The effect of temperature/gravity modulation on finite amplitude cellular convection with variable viscosity effect

The present paper deals with the theoretical study of a weakly non-linear Rayleigh–Bénard convection in temperature-dependent viscosity Newtonian liquids with temperature/gravity modulation. The effect of temperature-dependent variable viscosity and temperature/gravity modulation renders the problem analytically intractable. The imposed thermal boundary condition and gravity field consist of a steady part and a time-periodic oscillatory part as described by Venezian. The instability of convective rolls due to temperature/gravity modulation is expanded in terms of the power series of the amplitude of convection, which is quite small. The Ginzburg–Landau equation derived in this problem is a non-autonomous differential equation and is solved using the numerical technique. The authors have demonstrated that one can suppress or enhance heat transfer by tuning the parameters involved. The effect of different parameters on the heat transfer and streamlines is also studied. (author)