EFFECTS OF THREE TYPES OF GRAVITY MODULATION ON ROTATING RAYLEIGH-BÉNARD CONVECTION IN A SPARSELY PACKED POROUS LAYER IN THE PRESENCE OF THROUGHFLOW
Suman Shekhar, Ravi Ragoju, C. Kanchana
Abstract
In this paper, the effect of three different types of time-periodic vertical gravity modulation (trigonometric sine, triangular and square waveforms) on rotating Rayleigh- B´enard convection in a sparsely packed porous layer in the presence of throughflow has been investigated. We perform a weakly nonlinear stability analysis using a truncated Fourier series representation. The cubic Ginzburg-Landau equation (GLE) has been derived to include the influence of throughflow, rotation and gravity modulation. The solution of the Ginzburg-Landau equation (GLE) is used to quantify heat transport using the Nusselt number. Further, the time average Nusselt number is calculated. The influence of Peclet number (Pe), Darcy number (Da), Prandtl number (Pr), Taylor number (Ta), frequency of modulation (!) and the amplitude of modulation (1) on the stability of the system is investigated graphically. It is found that an increase in the positive value of the Peclet number is to enhance the heat transport whereas, an increase in the negative value of the Peclet number is to diminish the same. This leads to the conclusion that the throughflow plays a role of heat source/sink in the system depending on the sign of the Peclet number. The effect of increasing the value of the Taylor number is to diminish the heat transport. It has is found that the heat transport in the trigonometric type of gravity modulation lies between that of between triangular and square types of gravity modulation.