Boundary Effect on Marangoni Convection in a Variable Viscosity Fluid Layer

The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, R_v, Biot number, B_i, depth ratio, d_r and conductivity ratio, k_r, are significant on determining the critical Marangoni number M_c with the corresponding critical wavenumber α_c. The characteristics problem is solved numerically. Results show that the temperature-dependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.