Effect of Non-Uniform Temperature Gradient on Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid

The effect of non-uniform temperature gradient on the onset of convection driven by surface tension gradients in a relatively hotter or cooler layer of liquid is studied by means of linear stability analysis. The upper boundary is considered to be free where surface tension gradients arise on account of variation in temperature and the lower boundary is stress free, each subject to constant heat flux. The single-term Galerkin technique is used to obtain the eigenvalue equation. Eigenvalues are obtained and presented. The results are compared with the existing ones and found that even a single-term Galerkin expansion gives quite accurate results. Further, this analysis predicts that the critical eigenvalues for different non-uniform temperature gradients are greater in a relatively hotter layer of liquid than the cooler one under identical conditions otherwise. This qualitative effect is quite significant quantitatively as well.