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1

The effect of thermal modulation on double diffusive convection in the presence of applied magnetic field and internal heat source

Manjula S. H., Suresh P., Rao M. G.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 1

135--155

EN

The investigation of thermal modulation on double-diffusive stationary convection in the presence of an applied magnetic field and internal heating is carried out. A weakly nonlinear stability analysis has been performed using the finite-amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at the third order of the system. The study considers three different forms of temperature modulations. OPM-out of phase modulation, LBMO-lower boundary modulation, IPM-in phase modulation. The finite-amplitude is a function of amplitude ,Tδ frequency ω and the phase differenceθ . The effects of Tδ and ω on heat/mass transports have been analyzed and depicted graphically. The study shows that heat/mass transports can be controlled effectively by thermal modulation. Further, it is found that the internal Rayleigh number iR enhances heat transfer and reduces the mass transfer in the system.

2

Double-diffusive convection of synovial (couple-stress) fluid in the presence of Hall current through a porous medium

Singh M.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 4

963--976

EN

An investigation made on the effect of Hall currents on double-diffusive convection of a compressible synovial (couple-stress) fluid in the presence of a horizontal magnetic field through a porous layer is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. A dispersion relation governing the effects of viscoelasticity, compressibility, magnetic field and porous layer is derived. For the stationary convection, a synovial fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. The stable-solute gradient, compressibility, and magnetic field have postponed the onset of convection, whereas Hall currents and medium permeability have not postponed the onset of convection, moreover, a synovial fluid has a dual character in the presence of Hall currents, whereas in the absence of Hall current in synovial fluid have postponed the onset of convection, which is in contrast in case of thermal convection couple-stress fluid with same effects. These analytic results are confirmed numerically and the effects of various parameters are depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, magnetic field, porous medium and Hall currents which were non- existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

3

Effect of vertical vibrations on the onset of binary convection

Swamy M. S.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

899--910

EN

In the present work the linear stability analysis of double diffusive convection in a binary fluid layer is performed. The major intention of this study is to investigate the influence of time-periodic vertical vibrations on the onset threshold. A regular perturbation method is used to compute the critical Rayleigh number and wave number. A closed form expression for the shift in the critical Rayleigh number is calculated as a function of frequency of modulation, the solute Rayleigh number, Lewis number, and Prandtl number. These parameters are found to have a significant influence on the onset criterion; therefore the effective control of convection is achieved by proper tuning of these parameters. Vertical vibrations are found to enhance the stability of a binary fluid layer heated and salted from below. The results of this study are useful in the areas of crystal growth in micro-gravity conditions and also in material processing industries where vertical vibrations are involved.

4

Double diffusive convection in a high porosity anisotropic porous medium with externally regulated darcy and brinkman frictions

Siddheshwar P. G., Vanishree R. K.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 4

1147-1168

EN

A linear stability analysis is performed on the double diffusive porous system using the Rayleigh-Ritz technique. The condition for direct and Hopf bifurcations is obtained as a function of the parameters of the problem. A unique feature in this problem is that Darcy and Brinkman friction are temperature-dependent and hence are amenable to regulation. The study reveals that this external regulation of convection results in a preference for stationary convection over oscillatory mode. A low-porosity medium results for "finger" and "diffusive" instabilities are also discussed in the case of constant viscosity liquids.