English abstract
The present study considers the dynamics of a viscous porous fluid layer in which the
fluid is in local thermal non-equilibrium, obeying the Darcy-Brinkman equations in
the presence of the Maxwell-Cattaneo (MC) effect. We first examine the layer's linear
stability and then address the nonlinear problem numerically.
The linear stability is investigated when fluid and solid obey the MC relation between
the heat flux and the temperature. We first prove that the layer can support only steady
convection in the absence of the MC effect. The introduction of the MC effect, whether
in the solid only, in the fluid only, or in both, is accompanied by the appearance of
oscillatory modes. The stability boundary of the oscillatory mode bifurcates from that
of the steady through a Hopf bifurcation. The dependence of the stability boundary on
the different parameters of the problem is discussed in detail. The preferred mode of
convection is identified in the space of the parameters.
When the MC effect is present only in the solid, the layer can support oscillatory
convection if the thermal interphase interaction coefficient, H (which measures the
degree of nonlocal equilibrium), is large enough. On the other hand, when the MC
effect is present in the fluid only, oscillatory convection occurs for a small but non zero interaction coefficient. The presence of the MC effect in both fluid and solid
introduces a new situation when oscillatory convection can occur for intermediate
values of H.
Besides, this study also investigated the impact of the Maxwell-Cattaneo effect on the
flow and heat transfer dynamics of a porous medium in a local thermal non equilibrium (LTNE) state by focusing on the quantitative investigation of natural
convection in a square porous cavity filled with water and crude oil. The Darcy Brinkman model for the fluid flow is utilized by considering the MC relation of
temperature and heat flux for the fluid and solid. The role of the pertinent parameters
such as the Rayleigh number, thermal conductivity ratio, Darcy number, and Brinkman
number on streamlines, isotherms, and the average Nusselt numbers of fluid and solid
were also investigated and discussed in detail.
