Finite element simulation of combined buoyancy and thermocapillary driven convection in open cavities

Abstract

AbstractThermocapillary‐induced and buoyancy‐driven convective flows that commonly occur in crystal growth are numerically simulated using Galerkin finite element method. The physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls. The top gas–melt interface is free to deform subject to 90° contact angle boundary conditions at the two vertical walls. The unsteady two‐dimensional Navier–Stokes equations are discretized in time using Chorin‐type splitting scheme and pressure is determined from the Poisson's equation. The free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation. The governing equations for heat and momentum are solved in the Arbitrary Lagrangian Eulerian frame of reference to handle the moving boundary. The influence of Grashof number, Marangoni number, Bond number, Ohnesorge number and Prandtl number on the flow field and heat transfer is investigated.