A. Srivastava - Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-۲۲۱۰۰۵, India
B. S. Bhadauria - Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow ۲۲۶۰۲۵, India
A. K. Singh - Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-۲۲۱۰۰۵, India

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal heat source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal heat source, solute Rayleigh number, Lewis number, Vadász number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the heat and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation.

Ginzburg, Landau equation, Temperature dependent viscosity, diffusive convection, Gravity modulation, Weakly non, Porous media, Double, linear stability