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1

Boundary effects on electrothermal convection in a dielectric fluid layer

Ravisha M., Raghunatha K. R., Mamatha A. L., Shivakumara I. S.

Archives of Thermodynamics

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2019

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Vol. 40, no 1

3--19

EN

The instability characteristics of a dielectric fluid layer heated from below under the influence of a uniform vertical alternating current (AC) electric field is analyzed for different types of electric potential (constant electric potential/ electric current), velocity (rigid/free) and temperature boundary conditions (constant temperature/heat flux or a mixed condition at the upper boundary). The resulting eigenvalue problem is solved numerically using the shooting method for various boundary conditions and the solution is also found in a simple closed form when the perturbation heat flux is zero at the boundaries. The possibility of a more precise control of electrothermal convection (ETC) through various boundary conditions is emphasized. The effect of increasing AC electric Rayleigh number is to hasten while that of Biot number is to delay the onset of ETC. The system is more stable for rigid-rigid boundaries when compared to rigid-free and least stable for free-free boundaries. The change of electric potential boundary condition at the upper boundary from constant electric potential to constant electric current is found to instill more stability on the system.

2

Mixed convection heat transfer from a vertical heated plate embedded in a sparsely packed porous medium

Pal D., Shivakumara I. S.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

929-939

EN

An improved numerical study on mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium is undertaken by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by the Lapwood-Forchheimer-Brinkman extended Darcy model. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using a shooting algorithm with the Runge-Kutta-Fehlberg integration scheme to obtain velocity and temperature distributions. Besides, the skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence on decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability parameter considered. Further, the results under the limiting conditions were found to be in good agreement with the existing ones.

3

Onset of surface-tension-driven convection in superposed layers of fluid and saturated porous medium

Shivakumara I. S., Suma S. P., Chavaraddi K. B.

Archives of Mechanics

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2006

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Vol. 58, nr 2

71-92

EN

The onset of surface-tension-driven convection is studied in a two-layer system comprising an incompressible fluid-saturated porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer is either perfectly heat conducting or insulating, while the upper heat insulating fluid boundary is free and at which the surface tension effects are allowed for. At the contact surface between the fluid-saturated porous medium and the adjacent bulk fluid, both Beavers-Joseph and the Jones conditions are employed. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is obtained for insulating boundaries by using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection is investigated in detail. It is found that the parameter ..., the ratio of the thickness of the fluid layer to that of the porous layer, has a profound effect on the stability of the system.

4

Onset of convection in a sparsely packed porous layer with throughflow

Shivakumara I. S., Nanjundappa C. E.

Archives of Mechanics

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2001

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Vol. 53, nr 3

219-241

EN

The onset of Rayleigh-Bénard convection in a sparsely packed porous layer with vertical throughflow is investigated using Brinkman's modification of the Darcy flow model with fluid viscosity different from effective viscosity. The critical Rayleigh numbers are obtained for free-free, rigid-rigid and rigid-free boundaries which are insulated to temperature perturbations. It is noted that an increase in the value of viscosity ratio is to delay the onset of convection. Further, it is observed that the throughflow can be used either to suppress or augment convection, depending on the nature of boundaries and also on the values of physical parameters.

5

Rayleigh-Bénard convection with throughflow - a comparative study between the single-term and higher order Galerkin methods

Shivakumara I. S., Suma S. P.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 3

507-520

EN

Effects of non-uniform temperature gradient, vertical transport of momentum and vertical transport of perturbation temperature due to throughflow are investigated on the Rayleigh-Bénard convection for different hydrodynamic boundary conditions. The eigenvalue problem for the conducting boundaries is solved by the higher-order Galerkin method. It is shown that the throughflow in one particular direction destabilizes the system depending on the value of the Prandtl number. Also a comparison between the results of single-term and higher order Galerkin methods is made and limitations of the single-term Galerkin method are clearly brought out.