Convective Instability in a Horizontal Porous Layer Saturated Without Oil and a Layer of Gas Underlying It

The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy‐driven convection in a saturated porous medium

“…3,6,20 Kaviany 20 investigated the onset of thermal convection in a porous medium both theoretically and experimentally. Kim et al, 25 Kim et al, 26 and Kim and Kim 27 studied the onset of buoyancy-driven flow in a porous medium without basic flow. Ennis-King and Paterson 28 Ennis-King et al 29 and Hong and Kim 30 performed a linear stability analysis to investigate the role of permeability anisotropy on the onset of convection.…”

The linear stability of a developing thermal front in a porous medium: The effect of local thermal non-equilibrium

“…In that paper the authors introduce an approximation, named the quasi-steady-state approximation, which allows the authors to determine the growth rates of individual modes at chosen times. This approximation is slightly different from that made in [13] and therefore the critical time and wavenumber they compute are also slightly different.…”

“…Kim et al [12] also considered this internal heat generation problem where the basic state was still time-dependent and employed amplification theory. Later Kim et al [13] considered an application to an oil-saturated medium with gas diffusion from below, while Kim and Kim [14] determined criteria for the onset of convection in a porous layer where the temperature of the lower surface increases linearly with time. Again, amplification theory is applied.…”

“…Again, amplification theory is applied. Finally, it is essential to mention the work of Riaz et al [15] who undertook both a linear stability analysis and strongly nonlinear simulations of the problem considered by Kim et al [13]. In that paper the authors introduce an approximation, named the quasi-steady-state approximation, which allows the authors to determine the growth rates of individual modes at chosen times.…”

Linear stability analysis of a fluid-saturated porous layer subjected to time-dependent heating

“…Kim et al [11] analyzed the onset of Rayleigh-Bénard convection by employing the propagation theory which employs the thermal penetration depth as a length scaling factor and transforms the linearized equations into the similar forms. Later, Kim et al [12] applied propagation theory to the buoyancy-driven convection in the porous media. Tan and Thorpe [13] proposed maximum-Rayleigh number criterion wherein the temperature profile assumed to be linear within Z = Z max (t), and defined the onset time when newly defined transientRayleigh number reached the conventional steady-state Rayleigh number.…”