Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^{8}$ over a broad range of Rayleigh numbers $Ra$. Three magnetoconvection regimes are identified: two of the regimes are magnetically constrained in the sense that a leading-order balance exists between the Lorentz and buoyancy forces, whereas the third regime is characterized by unbalanced dynamics that is similar to non-magnetic convection. Each regime is distinguished by flow morphology, momentum and heat equation balances, and heat transport behaviour. One of the magnetically constrained regimes appears to represent an ‘ultimate’ magnetoconvection regime in the dual limit of asymptotically large buoyancy forcing and magnetic field strength; this regime is characterized by an interconnected network of anisotropic, spatially localized fluid columns aligned with the direction of the imposed magnetic field that remain quasi-laminar despite having large flow speeds. As for non-magnetic convection, heat transport is controlled primarily by the thermal boundary layer. Empirically, the scaling of the heat transport and flow speeds with $Ra$ appear to be independent of the thermal Prandtl number within the magnetically constrained, high-$Q$ regimes.

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Effect of magnetic field on parametrically driven surface waves

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2006.1789 ◽

2006 ◽

Vol 463 (2079) ◽

pp. 711-722 ◽

Cited By ~ 6

Author(s):

Supriyo Paul ◽

Krishna Kumar

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Liquid Metals ◽

Tricritical Point ◽

Thin Layers ◽

Vertical Magnetic Field ◽

Harmonic Solution ◽

Chandrasekhar Number ◽

The Magnetic Field ◽

Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

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Nonlinear interaction of magnetic field and convection

Journal of Fluid Mechanics ◽

10.1017/s0022112075002509 ◽

1975 ◽

Vol 71 (1) ◽

pp. 193-206 ◽

Cited By ~ 44

Author(s):

F. H. Busse

Keyword(s):

Magnetic Field ◽

Magnetic Energy ◽

Fluid Layer ◽

Boussinesq Equations ◽

Finite Amplitude ◽

Magnetic Reynolds Number ◽

Convection Rolls ◽

Rayleigh Numbers ◽

Horizontal Fluid Layer ◽

Chandrasekhar Number

The interaction between convection in a horizontal fluid layer heated from below and an ambient vertical magnetic field is considered. The analysis is based on the Boussinesq equations for two-dimensional convection rolls and the assumption that the amplitude A of the convection and the Chandrasekhar number Q are small. It is found that the magnetic energy is amplified by a factor of order R½m, where Rm is the magnetic Reynolds number. The ratio between the magnetic and kinetic energies can reach values much larger than unity. Although the magnetic field always inhibits convection, this influence decreases with increasing amplitude of convection. Thus finite amplitude onset of steady convection becomes possible at Rayleigh numbers considerably below the values predicted by linear theory.

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Magnetic-field effect on thermal convection of a nematic liquid crystal at large Rayleigh numbers

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.570 ◽

2013 ◽

Vol 716 ◽

Cited By ~ 4

Author(s):

Stephan Weiss ◽

Guenter Ahlers

Keyword(s):

Magnetic Field ◽

Thermal Conductivity ◽

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Thermal Convection ◽

Field Effect ◽

Magnetic Field Effect ◽

Vertical Magnetic Field ◽

Cylindrical Cell ◽

Rayleigh Numbers

AbstractWe report on near-turbulent thermal convection of a nematic liquid crystal heated from below in a cylindrical cell with an aspect ratio (diameter/height) equal to 0.50 for Rayleigh numbers $2\times 1{0}^{7} \lesssim \mathit{Ra}\lesssim 3\times 1{0}^{8} $ and a Prandtl number of about 355. The Nusselt number $\mathit{Nu}$ as a function of $\mathit{Ra}$ did not differ significantly from that of an isotropic fluid. In a vertical magnetic field $\mathbi{H}$, we found $\mathit{Nu}(H)/ \mathit{Nu}(0)= 1+ a(\mathit{Ra}){H}^{2} $, with $a(\mathit{Ra})= 0. 24{\mathit{Ra}}^{0. 75} ~{\mathrm{G} }^{- 2} $. We present a model that describes the $H$ dependence in terms of a change of the thermal conductivity in the thermal boundary layers due to a field-induced director alignment.

