ARTICLE | doi:10.20944/preprints202108.0560.v1
Subject: Physical Sciences, Fluids & Plasmas Keywords: Magnetohydrodynamics, Variational Principles, Reduction of Variables
Online: 31 August 2021 (11:16:47 CEST)
The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.
ARTICLE | doi:10.20944/preprints201810.0097.v1
Subject: Physical Sciences, Mathematical Physics Keywords: Bioconvection, Magnetohydrodynamics, Scaling group of transformations, Slip boundary conditions, Chemical reaction
Online: 5 October 2018 (11:39:39 CEST)
Bioconvective flows have attracted attention in recent years due to actual and potential applications. In this paper, we consider a steady and laminar convective MHD flow of a nanofluid with heat, mass and microorganism transfer with a heat source/sink present. In addition, we assume there exists a first order chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) using the scaling group transformation and the associated boundary value problem is then solved. The influences of selected governing parameters on the dimensionless velocity, temperature, nanoparticle concentration, density of motile microorganisms, skin friction, heat transfer, mass transfer, and motile microorganism density rates are computed and discussed
ARTICLE | doi:10.20944/preprints202112.0295.v1
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: nano-fluid; nanoparticles removing; magnetohydrodynamics; stability of the flow; water treatment; exact solution; instability of the flow
Online: 20 December 2021 (09:37:36 CET)
The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a spongy with a mix of water with nanoparticles and contaminants. It is assumed that fluid is homogeneous at the starting moment, the parameters of the nanoparticles and contaminants are known, and there is a constant non-homogeneous magnetic field applied to the system. The flow starts moving when the walls of the channel shift to each other. Exact and numerical solutions of the system of ordinary differential equations are used to receive the results. The article gives an answer to the question about stability of the flow and proposes the technique to evaluate the essential characteristics of the system to achieve the treatment process efficiency. The main result is that the considered system shows excellent treatment properties during some part of squeezing stage. This effect does not appear without magnetic field.
ARTICLE | doi:10.20944/preprints202208.0219.v1
Subject: Physical Sciences, Fluids & Plasmas Keywords: Fluid dynamics; Turbulent cascades; Fluid equilibria; Casimir constraints; Euler equation; Quasigeostrophic equations; Rossby waves; Axisymmetric flows; Shallow water equations; Magnetohydrodynamics
Online: 11 August 2022 (11:48:18 CEST)
An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored.