Marangoni instability with non-uniform volumetric energy sources due to incident radiation

Abstract

The effects of non-uniform volumetric energy sources, temperature-dependent viscosity and surface-tension on Marangoni convection in an incompressible fluid layer are studied. The nonlinear temperature profile arises from external incident radiation. The critical conditions for the onset of Marangoni instability in a microgravity environment ( 10 −6–10 −3 g ) are determined numerically after a normal mode-type linear stability analysis. The perturbation equations are solved as an optimal control problem in the calculus of variations using Miele's sequential gradient-restoration algorithm (SGRA). The results indicate that viscosity plays a significant role in Marangoni convection relative to surface-tension. External radiation is a destabilizing factor while the degree of heat transfer (larger values of Bi) from the fluid to the adjacent gas is a stabilizing factor in Marangoni instability.