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Overstable rotating convection in the presence of a vertical magnetic field

Physics of Fluids ◽

10.1063/5.0035555 ◽

2021 ◽

Vol 33 (3) ◽

pp. 034130

Author(s):

Ankan Banerjee ◽

Manojit Ghosh ◽

Lekha Sharma ◽

Pinaki Pal

Keyword(s):

Magnetic Field ◽

Vertical Magnetic Field ◽

Rotating Convection

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Rayleigh-Taylor instability with vertical magnetic field and heat transfer

10.1063/5.0052998 ◽

2021 ◽

Author(s):

Atul Kumar Shukla ◽

Mukesh Kumar Awasthi

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Taylor Instability ◽

Vertical Magnetic Field ◽

Rayleigh Taylor Instability

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Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

Mechanics & Industry ◽

10.1051/meca/2019022 ◽

2019 ◽

Vol 20 (5) ◽

pp. 502 ◽

Cited By ~ 3

Author(s):

Aaqib Majeed ◽

Ahmed Zeeshan ◽

Farzan Majeed Noori ◽

Usman Masud

Keyword(s):

Magnetic Field ◽

Temperature Field ◽

Velocity Field ◽

Differential Equations ◽

Heat Transport ◽

Viscous Dissipation ◽

Heat Generation ◽

Fluid Motion ◽

Numerical Procedure ◽

The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

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Effects of a Vertical Magnetic Field on Particle Confinement in a Magnetized Plasma Torus

Physical Review Letters ◽

10.1103/physrevlett.93.165003 ◽

2004 ◽

Vol 93 (16) ◽

Cited By ~ 39

Author(s):

S. H. Müller ◽

A. Fasoli ◽

B. Labit ◽

M. McGrath ◽

M. Podestà ◽

...

Keyword(s):

Magnetic Field ◽

Magnetized Plasma ◽

Vertical Magnetic Field ◽

Plasma Torus ◽

Particle Confinement

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Heat transport by parallel-roll convection in a rectangular container

Journal of Fluid Mechanics ◽

10.1017/s0022112087003148 ◽

1987 ◽

Vol 185 ◽

pp. 205-234 ◽

Cited By ~ 9

Author(s):

R. W. Walden ◽

Paul Kolodner ◽

A. Passner ◽

C. M. Surko

Keyword(s):

Rayleigh Number ◽

Heat Transport ◽

Critical Rayleigh Number ◽

Equation Model ◽

Onset Of Convection ◽

Infinite Layer ◽

Lateral Extent ◽

Prandtl Numbers ◽

Rayleigh Numbers ◽

Good Agreement

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

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ELECTROMAGNETIC FIELDS OF CHARGED AND MAGNETIZED CYLINDRICAL CONDUCTORS IN NUT SPACE

International Journal of Modern Physics D ◽

10.1142/s0218271805005979 ◽

2005 ◽

Vol 14 (03n04) ◽

pp. 687-695 ◽

Cited By ~ 2

Author(s):

B. J. AHMEDOV ◽

A. V. KHUGAEV ◽

N. I. RAKHMATOV

Keyword(s):

Magnetic Field ◽

Gravitational Field ◽

Electromagnetic Fields ◽

Electric Charge ◽

Maxwell Equations ◽

Analytic Solutions ◽

Vertical Magnetic Field ◽

General Relativistic ◽

Azimuthal Current ◽

Cylindrical Conductors

We present analytic solutions of Maxwell equations for infinitely long cylindrical conductors with nonvanishing electric charge and currents in the external background spacetime of a line gravitomagnetic monopole. It has been shown that vertical magnetic field arising around cylindrical conducting shell carrying azimuthal current will be modified by the gravitational field of NUT source. We obtain that the purely general relativistic magnetic field which has no Newtonian analog will be produced around charged gravitomagnetic monopole.

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