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 and insulating where surface tension gradients arise on account of variation in temperature and the lower boundary is rigid. the single-term Galerkin technique is used to obtain the eigenvalue equation. Eigenvalues are obtained and presented for both thermally conducting and insulating cases of the lower boundary. this analysis predicts that in either case 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.