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Investigating thermal convection within porous media permeated by fluids and micro-organisms stands as a significant inquiry with broad relevance across geophysical and engineering domains. Studying convection within porous media can aid in controlling temperature and nutrient distribution for cell growth and tissue regeneration, as well as the efficiency of biofuel fermentation and production processes. Hence, the primary objective of this study is to investigate the influence of time-periodic gravitational forces on Darcy–Brinkman bio-thermal convection within a porous medium layer. This medium is saturated with a Newtonian fluid that encompasses gyrotactic micro-organisms. The gravity modulation amplitude is assumed to be very small. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection. The heat transport, measured by the Nusselt number, is governed by a non-autonomous Ginzburg–Landau equation. The research explores the influence of several parameters on heat transport, including the Vadaszs number, the modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency, and modulation amplitude. The results are presented graphically, illustrating the impact of these parameters on heat transfer. The findings reveal that both the Vadaszs number and the modulation amplitude have a positive effect on heat transfer, enhancing the process. On the other hand, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. Furthermore, a comparison between the modulated and unmodulated systems indicates that the modulated systems have a more significant influence on the stability problem compared to the unmodulated systems. This highlights the effectiveness of external modulation in controlling heat transport within the system. [ABSTRACT FROM AUTHOR]

In this study, within the framework of electron magnetohydrodynamics, taking into account thermomagnetic phenomena, we obtained a new large-scale instability of the α -effect type, which ensures the generation of large-scale vortex and magnetic fields. This instability occurs in a flat layer of temperature-stratified plasma under the influence of an external uniform magnetic field inclined relative to the layer, combined with a small-scale external force having zero helicity. The external force is presented as a source of small-scale oscillations in the speed of electrons with a low Reynolds number R ≪ 1. The presence of a small parameter in the system allowed us to apply the method of multiscale asymptotic expansions to derive nonlinear equations for vortex and magnetic disturbances. These equations were obtained in third-order Reynolds number. Using solutions for the velocity field in zero order in Reynolds number, we determined the average helicity H = v 0 · rot v 0 ¯ and its relation to the α -effect. A necessary condition for the generation of average helicity in stratified magnetized plasma is the inclined orientation of the external magnetic field and the presence of a small-scale force. A new effect related to the influence of thermal force (the Nernst effect) on large-scale instability is discussed. It is shown that an increase in the Nernst parameter leads to a decrease in the amplification factor α and thereby prevents the development of large-scale instability. With the help of numerical analysis, stationary solutions to the vortex and magnetic dynamo equations in the form of localized structures like nonlinear waves of the Beltrami were obtained. [ABSTRACT FROM AUTHOR]

Thermotaxis, the movement in response to temperature gradients, is a widely observed phenomenon prevalent in various natural occurrences, spanning from biological processes to the migration of colloidal particles. Results from studies of thermotaxis may inspire the development of new technologies, such as sensors that mimic the navigation strategies of organisms that respond to temperature gradients. By adjusting temperature gradients through temperature modulation, microorganisms can be manipulated. Therefore, the main aim of this study is to investigate the effect of thermal modulation on biothermal convection in a layer of liquid that contains thermotactic microorganisms. In this study, we explore the impact of non-uniform, time-varying boundary conditions on the system. Our study involves an analysis of weak nonlinear stability based on the Ginzburg-Landau model, leading to the derivation of heat (Nusselt number Nu) and mass (Sherwood number Sh) transfer coefficients that are dependent on various system parameters. In-phase modulation (IPM) has a relatively weak effect on both heat transfer and mass transfer, which closely resembles the unmodulated scenario. On the contrary, in the cases of out-of-phase modulation (OPM) and lower bound modulation (LBM), significant changes in heat and mass transfer are observed. It has been determined that the Peclet number, a parameter characterizing thermotaxis, can either induce stabilization or destabilization within the system. TM instability. [ABSTRACT FROM AUTHOR]

