flow patterns. It is observed that the solute dissolution, without the temperature influence, mainly depends on the annulus gap width (L) and the convection rate. Additionally, it is also observed that, for the Rayleigh numbers greater than 105, the unit circular-shaped solute initially dissolves uniformly from the outer surface, but as the time progresses, due to the influence of laminar boundary layer flow around the solute, it changes into an egg-shape.