Study of Heat Transport in Bénard-Darcy Convection with g-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids

Abstract

The effects of temperature-dependent viscosity, gravity modulation and thermomechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg-Landau model. The effect of gravity modulation is to decrease the Nusselt number, N u and variable viscosity leads to increase in N u. The thermo-mechanical anisotropies have opposite effect on N u with thermal anisotropy decreasing the heat transport.

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].…”

“…With the aim of deriving the Ginzburg-Landau equation for the amplitude of convection, we now use the following asymptotic expansion in Eq. (27) [6]…”

“…Following Siddheshwar et al [27], the first-and second-order solutions may be shown to be the following:…”

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

“…Nonlinear energy stability theory has been derived by Richardson and Straughan (1993) for the problem of convection in porous medium when the viscosity depends on the temperature for vanishingly small initial data thresholds, Payne et al (1999) has been studied the unconditional nonlinear stability for temperature sensitive fluid in porous media, further more Payne and Straughan (2000) extend their analysis for the cases when the viscosity variation may be quadratic or when convection is penetrative. Qin and Chadam (1996) studied the nonlinear energy stability by considering the temperature dependent viscosity and inertial drag by taking higher-order approximations for the viscosity-temperature and density-temperature relation, Nield (1996), Holzbecher (1998) studied the thermal instability for the variable viscosity fluid in porous layer using the FAST-C(SD) code for numerical modeling, Rees et al (2002), Siddheshwar and Chan (2004), Vanishree and Siddheshwar (2010) investigated the linear thermal instability for the temperature dependent fluid using weighted residual technique, Siddheshwar et al (2012b) studied the effects of variable viscosity and the gravity modulation on the heat transfer in an anisotropic porous medium, Srivastava et al (2013) analyse the non-linear effect of internal heat source and gravity modulation on the heat transfer for variable viscosity fluid in an anisotropic porous layer.…”

A study on the onset of thermally modulated Darcy–Bénard convection

“…(35), we use the standard Fredholm solvability condition, which requires that the right-hand side lie in the kernel of the operator. Applying the solvability condition [18,21,22] to the second-order system (35), the correction Rayleigh number Ra (2) c can be, on rearrangement, obtained in the form…”