Beginning Of Convection Research Articles

Convection in a Ferromagnetic Fluid Layer Influenced by Changeable Gravity and Viscosity

The motive of this work is to numerically evaluate the effect of changeable gravitational fields and varying viscosity on the beginning of convection in ferromagnetic fluid layer. The fluid layer is constrained by two free boundaries and varying gravitational fields that vary with distance across the layer. The authors hypothesized two categories of gravitational field variation, which can be subdivided into six distinct cases: (i) f(z)=z, (ii) f(z)=ez, (iii) f(z)=log(1+z), (iv) f(z)=−z, (v) f(z)=−z2, and (vi) f(z)=z2−2z. The normal mode method was applied, and the single term Galerkin approach was used to solve the ensuing eigenvalue problem. The results imply that, in the first three cases, the gravity variation parameter speeds up the commencement of convection, while, in the last three cases, the viscosity variation parameter and gravity variation parameter slow down the onset of convection. It was also observed that, in the absence of the viscosity variation parameter, the non-buoyancy magnetization parameter destabilizes the impact on the beginning of convection but, in the presence of the viscosity variation parameter, it destabilizes or stabilizes impact on the beginning of convection. In the case of oscillatory convection, the results illustrate that oscillatory modes are not permitted, suggesting the validity of the theory of exchange of stabilities. Additionally, it was also discovered that the system is more stable for case (vi) and more unstable for case (ii).

Combined impact of variable viscosity and throughflow effects on the onset of convection in an anisotropic porous layer

In the present article, the combined impact of vertical throughflow and temperature-reliant viscosity on the fluid-saturated anisotropic porous matrix is considered for investigation numerically by the Galerkin technique. The temperature-reliant viscosity is known to be exponential. The porous matrix is subject to continuous vertical throughflow. A parametric analysis is conducted by adjusting the following parameters: throughflow parameter, viscosity parameter, mechanical anisotropic parameter, and anisotropic thermal parameter. The findings reveal that the impacts of raising the viscosity parameter, downward throughflow parameter, and anisotropic thermal parameter delay the beginning of convection, whereas increasing mechanical anisotropic parameter and upward throughflow parameter destabilizes the porous system.

THE VARIABLE GRAVITY FIELD AND VISCOUS DISSIPATION EFFECTS ON THE CONVECTIVE INSTABILITY IN A POROUS LAYER WITH THROUGHFLOW: BRINKMAN MODEL

The present investigation aims to study the combined effect of viscous dissipation, vertical throughflow, and variable gravity field on the onset convective instability in a horizontal porous layer of finite thickness restricted between two permeable boundaries. The Brinkman extended Darcy model is accounted into the momentum equation of the governing flow through the porous layer. Also, linear, quadratic, and exponential gravity variation has been considered to study the present problem. The linear stability of the basic state is studied for the normal mode perturbations, and the corresponding eigenvalue problem is solved numerically using the bvp4c routine in MATLAB. The influence of throughflow parameter (Q), viscous dissipation (Ge), Darcy number (Da), and gravity variation parameter (λ) on the instability mechanism is discussed for the above three gravity field variations. The results indicate that the beginning of convection is postponed in the presence of Darcy number, throughflow, and gravity field parameter, while it is advanced in the presence of a significant viscous dissipation. Rac elevates to maximum at around 299% for linear variations of the gravity field, while it was 74% and 868% for quadratic and exponential varying gravity fields, respectively, when λ increases from 0 to 1.5. The value of Rac increased 6.5%, 5.4%, and 10.6%, respectively, for the linear, quadratic, and exponential gravity field variables, respectively, on changing the values of throughflow parameter from 0 to 1 and the increase in Rac is more for enhancing the value of the throughflow parameter from 1 to 2. Further, the system becomes more stable in the presence of an exponential gravity field.

UNSTABLE HELIUM SHELL BURNING ON ACCRETING WHITE DWARFS

AM Canum Venaticorum (AM CVn) binaries consist of a degenerate helium donor and a helium, C/O, or O/Ne white dwarf accretor, with accretion rates of . For accretion rates <10−6 M☉ yr−1, the accreted helium ignites unstably, resulting in a helium flash. As the donor mass and decrease, the ignition mass increases and eventually becomes larger than the donor mass, yielding a "last-flash" ignition mass of ≲0.1 M☉. Bildsten et al. have predicted that the largest outbursts of these systems will lead to dynamical burning and thermonuclear supernovae. In this paper, we study the evolution of the He-burning shells in more detail. We calculate maximum achievable temperatures as well as the minimum envelope masses that achieve dynamical burning conditions, finding that AM CVn systems with accretors ≳0.8 M☉ will undergo dynamical burning. Triple-α reactions during the hydrostatic evolution set a lower limit to the 12C mass fraction of 0.001–0.05 when dynamical burning occurs, but core dredge-up may yield 12C, 16O, and/or 20Ne mass fractions of ∼0.1. Accreted 14N will likely remain 14N during the accretion and convective phases, but regardless of 14N's fate, the neutron-to-proton ratio at the beginning of convection is fixed until the onset of dynamical burning. During explosive burning, the 14N will undergo 14N(α, γ)18F(α, p)21Ne, liberating a proton for the subsequent 12C(p, γ)13N(α, p)16O reaction, which bypasses the relatively slow α-capture onto 12C. Future hydrodynamic simulations must include these isotopes, as the additional reactions will reduce the Zel'dovich–von Neumann–Döring length, making the propagation of the detonation wave more likely.

Convective stability of a horizontal layer of chemically active liquid in the presence of transverse flow of reactant

This work investigates conditions of the appearance of convection in a horizontal layer of a chemically active liquid with penetrable boundaries held at the same temperature. Heat is liberated throughout the volume of the liquid as a result of a zero-order reaction. There is uniform transverse movement of reactant through the penetrable boundaries at a constant rate. The possibility of the existence of time-independent processes of heat transfer in such a system, with free convection absent, was analyzed in [i]. The linear problem of convective stability under stable heat-conduction conditions, described in [i], is solved here. We obtained, for different values of the parameters, limits of stability defining the threshold of the beginning of convection. The convective stability o~ reacting liquids in the absence of sparging was examined in [2-4]. The effect of transverse movement on the convective stability of a horizontal layer of nonreactive liquid was studied in [5].