Effect of Vertical Modulation on the Onset of Filtration Convection

Abstract

The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal layer of fluid saturating a porous medium. A constant temperature distribution is assigned on the rigid boundaries, so that there exists a vertical temperature gradient. The mathematical model is described by equations of filtration convection in the Darcy-Oberbeck-Boussinesq approximation. The linear stability analysis for the quasiequilibrium solution is performed using Floquet theory. Employment of the method of continued fractions allows derivation of the dispersion equation for the Floquet exponent σ in an explicit form. The neutral curves of the Rayleigh number Ra versus horizontal wave number α for the synchronous and subharmonic resonant modes are constructed for different values of frequency Ω and amplitude A of vibration. Asymptotic formulas for these curves are derived for large values of Ω using the method of averaging, and, for small values of Ω, using the WKB method. It is shown that, at some finite frequencies of vibration, there exist regions of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility to convection. (2000). 76E15, 76S05, 35Q35. Mathematics Subject Classification

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

“…(16)- (17) was discussed by Strong [8] and they proved that none of the coefficients θ n can become zero for a solution of a system (16). From Eq.…”

“…Zenkovskaya and Rogovenko [6] and Govender [7] have investigated the effect of vertical vibration on the onset of convection in a Darcian porous layer subject to high frequency and low-amplitude vibrations respectively. Recently, Strong [8] reported the results of this problem for arbitrary range of modulation parameters by the use of continued fraction method. There are also few recent works available in the literature dealing with thermovia e-mail: thirumalaisiva@gmail.com brational convection in a more general Brinkman porous medium (see [9][10][11][12]).…”

Study of Heat and Mass Transport in Bénard-Darcy Convection with G-Jitter and Variable Viscosity Liquids in a Porous Layer with Internal Heat Source

“…Gravity modulation can be taken as an effective mechanism to control the heat transfer by an external regulation. Documented article in this area are given by Malashetty and Padmavathi (1997), Rees and Pop (2000), Rees and Pop (2001), Rees and Pop (2003), Govender (2005), Kuznetsov (2005), Kuznetsov (2006b), Kuznetsov (2006a), Strong (2008), Strong (2009), Razi et al (2009), Vanishree and Siddheshwar (2010, Siddheshwar et al (2012a), Swamy et al (2013), Swamy (2014).…”