IMPACT OF ALIGN MAGNETIC FIELD ON VISCOUS FLOW WITH COMBINED CONVECTIVE TRANSPORT

2021 ◽  
Vol 23 (1) ◽  
pp. 127-137
Author(s):  
Siti Farah Haryatie Mohd Kanafiah ◽  
Hussein Ali Mohammed Al-Sharifi
2010 ◽  
Vol 21 (17) ◽  
pp. 175702 ◽  
Author(s):  
Lioz Etgar ◽  
Arie Nakhmani ◽  
Allen Tannenbaum ◽  
Efrat Lifshitz ◽  
Rina Tannenbaum

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.


The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.


In this paper the theory of the stability of viscous flow between two rotating coaxial cylinders which has been developed by Taylor, Jeffreys and Meksyn is extended to the case when the fluid considered is an electrical conductor and a magnetic field along the axis of the cylinders is present. A differential equation of order eight is derived which governs the situation in marginal stability; and a significant set of boundary conditions for the problem is formulated. The case when the two cylinders are rotating in the same direction and the difference ( d ) in their radii is small compared to their mean (R 0 ) is investigated in detail. A variational procedure for solving the underlying characteristic value problem and determining the critical Taylor numbers for the onset of instability is described. As in the case of thermal instability of a horizontal layer of fluid heated below, the effect of the magnetic field is to inhibit the onset of instability, the inhibiting effect being the greater, the greater the strength of the field and the value of the electrical conductivity. In both cases, the inhibiting effect of the magnetic field depends on the strength of the field ( H ), the density ( ρ ) and the coefficients of electrical conductivity ( σ ), kinematic viscosity ( v ) and magnetic permeability ( μ ) through the same non-dimensional combination Q =μ 2 H 2 d 2 σ/ pv ; however, the effect on rotational stability is more pronounced than on thermal instability. A table of the critical Taylor numbers for various values of Q is provided.


1958 ◽  
Vol 36 (11) ◽  
pp. 1509-1525 ◽  
Author(s):  
E. R. Niblett

Chandrasekhar's theory of the stability of viscous flow of an electrically conducting fluid between coaxial rotating cylinders with perfectly conducting walls is extended to include the case of non-conducting walls, and it is found that their effect is to reduce the critical Taylor numbers and increase the wavelength of the instability patterns by considerable amounts. An experiment designed to measure the values of magnetic field and rotation speed at the onset of instability in mercury between perspex cylinders is described. The radioactive isotopes Hg197 and Hg203 were used to trace the flow. The results support the theoretical prediction that the boundary conditions can have a large effect on the motion.


2001 ◽  
Vol 500 (1-2) ◽  
pp. 95-99 ◽  
Author(s):  
Kyle M. Grant ◽  
Jared W. Hemmert ◽  
Henry S. White

2010 ◽  
Vol 8 (3) ◽  
pp. 383-386
Author(s):  
Lioz Etgar ◽  
Arie Nakhmani ◽  
Allen Tannenbaum ◽  
Efrat Lifshitz ◽  
Rina Tannenbaum

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