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The interplay between variations in permeability and viscosity on the onset of local thermal non-equilibrium in Darcy–Bénard convection has been investigated. Specifically, permeability is modeled as decreasing linearly with depth, while viscosity decreases exponentially. The validity of the principle of exchange of stabilities is confirmed. A linear instability analysis of the quiescent state is conducted through normal mode decomposition of disturbances, with threshold values for instability onset computed numerically using the Galerkin method. The individual and combined effects of increasing the variable permeability and viscosity parameters on the instability characteristics of the system are examined in detail, highlighting both commonalities and distinctions. It is observed that increasing each parameter individually hastens the onset of convection. However, their combined influence produces both stabilizing and destabilizing effects under certain parametric conditions. In all scenarios, an increase in the scaled interphase heat transfer coefficient consistently delays the onset of convection, whereas a higher ratio of porosity-modified conductivities has the opposite effect. Furthermore, the size of the convection cells remains unchanged at the extreme values of the scaled interphase heat transfer coefficient. [ABSTRACT FROM AUTHOR]

The study explores the initiation of two-dimensional double-diffusive convection in a horizontal layer of an electrically conducting non-Newtonian Navier–Stokes–Voigt fluid, subjected to a uniform vertical magnetic field and cross-diffusion effects. The numerical results are presented by obtaining the analytical solutions for both steady and oscillatory onset scenarios. The viscoelastic nature of the fluid either delays or hastens the onset of oscillatory convection depending on the strength of solute concentration. The analysis also uncovers contradictions in the linear instability characteristics with and without cross-diffusion terms, even when other input parameters are identical. Under specific conditions, three novel phenomena are observed that are not typically seen in double-diffusive cases: (i) an electrically conducting Navier–Stokes–Voigt fluid layer, initially linearly stable in the presence of a magnetic field, can become destabilized with the addition of a heavy solute to the fluid's bottom; (ii) a stable double-diffusive electrically conducting Navier–Stokes–Voigt fluid layer can be destabilized by the application of a magnetic field; and (iii) the requirement of three critical values of the thermal Rayleigh number to determine linear instability, as opposed to the usual single value owing to the existence of disconnected closed convex oscillatory neutral curves. The results are shown to align with previously published findings in the limiting cases. [ABSTRACT FROM AUTHOR]

The stability of thermally driven buoyant flow of a viscoelastic fluid saturating a vertical porous layer with viscosity depending linearly on temperature is investigated numerically. The rheological behavior of the fluid is described through the Oldroyd-B model, leading to a modified Darcy's law of momentum transfer in the porous medium. The study explores the linear stability of the base flow by analyzing the behavior of normal modes of perturbation. Neutral stability curves and the critical Darcy–Rayleigh number are determined for a wide range of viscoelastic and viscosity parameters. Transition curves from stability to instability in the viscoelastic parameters space are also provided for both constant and variable viscosity cases. Additionally, the results for Newtonian, Boger, and Maxwell fluids are delineated as particular cases from this study. [ABSTRACT FROM AUTHOR]

The stability of buoyant flow in an infinite vertical fluid layer bounded by imperfectly conducting rigid walls, called imperfectly conducting eigenflows, is discussed. The third kind boundary conditions describing heat transfer to the external environment are applied to perturbations in temperature. The linear stability analysis is carried out numerically by employing the Chebyshev collocation method. Instability arises when the Grashof number G exceeds its critical value, which depends on the Prandtl number P r and the Biot number B i. It is found that the onset of instability changes dramatically depending on the magnitude of Prandtl and Biot numbers particularly when the instability is through the traveling-wave mode. The numerical results show that the Biot number plays a pivotal role in determining the transition Prandtl number P r T at which the instability switches over from one mode to another mode. The novel outcomes suggest the presence of a single P r T for B i < 2.1739 while three distinct values of P r T for B i ≥ 2.1739. The departure from the conventional single value typically observed at isothermal boundaries signifies the complexity of the instability mechanism. [ABSTRACT FROM AUTHOR]