An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

Abstract

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the GinzburgLandau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.

Synchronous and asynchronous boundary temperature modulations of Bénard–Darcy convection

“…The following conclusions may be summarized from the figures documented in the paper: These conform to reported results of earlier works pertaining to temperature/gravity modulated Bé nard-Darcy convection [27,28].…”

“…(27) it has been assumed that the modulation is of small amplitude and hence E ¼ d 2 E 2 . This is in keeping with the assumption of Govender [12] and Siddheshwar et al [28,29]. With the aim of deriving the Ginzburg-Landau equation for the amplitude of convection, we now use the following asymptotic expansion in Eq.…”

Throughflow and g-jitter effects on binary fluid saturated porous medium

“…The linear and nonlinear stabilities of double diffusive convection in porous media have been studied extensively in the presence of uniform temperature and concentration gradients by Nield and Bejan [6] and Shivakumara and Sumithra [20] . Siddheshwar et al [21] investigated temperature and gravity modulation effects on double diffusive convection in porous media. They found that both modulations can be used simultaneously to enhance or diminish heat and mass transfer in the system while considering a weakly nonlinear theory for stationary mode.…”

“…They found that both modulations can be used simultaneously to enhance or diminish heat and mass transfer in the system while considering a weakly nonlinear theory for stationary mode. Bhadauria [22] also analyzed the additional effects of internal heating and anisotropy of Siddheshwar et al [21] . He found that internal heat and anisotropy also can be used to enhance or diminish heat and mass transfer in the system.…”

Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above

“…Recently, Strong [20] brational thermosolutal convection in a horizontal Darcy porous layer and constructed the neutral curves for synchronous, subharmonic and quasiperiodic instability modes. More recently, Siddheshwar et al [21] performed a weakly nonlinear analysis for this problem using Ginzburg-Landau equation in the presence of small amplitude oscillations. In the present study, our aim is to investigate the effect of vertical harmonic vibration on the onset of thermosolutal convection for a wide range of modulation parameters in a Brinkman porous medium heated from above.…”