The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

Experimental observation of metal-electrolyte interface stability in a model of liquid metal battery

An electric current is passed through the interface of liquid gallium and aqueous electrolyte in a square cross-section cell under a background vertical magnetic field. The oscillation increment of surface waves is calculated from potential measurements at variable current strengths. The surface is also visually observed through transparent side walls. No growing surface waves occur for the Sele parameter as high as 1.5. Instead, a quasi-static surface deformation is caused by the rotation of the metal and electrolyte. The maximum height of this surface deformation increases approximately in proportion to the current. Figs 7, Refs 15.

Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

Effect of Flow and Heat Transfer of Vertical Magnetic Field to Fe3O4-H2O Nanofluids

Heat transfer coefficient is a key parameter for efficiency evaluation of heat exchangers. Good stability and high heat transfer coefficient are essential for the application of nanofluids in heat exchangers and solar systems. In this work, nanofluids with good stability were prepared, and the influence of vertical magnetic field on flow and heat exchange of magnetic nanofluids under laminar and turbulent conditions was mainly studied. The flow and heat transfer rules of Fe3O4 nanofluids with or without magnetic field conditions, magnetic field strength, magnetic field distribution, the nanoparticle concentration and nanofluids temperature were systematically studied by setting up an experimental platform. The results show that the intensity and distribution of magnetic field had a significant influence on the heat transfer of magnetic nanofluids, whether in laminar or turbulent flow. When the magnetic field strength is 800G and 1000G, the convective heat transfer coefficient increases by an average of 23.89% and 26.12%. However, the influence of magnetic field on its flow characteristics is not obvious, and the effect on resistance coefficient increases by only 2.01%. In addition, the characteristics of magnetic nanofluids also have a certain influence on its flow and heat transfer. When the temperature of magnetic nanofluids is increased, the convective heat transfer coefficient will increase. When the concentration of magnetic nanofluids is increased, the pressure drop will also increase, but it has little effect on the drag coefficient.

Combined effects of nonuniform temperature gradients and heat source on double diffusive Benard-Marangoni convection in a porous-fluid system in the presence of vertical magnetic field

The physical configuration of the problem is a porous-fluid layer which is horizontally unbounded, in the presence of uniform heat source/sink in the layers enclosed by adiabatic and isothermal boundaries. The problem of double diffusive Bènard-Marangoni convection in the presence of vertical magnetic field is investigated on this porous-fluid system for non-Darcian case and is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary conditions. The influence of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer and the applied magnetic field play an important role in controlling Benard-Marangoni convection. The parameters which direct this convection are determined and the effect of porous parameter is relatively interesting.

Hall current effects on a magnetic nanofluid layer under temperature gradient

In the Bénard convection governed nanofluid confined between two horizontal infinite free-free boundaries, the effect of Hall current is investigated when it is subjected to the constant vertical magnetic field. The Buongiorno mathematical model for hydromagnetic flow with Hall currents has been considered. The Brownian motion effects and thermophoresis of nanoparticles have been included in the energy equation. A realistic boundary condition based on zero nanoparticle mass flux at the walls is incorporated for the analysis. The impacts of Brownian motion, convective heat transfer, thermophoresis of nanoparticles and zero mass flux conditions are also deliberated through the behaviour of the related parameters. The parameters representing the model incorporate the consequences of newly introduced physically realistic boundary conditions and Hall currents. For comprehensive physical interpretation the embedded parameters have been plotted and deliberated graphically. It is found that Hall current is responsible to enhances the instability of the system and sets the convection earlier. A rigorous comparison has been made with the existing results. The results are shown graphically and verified numerically.