On nonlinear evolution of convective flow in an active mushy layer

Bhatta, Dambaru; Riahi, Daniel N.; Muddamallappa, Mallikarjunaiah S.

doi:10.1007/s10665-011-9501-5

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…However, the issues of nonlinear effects and transition effects on the chimney formation did not feature in their investigation. Bhatta et al (2010) studied weakly nonlinear convective flow in an active (variable permeability) mushy layer with permeable mushliquid interface. Bhatta et al (2012) studied weakly nonlinear convective flows in mushy layers with and without the magnetic effect and permeable mushliquid interface.…”

Section: Introductionmentioning

confidence: 99%

“…There have been some research studies on the effect of hydraulic resistivity (Rubin 1981;Bhatta and Riahi 2017) as well as related ones on variable permeability with or without magnetic field (Bhatta et al 2010(Bhatta et al , 2012. Bhatta et al (2010Bhatta et al ( , 2012 studied nonlinear convective flow in a mushy layer, which is a porous layer formed between the solid and liquid layers during the solidification process of binary alloy. The mushy layer that they considered has variable permeability and hence variable resistivity, and they determine the flow evolution for both cases in the absence or presence of a vertically oriented magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Bhatta¹,

Riahi²

2020

JAFM

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Heat and mass transfer through porous media has been a topic of research interest because of its importance in various applications. The flow system in porous media is modelled by a set of partial differential equations. The momentum equation which is derived from Darcy's law contains a resistivity parameter. We investigate the effect of hydraulic resistivity on a weakly nonlinear thermal flow in a horizontal porous layer. The present study is a realistic study of nonlinear convection flow with variable resistivity whose rate of variation is arbitrary in general. This is a first step for considering more general problems in applications that involve variable resistivity that may include both variations in permeability and viscosity of the porous layer. Such problems are important for understanding properties of underground flow, migration of moisture in fibrous insulations, underground disposal of nuclear waste, welding process, petrochemical generation, drug delivery in vascular tumor, etc. Using weakly non-linear procedure, the linear and first-order systems are derived. The critical Rayleigh number and the critical wave number are obtained from the linear system using the normal mode approach for the two-dimensional case. The linear and first-order systems are solved numerically using the fourth-order Runge-Kutta and shooting methods. Numerical results for the temperature are presented in tabular and graphical forms for different resistivities. Through this study, it is observed that a stabilizing effect on the dependent variables occurs in the case of a positive vertical rate of change in resistivity, whereas a destabilizing effect is noticed in the case of a negative vertical rate of change in resistivity. The results obtained indicate that the convective flow due to the buoyancy force is more effective for weaker resistivity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Bhatta¹,

Riahi²

2020

JAFM

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“…Muddamallappa et al [20] investigated linear marginal stabilities for magnetoconvection cases. Bhatta et al [21,22,24] studied weakly nonlinear convective flow in mushy layer with permeable mush-liquid interface for constant and variable permeability cases. Lee et al [23] carried out numerical modeling of one-dimensional binary alloy solidification with a mushy layer evolution.…”

Section: Introductionmentioning

confidence: 99%

Amplitude Equation for a Nonlinear Three Dimensional Convective Flow in a Mushy Layer

Bhatta¹,

Riahi²

2015

Springer Proceedings in Mathematics &Amp; Statistics

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We consider a nonlinear three-dimensional convective flow in a mushy layer. A mushy layer is a partially solidified region formed during solidification of binary alloys. During solidification, fluid flow within the mushy layer can cause vertical chimneys or channels void of solid. These chimneys can generate imperfections in the final form of the solidified alloy. The equations governing the mushy layer system are the continuity equation, heat equation, solute equation, and conservation of momentum which is governed by Darcy's law. A quadratic nonlinear evolution equation satisfied by the amplitude is derived for hexagonal cells. This equation is obtained from the first-order system using the adjoint of the linear system. An explicit solution of the amplitude equation is also presented.

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Convection with Change of Phase

Nield

Bejan

2012

Convection in Porous Media

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On nonlinear evolution of convective flow in an active mushy layer

Cited by 7 publications

References 19 publications

Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Amplitude Equation for a Nonlinear Three Dimensional Convective Flow in a Mushy Layer

Convection with Change of Phase

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