In recent years, experiments with flows of liquid metals in a helical magnetic field have been actively carried out. The study of the processes of mixing and crystallization of a liquid metal is of practical importance for metallurgy. With the development of nanotechnology, more and more new types of nanofluids (hybrid, ternary nanofluids) are being synthesized, and the thermophysical characteristics of which can compete with liquid metals. This circumstance served as a motivation for conducting this theoretical study. In this study, the criterion for the onset of convection in a Darcy–Brinkman porous medium layer saturated by an electrically conductive nanofluid under a helical magnetic field is investigated. The Brownian motion and thermophoresis effects are combined in the model for nanofluids, whereas the Darcy–Brinkman model is used for porous media. Instead of prescribing the nanoparticle volume fraction on the borders, we adopted a boundary condition in which the nanoparticle flow is considered to be zero. In the absence of a temperature gradient, a new type of instability in a helical magnetic field in a thin layer of a nanofluid is considered. The growth rate and the region of the development of this instability are numerically obtained depending on the profile of the azimuthal magnetic field (the magnetic Rossby number Rb) and the radial wave number k. In the presence of temperature, the stationary regime of nonuniformly rotating magnetoconvection is studied. The accurate analytical equation for the critical Rayleigh–Darcy number in terms of various non-dimensional parameters is determined using the linear stability theory. The results show that rotation and the axial (vertical) part of the helical magnetic field retard the onset of convection. While the azimuthal part of the helical magnetic field has a destabilizing effect at positive Rossby numbers Rb. The conditions for stabilization and destabilization of stationary convection in a helical magnetic field are determined for metal oxide, metallic, and semiconductor nanofluids. [ABSTRACT FROM AUTHOR]

The chaotic behavior of thermal convection in a nonuniformly rotating electrically conductive fluid under the action of a constant vertical magnetic field B0 is studied. In the presence of vertical temperature gradients ∇T0 and the thermo-electromotive force coefficient ∇Tα, thermomagnetic (TM) instability arises, leading to the generation of magnetic fields. The magnetic field B1 excited by the effect of the Biermann battery is directed perpendicular to the plane of the vectors ∇T0, ∇Tα and the gradient of temperature disturbances ∇T1. This magnetic field changes the heat transfer regime, and due to the effects of convective heat transfer and Righi-Leduc, a positive feedback is established, which leads to an increase in magnetic field disturbances. Using the truncated Galerkin method, a nonlinear dynamic system of equations is obtained, which describes the processes of generation and regeneration of the magnetic field. Numerical analysis of these equations showed the existence of a regular, quasi-periodic, and chaotic behavior of magnetic field disturbances, accompanied by its inversions. Applying the method of perturbation theory to the nonlinear dynamic system of equations, we obtained the Ginzburg-Landau equation for the weakly nonlinear stage of nonuniformly rotating magnetic convection, taking into account TM effects. The solution of this equation showed that the stationary level of the generated magnetic fields increases with allowance for the influence of the TM instability. [ABSTRACT FROM AUTHOR]

In this paper, the three-dimensional Casson flow of a ternary hybrid nanofluid over a porous linearly stretching/shrinking surface in the presence of an external magnetic field is considered. The surface deformation process is described by introducing two parameters of stretching/shrinking in the lateral directions. Using similarity transformations, the basic set of nonlinear partial differential equations is converted into ordinary differential equations. An exact analytical solution to this boundary value problem is obtained. The influence of the Casson parameter, magnetic field, porosity medium, and stretching/shrinking parameter, taking into account mass transpiration, on the velocity profiles and the skin friction coefficients is considered in detail. It has been established that the results obtained in some limited cases are in excellent agreement with the available data. Tables show the new results for the skin friction coefficients in the lateral directions (x and y) for different variants of surface deformation. [ABSTRACT FROM AUTHOR]

The paper investigates the stability of small axisymmetric disturbances in a nonuniformly rotating viscous electrically conductive fluid taking into account galvanometric and thermo-magnetic phenomena. In the local geometrical optics approximation, we obtained a dispersion equation taking into account the Hall, the Nernst, the Right-Leduc effects and gradients of temperature ⛛T0 and thermo-electromotive force coefficient ⛛α in constant magnetic field B0 0 and gravitational field g. The growth rates of thermomagnetic instability (TMI) in a nonuniformly rotating electrically conducting fluid without an external magnetic field (B0 = 0) are obtained for the case of "smooth" (a weakly inhomogeneous medium) gradients (⛛T0 and ⛛α). The regions of the development of TMI are established depending on the profile of the angular velocity of rotation (Rossby number Ro) and the radial wave number kR. The conditions under which the generation of a magnetic field with sharp gradients of temperature and thermo-electromotive force coefficient in the media with low (σ → 0) and high (σ → ∞) conductivity are found. The regions of the development of the Hall magnetorotational instability in an external magnetic field (B0 ≠ 0) are established depending on the profile of the angular rotation velocity (Rossby number Ro) and the axial wavenumber kz. The growth rates of TM instabilities for the propagation of perturbations with a wave vector k in the radial direction k∥eR are obtained taking into account the Nernst effect in an external magnetic field B0, the Righi-Leduc effect, the inhomogeneity of the equilibrium temperature and specific thermopower, and the buoyancy force in a temperature-stratified medium. [ABSTRACT FROM AUTHOR]

