On the linear stability analysis of a Maxwell fluid with double-diffusive convection

Abstract

a b s t r a c tThe problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy-Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy-Rayleigh numbers is investigated. Analytical expressions of the critical Darcy-Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy-Rayleigh number for over-stability. In the limiting case some previously published results are recovered.

Linear and nonlinear stability analysis of binary Maxwell fluid convection in a porous medium

“…Analogous studies on viscoelastic fluid convection in porous media are those by Siddheshwar and Srikrishna [25], Shekar and Jayalatha [26], Kim et al [27], Tan and Masuoka [28], Sheu [29,30] and Shivakumara et al [31]. Awad et al [32] very recently studied double diffusive convection in Newtonian liquids (see also references therein) and analogous problems in porous media were studied by Wang and Tan [33].…”

Double-diffusive convection in a viscoelastic fluid

“…The heat transport in Rayleigh-Beńard convection in viscoelastic liquid with/without gravity modulation using a most minimal representation of Fourier series and a representation with higher modes is studied by Siddeshwar et al [23] and shown that the effect of gravity modulation is stabilizing thereby leading to a situation of reduced heat transfer. The problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media by using the modified Darcy-Brinkman model has been considered by Awad et al [24] and analytical expression of the critical Darcy-Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Recently, Wang and Tan [25] have studied the double-diffusive convection of viscoelastic fluid with Soret effect in a porous medium by using a modified-Maxwell-Darcy model and have shown that for oscillatory convection the system is destabilizing in the presence of Soret effect.…”

Energy Stability of Benard-Darcy Two-Component Convection of Maxwell Fluid

“…An analogous problem in Newtonian fluid-saturated porous media is now well investigated (see the monographs by Bejan (2004) , Nield and Bejan (2006), Vafai (2000) and Alloui et al (2010), and references therein). Some aspects of the problem involving a viscoelastic liquid were studied by Sharma and Sunil (1994), Haro et al (1996), Srikrishna (2001), Srikrishna (2001)-(2003), Kim et al (2003), Kumar and Singh (2006), Fu et al (2007) , Shivakumara and Sureshkumar (2008), Long et al ((2009Long et al (( )-(2008), Malshetty et al (2009), Malashetty and Kulkarni (2009),Tan and Masuoka (2007, Wang and Tan (2008), and Awad et al (2010). The main result that can be conjured up from these works focusing on the onset of convection is that Maxwell fluids are generally more unstable than Jeffreys liquids while Rivlin-Ericksen and Newtonian liquids are comparatively more stable.…”