Roberta Nibbi

We develop a theory for thermal convection in a double porosity material of Brinkman–Forchheimer type when there is a single temperature. The saturating fluid is one of Kelvin–Voigt type, and the equation for the temperature is one due to C.I. Christov. It is shown that the global nonlinear stability threshold coincides with the linear stability one. A thoroughly analytical discussion of both linear instability analysis and global nonlinear energy stability is provided. Numerical results show that the relative permeability and Brinkman viscosity between the macro and micro pores are key parameters which play a dominant role in determining the critical Rayleigh number for the onset of convective motions.

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise. Article Highlights: A two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem. The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven. Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

In this paper, once and for all, we want to strongly affirm that the thermodynamic framework for complex materials based on extra fluxes can lead to more severe restrictions with respect to the virtual powers scheme. Even if formally converging to the same final constitutive results, it seems only the consequence of an inappropriate approach to the problem itself. To achieve this goal, we proceed with a quick critical comparison between the different steps of the two methodologies: by way of example, we address novel constitutive settings for the third-order infinitesimal elasticity and viscoelasticity with an extension to thermo-elasticity, based on nonlocal revisited Green-Naghdi like thermal properties. Finally, suitable thermodynamic restrictions are derived from the generalized Clausius-Duhem inequality.

We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for self-gravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes.

This paper studies a model for thermoelasticity where the body has a double porosity structure. There are the usual pores associated to a porous body, herein called macro pores. In addition, the solid skeleton contains cracks or fissures that give rise to a micro porosity. The fully anisotropic situation is analyzed. We firstly establish uniqueness of a solution to the boundary‐initial value problem when the elastic coefficients are sign indefinite and are required to satisfy only major symmetry. Furthermore, in the quasi‐equilibrium case, where the solid acceleration is neglected, we demonstrate that a solution to the boundary‐initial value problem with zero boundary conditions will decay to zero in a certain sense, under the assumption that there are no sources and external body force involved.

We consider a model for flow in a porous medium which has a double porosity structure. There is the usual porosity herein called macro porosity, but in addition, we allow for a porosity due to cracks or fissures in the solid skeleton. The cracks give rise to a micro porosity. The model considered also allows for temperature effects with a single temperature T . This paper analyses three aspects of structural stability. The first establishes continuous dependence of the solution on the interaction coefficient between the velocities associated with the macro and micro porosity. The second analyses continuous dependence on the viscosity coefficients, while the third establishes continuous dependence on the radiation constant when Newton’s law of cooling is involved on the boundary.

In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise to micro pores. The temperatures in the solid skeleton and in the fluids in the macro and micro pores are all allowed to be independent. After presenting the general model, we derive a result of universal stability, which guarantees exponential decay of the solution for all initial data. We further present a concrete example by specializing the model to the problem of thermal convection in a layer heated from below.