Instability of MHD couette flow of an electrically conducting fluid

Hussain, Zakir; Hussain, Sultan; Kong, Tiantian

doi:10.1063/1.5051624

Cited by 14 publications

(8 citation statements)

References 20 publications

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“…Te governing ( 9)-( 13) are nonlinear partial diferential equations, therefore cannot be solved analytically. Te numerical method for nonlinear partial diferential equations of momentum, concentration, energy, and induced given in ( 9)-( 13) are solved using the fnite diference method subject to the initial and boundary condition (14). Te condition for time stability is the Courant-Friedrichs-Lewy or CFL condition which depends on space and time discretization.…”

Section: Numerical Solutionmentioning

confidence: 99%

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Effects of Chemical Reaction and Joule Heating on MHD Generalized Couette Flow between Two Parallel Vertical Porous Plates with Induced Magnetic Field and Newtonian Heating/Cooling

Mng’ang’a

2023

International Journal of Mathematics and Mathematical Sciences

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In this article, the effects of chemical reaction and Joule heating on MHD generalized Couette flow between two vertical porous plates with induced magnetic field and Newtonian heating/cooling have been investigated. The mathematical model used for the MHD generalized Couette flow takes into account the effect of viscous dissipation. The system of nonlinear partial differential equations governing the flow was solved numerically using the finite difference method. The resulting numerical schemes are simulated in MATLAB to obtain the profiles of the flow variables such as velocity, induced magnetic field, temperature, and concentration profiles graphically. Also, the effects of the flow parameters on the skin-friction coefficient, Nusselt number, and Sherwood number are obtained and discussed numerically through tabular forms. The findings show that an increase in the chemical reaction parameter leads to a decrease in the concentration profiles. Also, increase in the Joule heating parameter and heat generation parameter leads to an increase in the temperature profiles. Induced magnetic field profiles increase with an increase in Reynold’s number. The findings of this study are important due to its application in developing a variety of chemical technologies, including polymer manufacturing, MHD pumps, food processing, chemical catalytic reactors, astronomy, MHD flow meters, and lubrication.

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Section: Numerical Solutionmentioning

confidence: 99%

“…Also, Ali et al [13] analyzed the Couette fow of a maxwell fuid for three dimensional with periodic injection/suction. Hussain et al [14] analyzed instability of the MHD Couette fow of an electrically conducting fuid. Anyanwu et al [15] discussed the infuence of radioactive and a constant pressure gradient on an unsteady MHD Couette fow.…”

Section: Introductionmentioning

confidence: 99%

Effects of Chemical Reaction and Joule Heating on MHD Generalized Couette Flow between Two Parallel Vertical Porous Plates with Induced Magnetic Field and Newtonian Heating/Cooling

Mng’ang’a

2023

International Journal of Mathematics and Mathematical Sciences

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“…This is problably one of the simplest setting to understand some quantitative hydromagnetic stability properties of shear flows, which is a problem of significant physical interest [12,17,22]. The presence of a background magnetic field could dramatically change stability features of the shear flow considered: i) it can have a destabilizing effect for shear flows that are linearly stable without the magnetic field (as the Couette flow) [15,[21][22][23]47]. ii) it can suppress instabilities as the Kelvin-Helmholtz one [34] or lift-up effects in 3D fluids [33].…”

Section: Introductionmentioning

confidence: 99%

Stability Threshold of the 2D Couette Flow in a Homogeneous Magnetic Field Using Symmetric Variables

Dolce

2024

Commun. Math. Phys.

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We consider a 2D incompressible and electrically conducting fluid in the domain $${\mathbb {T}}\times {\mathbb {R}}$$ T × R . The aim is to quantify stability properties of the Couette flow (y, 0) with a constant homogenous magnetic field $$(\beta ,0)$$ ( β , 0 ) when $$|\beta |>1/2$$ | β | > 1 / 2 . The focus lies on the regime with small fluid viscosity $$\nu $$ ν , magnetic resistivity $$\mu $$ μ and we assume that the magnetic Prandtl number satisfies $$\mu ^2\lesssim \textrm{Pr}_{\textrm{m}}=\nu /\mu \le 1$$ μ 2 ≲ Pr m = ν / μ ≤ 1 . We establish that small perturbations around this steady state remain close to it, provided their size is of order $$\varepsilon \ll \nu ^\frac{2}{3}$$ ε ≪ ν 2 3 in $$H^N$$ H N with N large enough. Additionally, the vorticity and current density experience a transient growth of order $$\nu ^{-\frac{1}{3}}$$ ν - 1 3 while converging exponentially fast to an x-independent state after a time-scale of order $$\nu ^{-\frac{1}{3}}$$ ν - 1 3 . The growth is driven by an inviscid mechanism, while the subsequent exponential decay results from the interplay between transport and diffusion, leading to the dissipation enhancement. A key argument to prove these results is to reformulate the system in terms of symmetric variables, inspired by the study of inhomogeneous fluid, to effectively characterize the system’s dynamic behavior.

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“…The electric current flowing through the conductive fluid generates a force on the fluid and affects the magnetic field. The electrically conductive flows were analyzed by numerical simulation in various applications, such as, in parallel film [2][3], applied magnetic field [4], and treating of polymer in microgravity [5].…”

Section: Introductionmentioning

confidence: 99%

“…The latest references concerning instability explorations can be illustrated by [2][3][4][5]. Stability of two fluids MHD flow inside a flat channel was explored by Z. Hussain et al in [5] where the corresponding exact solution has been presented.…”

Section: Introductionmentioning

confidence: 99%

Nanoparticle Based Water Treatment Model in Squeezing Channel under Magnetic Field

Zuev¹,

Hussain²,

Kabalyants³

2021

Preprint

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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.

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Instability of MHD couette flow of an electrically conducting fluid

Cited by 14 publications

References 20 publications

Effects of Chemical Reaction and Joule Heating on MHD Generalized Couette Flow between Two Parallel Vertical Porous Plates with Induced Magnetic Field and Newtonian Heating/Cooling

Effects of Chemical Reaction and Joule Heating on MHD Generalized Couette Flow between Two Parallel Vertical Porous Plates with Induced Magnetic Field and Newtonian Heating/Cooling

Stability Threshold of the 2D Couette Flow in a Homogeneous Magnetic Field Using Symmetric Variables

Nanoparticle Based Water Treatment Model in Squeezing Channel under Magnetic Field

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