This study investigates the combined influence of the Hall current and the axial magnetic field on the criterion for the onset of convection in a nonuniformly rotating layer of electrically conductive nanofluids taking into account the effects of Brownian diffusion and thermophoresis. The analytical and numerical computations are presented for water-based nanofluids with alumina nanoparticles. In the absence of a temperature gradient, a new type of magnetorotational instability in an axial magnetic field in a thin layer of a nanofluid is considered. The growth rate and regions of development of this instability are numerically obtained depending on the angular velocity profile (the Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, the stationary regime of nonuniformly rotating magnetoconvection is studied. The exact analytical expression for critical Rayleigh number Ra s t is obtained in terms of various nondimensional parameters. The results indicate that the increase in the Lewis number, the modified diffusivity ratio, and the concentration Rayleigh number is to accelerate the onset of convection. The increase in the Hall current parameter can delay or enhance the onset of convective instability. Rotation profiles with negative Rossby numbers lower the threshold for the development of thermal instability and stimulate the onset of convection. The conditions for stabilization and destabilization of stationary convection in an axial magnetic field are determined. The results are represented graphically and verified numerically. [ABSTRACT FROM AUTHOR]

In this work, the processes of spontaneous generation of magnetic fields by Rayleigh–Benard convection in a thin layer of plasma in a constant gravitational field are investigated. The values of the critical Rayleigh number for stationary convection are obtained, and the criteria for the occurrence of instability leading to the generation of magnetic fields are determined within the framework of electron magnetic hydrodynamics (EMHD). The weakly nonlinear regime of magnetic fields generation is studied using the method of perturbation theory with respect to the small supercriticality parameter ε = (Ra − Ra c) / Ra c of the stationary Rayleigh number Ra c . A nonlinear equation of the Ginzburg–Landau type is obtained, which describes the evolution of the stationary level of excited magnetic fields. [ABSTRACT FROM AUTHOR]

In this paper we have studied the large-scale instability in a rotating stratified moist atmosphere with a small-scale turbulence. The axis of rotation of the medium is deviated from the vertical direction. The turbulence is excited by an external small-scale force with zero helicity and a low Reynolds number. The nonlinear equations of a vortex dynamo were obtained on the basis of the method of multiscale asymptotic expansions. The linear instability and stationary nonlinear modes were studied. The solutions in a form of localized vortex structures were obtained. [ABSTRACT FROM AUTHOR]

This paper studies, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient ▽T0 and thermoelectromotive coefficient gradient ▽α . The influence of the generation of a toroidal magnetic field by TM instability on the convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field B0 || OZ is established. By applying the method of perturbation theory for the small parameter ϵ = √ Ra-Rac/Rac of the supercriticality of the stationary Rayleigh number Rac, a nonlinear equation of the Ginzburg-Landau type was obtained. This equation describes the evolution of the finite amplitude of perturbations. Numerical solutions of this equation made it possible to determine the heat transfer in the fluid layer with and without TM effects. It is shown that the amplitude of the stationary toroidal magnetic field noticeably increases with allowance for TM effects. [ABSTRACT FROM AUTHOR]

The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number Ro) and on the profile of the external azimuthal magnetic field (magnetic Rossby number Rb). The non-linear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of convective flows. The criteria of the occurrence of chaotic movements are found. It depends on the parameters of convection: dimensionless numbers of Rayleigh Ra, Chandrasekhar Q, Taylor Ta, and external azimuthal magnetic field with the Rossby magnetic number Rb for Rayleigh (Ro = −1) and Kepler profiles of the angular rotation velocity of the medium. [ABSTRACT FROM AUTHOR]