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Electrothermal convection in a poorly conducting fluid in an alternating electric field of a horizontal capacitor is studied. The nonlinear regimes of electric convection in weightlessness are studies at low frequencies of the electric field on the basis of the pentamodal model within the framework of the electroconductive charge formation mechanism. Hysteresis transitions between two different synchronous and subharmonic regimes are found to exist. Transitions to chaos occur by means of either interemittance or a subharmonic cascade.

The global solvability and local uniqueness of boundary value problem’s solutions for stationary magnetic hydrodynamic equations for heat conducting fluid with variable coefficients are proved. Maximum and minimum principle for temperature is established. Multiplicative control problem for the model under consideration is studied. The role of the control is played by the high thermal conductivity coefficient. For the power-low thermal exchange and the thermal conductivity coefficients the optimality system for considered control problem is obtained. The solvability of control problem is proved under minimal requirements for the smoothness of control; and optimality system is derived with minimal smoothness of the specified functions of boundary value problem.

The evolution of a viscous conducting fluid flow on a rotating plate in the presence of a magnetic field is studied. The analytical solution of the three-dimensional time-dependent magnetohydrodynamics equations is found. In this case, the full magnetic induction equation is used, i.e., both the dissipation effect and the energy dissipation as a result of the electric current flow are taken into account. The fluid, together with the bounding plane, rotates as a whole at a constant angular velocity about a direction not perpendicular to the plane. The velocity field and the induced magnetic field in the flow of viscous electrically conducting fluid that occupies a half-space bounded by a flat wall are determined. The motion of wall is considered in a series of particular cases. Based on the results obtained, the individual structures of the near-wall boundary layers are investigated

Numerical and physical simulations of the magnetohydrodynamic mixed convective flow of electrically conducting fluid along avertical magnetized and symmetrically heated plate with slip velocity and thermal slip effects have been performed. The novelty of the present work is to evaluate heat transfer and magnetic flux along the symmetrically magnetized plate with thermal and velocity slip effects. For a smooth algorithm and integration, the linked partial differential equations of the existing fluid flow system are converted into coupled nonlinear ordinary differential equations with specified streaming features and similarity components. By employing the Keller Box strategy, the modified ordinary differential equations (ODEs) are again translated in a suitable format for numerical results. The MATLAB software is used to compute the numerical results, which are then displayed in graphical and tabular form. The influence of several governing parameters on velocity, temperature distribution and magnetic fields in addition to the friction quantity, magnetic flux and heat transfer quantity has been explored. Computational evaluation is performed along the symmetrically heated plate to evaluate the velocity, magnetic field, and temperature together with their gradients. The selection of the magnetic force element, the buoyancy factor 0<ξ<∞ , and the Prandtl parameter range 0.1≤Pr≤7.0 were used to set the impacts of magnetic energy and diffusion, respectively. In the domains of magnetic resonance imaging (MRI), artificial heart wolves, interior heart cavities, and nanoburning systems, the present thermodynamic and magnetohydrodynamic issuesare significant.

Rayleigh–Bénard convection is a fundamental fluid dynamics phenomenon that significantly influences heat transfer in various natural and industrial processes, such as geophysical dynamics in the Earth’s liquid core and the performance of heat exchangers. Understanding the behavior of conductive fluids under the influence of heating, rotation, and magnetic fields is critical for improving thermal management systems. Utilizing the Boussinesq approximation, this study theoretically examines the nonlinear convection of a planar layer of conductive liquid that is heated from below and subjected to rotation about a vertical axis in the presence of a magnetic field. We focus on the onset of stationary convection as the temperature difference applied across the planar layer increases. Our theoretical approach investigates the formation of parallel rolls aligned with the magnetic field under free–free boundary conditions. To analyze the system of nonlinear equations, we expand the dependent variables in a series of orthogonal functions and express the coefficients of these functions as power series in a parameter ϵ. A solution for this nonlinear problem is derived through Fourier analysis of perturbations, extending to O(ϵ8), which allows for a detailed visualization of the parallel rolls. Graphical results are presented to explore the dependence of the Nusselt number on the Rayleigh number (R) and Ekman number (E). We observe that both the local Nusselt number and average Nusselt number increase as the Ekman number decreases. Furthermore, the flow appears to become more deformed as E decreases, suggesting an increased influence of external factors such as rotation. This deformation may enhance mixing within the fluid, thereby improving heat transfer between different regions.

