Numerical simulation of unsteady thermal Marangoni flows

A two-dimensional numerical code for the analysis of unsteady thermal Marangoni flows which solves the full Navier-Stokes equation for natural, Marangoni, or combined free convection in plane and axisymmetric geometries and arbitrary variations of surface tension with temperature is developed. The equations are discretized using a semi-implicit finite difference scheme that preserves conservative and transport properties within cell mesh and allows the use of time-steps much larger than those relative to a purely explicit technique. Results pertain to a plane configuration with surface tension varying linearly with temperature. The time evolution of the velocity and temperature fields, and the assessement of the range of validity of the so-called shallow-cavity approximation for steady state are discussed.