In this work we have investigated buoyancy driven convection in
bi-viscous Bingham fluid layer under gravity modulation and its weakly
non-linear and linear stability analyses. We derive the critical
Rayleigh number expression from linear analysis. From non-linear
analysis we compute the heat and mass transport parameters Nu and
Sh respectively based on Ginzburg-Landau equation.These numbers
are obtained as a function of wavenumber and amplitude of modulation.
The Gravity modulation effect on heat and mass transport are obtained in
terms of Nusselt number ( Nu) and Sherwood number( Sh)
respectively. Further, various parameters have significant effect on
heat and mass transport. This is also analysed and depicted graphically.