The proposed planer layer dynamo physical model has real-world applications, especially in the Earth’s liquid core. Thus, in this paper, an attempt is made to understand the finite amplitude convection when there exists a coupling between the Lorentz force and the Coriolis force. In particular, the effect of a horizontally applied magnetic field is studied on the Rayleigh–Bénard convection (RBC) that contains the electrically conducting fluid and rotates about its vertical axis. Free–free boundary conditions are assumed on the geometry. Attention is focused on the nonlinear convective flow behavior during the occurrence of cross rolls which are perpendicular to the applied magnetic field and parallel to the rotation axis. The visualization of cross rolls is achieved using the Fourier analysis of perturbations up to the O(ε8). The relationship of the Nusselt number (Nu) with respect to the Rayleigh number (R), the Ekman number (E), and the Elsasser number (Λ) is investigated. It is observed that E generates a strong damping effect on the flow velocity and on the heat transfer at high rotation rates. Using the heatline concept, it is observed that the temperature within the central regime is enhanced as the Λ increases. The results show that either E decreases or Λ increases, then the heat transfer rate increases.

To the naked eye, turbulent flows exhibit whirls of many different sizes. To each size, or scale, corresponds a fraction of the total energy resulting from a cascade in five dimensions: scale, time, and three-dimensional space. Understanding this process is critical to strategies for modeling geophysical and industrial flows. By tracking the flow regions containing energy in different scales, we have detected the statistical predominance of a cross-scale link whereby fluid lumps of energy at scale Δ appear within lumps of scale 2Δ and die within those of scale Δ/2. Our approach uncovers the energy cascade in a simple water-like fluid, offering insights for turbulence models while paving the way for similar analyses in conducting fluids, quantum fluids, and plasmas.

Purpose This paper aims to numerically investigate the influence of magnetic field and recess configurations on performance of hydrostatic thrust bearing. Electrically conducting fluid is supplied to bearing, operating in external magnetic field. Influences of recess geometric shapes (circular, rectangular, elliptical and triangular) and restrictor (capillary and orifice) are numerically examined on stead-state and dynamic performance characteristics of bearing. Design/methodology/approach Numerical simulation of hydrostatic thrust bearing has been performed using finite element (FE) method based on Galerkin’s technique. An iterative source code based on FE approach, Gauss–Siedel and Newton–Raphson method is used to compute steady-state and dynamic performance indices of bearings. Findings The presence of magnetic field is observed to be enhancing load-carrying capacity and damping coefficient of bearings. The effect is observed to be more pronounced at low value of Hartmann number, because of the saturation effect observed at higher values of Hartmann number. The enhancement in abovementioned performance indices is observed to be highly dependent on geometry of recess and restrictor. Research limitations/implications This study presents a FE-based approach to numerically simulate a hydrostatic thrust bearing. It will help bearing designers and academician in selecting an appropriate recess shape, restrictor and strength of magnetic field, for obtaining optimum performance from hydrostatic thrust bearing. Originality/value The present investigation provides a coupled solution of modified Reynolds equation and restrictor equation, which is essential for accurately predicting the performance of hydrostatic thrust bearings.

The generation of a magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary science and astrophysics, since magnetic fields are known to play a key role in the dynamics of these systems. This paper gives an introduction to dynamo theory for the fluid dynamicist. It proceeds by laying the groundwork, introducing the equations and techniques that are at the heart of dynamo theory, before presenting some simple dynamo solutions. The problems currently exercising dynamo theorists are then introduced, along with the attempts to make progress. The paper concludes with the argument that progress in dynamo theory will be made in the future by utilising and advancing some of the current breakthroughs in neutral fluid turbulence such as those in transition, self-sustaining processes, turbulence/mean-flow interaction, statistical and data-driven methods and maintenance and loss of balance.

In this study, the isothermal electroosmotic flow of two immiscible electrical conducting fluids within a uniform circular microcapillary was theoretically examined. It was assumed that an annular layer of liquid adjacent to the inside wall of the capillary exists, and this in turn surrounds the inner flow of a second liquid. The theoretical analysis was performed by using the linearized Poisson-Boltzmann equations, and the momentum equations for both fluids were analytically solved. The interface between the two fluids was considered uniform, hypothesis which is only valid for very small values of the capillary number, and shear and Maxwell stresses were considered as the boundary condition. In addition, a zeta potential difference and a charge density jump were assumed at the interface. In this manner, the electroosmotic pumping is governed by the previous interfacial effects, a situation that has not previously been considered in the specialized literature. The simplified equations were nondimensionalized, and analytical solutions were determined to describe the electric potential distribution and flow field in both the fluids. The solution shows the strong influence of several dimensionless parameters, such as μr, εr, , and , and , on the volumetric flow. The parameters represent the ratio of viscosity, the ratio of electric permittivity of both fluids, the dimensionless zeta potential of the microcapillary wall, the dimensionless charge density jump and charge density between both fluids, and the electrokinetic parameters, respectively.