Impact of Thermal Non-equilibrium on Weak Nonlinear Rotating Porous Convection

Abstract

The consequences of local thermal non-equilibrium (LTNE) on both stationary and oscillatory weak nonlinear stability of gravity-driven porous convection in an incompressible fluid-saturated rotating porous layer are investigated. A stability map is drawn in the Darcy-Taylor and scaled Vadasz number plane to demarcate the regions of stationary and oscillatory convection, and thereby, co-dimension-2 points are determined. It is found that the effect of increasing interphase heat transfer coefficient is to enhance the region of stationary convection and decrease the region of oscillatory convection. The complex Ginzburg-Landau equations are derived using the multi-scale method, and pitchfork and Hopf bifurcations occur at stationary and oscillatory critical Darcy-Rayleigh numbers, respectively. The linear and nonlinear oscillatory neutral curves are illustrated, and at the quartic point, the transition from supercritical to subcritical bifurcations is identified for the governing parameters. The impact of LTNE model is to enhance the region of forward bifurcation and post-transient amplitude compared to LTE case. Heat transfer is obtained in terms of Nusselt number for both stationary and oscillatory convection. The region of enhancement in heat flux for oscillatory convection in the smaller scaled Vadasz number domain with increasing Darcy-Taylor number increases with increasing interphase heat transfer coefficient and the porosity-modified conductivity ratio. Keywords Nonlinear convection • Local thermal non-equilibrium • Porous medium • Rotation List of Symbols a Horizontal wave number c Specific heat Da Darcy number, K d 2 B R. N. Dayananda

Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects

“…Other aspect of the effect of thermal non-equilibrium on the onset of convection porous layer involving effects like rotation, variable viscosity, density maximum, heterogeneous permeability, and viscous dissipation have been studied by many researchers, e.g., Malashetty and Swamy [29], Shivakumara et al [30,31], and Barletta and Celli [32]. Further work using thermal non-equilibrium model has been given by Straughan [5,33], Dayananda and Shivakumara [34], and Santamaria-Holek [35].…”

Natural convection in a fluid saturating an anisotropic porous medium in LTNE: effect of depth-dependent viscosity

“…The problem of thermal convection in porous media in LTNE has been widely studied over the last years, starting from [23,24], in which both a linear and nonlinear analysis is carried out. Many papers analysed the effect of LTNE on the onset of convection, coupled to rotation and/or anisotropy [25][26][27][28][29], magnetic field [30], vertical throughflow [31,32], and also in non-horizontal porous layer [33][34][35]. Interesting results are obtained once the assumption of LTNE is combined with the Cattaneo's law for heat conduction in the solid matrix, since in such a case convection by means of oscillatory motions can occur [36][37][38][39].…”