Variable Viscosity Effects on Penetrative Convection in a Fluid Layer

2017 ◽  
Vol 13 (3) ◽  
pp. 51-65
Author(s):  
Gangadharaiah Y H
Keyword(s):  
Surface Deformation ◽  
Variable Viscosity ◽  
Fluid Layer ◽  
Perturbation Technique ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Decisive Role ◽  
Wave Number ◽  
Regular Perturbation ◽  
Penetrative Convection

The effect of variable viscosity on the onset of penetrative convection simulated via internal heating in a fluid layer. The upper surface of a fluid layer is assumed to be deformably free and dependence of viscosity is assumed to be exponential. The resulting eigen value problem is solved using a regular perturbation technique with wave number a as a perturbation parameter. The viscosity parameter, surface deformation and the presence of internal heat source play a decisive role on the stability characteristics of the system.

scholarly journals Effects of Internal Heat Generation and Variable Viscosity on Onset of Rayleigh-Benard Convection

2013 ◽  
Vol 5 (3) ◽  
pp. 200-213
Author(s):  
Gangadharaiah Y. H. ◽  
Suma S. P.
Keyword(s):  
Heat Source ◽  
Convective Instability ◽  
Variable Viscosity ◽  
Fluid Layer ◽  
Perturbation Technique ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Wave Number ◽  
Regular Perturbation ◽  
Rayleigh Benard

In the present study, onset of stationary Rayleigh-Benard convective instability in a fluid layer, with internal heating and thermally dependent viscosity has been investigated by means of linear stability analysis. The dependence of viscosity is assumed to be exponential. The resulting eigen value problem is solved using a regular perturbation technique with wave number a as a perturbation parameter. The viscosity parameter and the presence of internal heat source play a decisive role on the stability characteristics of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and variable viscosity so that a more precise control (suppress or augment) of thermal convective instability in a fluid layer is possible.

scholarly journals Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source

2019 ◽  
Vol 8 (1) ◽  
pp. 546-558 ◽  
Author(s):  
Amit Mahajan ◽  
Reena Nandal
Keyword(s):  
Porous Media ◽  
Heat Generation ◽  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Heat Extraction ◽  
Graphical Form ◽  
Nonlinear Stability Analysis ◽  
Penetrative Convection ◽  
Onset Of Convection

Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.

scholarly journals VARIABLE GRAVITY FIELD AND THROUGHFLOW EFFECTS ON PENETRATIVE CONVECTION IN A POROUS LAYER

2013 ◽  
Vol 5 (3) ◽  
pp. 172-191 ◽  
Author(s):  
Gangadharaiah Y. H. ◽  
Suma S. P ◽  
Ananda K.
Keyword(s):  
Porous Medium ◽  
Gravity Field ◽  
Porous Layer ◽  
Perturbation Technique ◽  
Internal Heat ◽  
Wave Number ◽  
Penetrative Convection ◽  
Variable Gravity ◽  
Vertical Throughflow ◽  
The Stability

The effect of vertical throughflow and variable gravity field on the onset of penetrative convection simulated via internal heating in a porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigen value problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The variable gravity parameter, the direction of throughflow and the presence of volumetric internal heat source in a porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced due to the simultaneous presence of a volumetric source, gravity field and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of porous medium is possible.

scholarly journals Effect of Vertical Vibrations on the Onset of Binary Convection

2013 ◽  
Vol 18 (3) ◽  
pp. 899-910 ◽  
Author(s):  
M.S. Swamy
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Lewis Number ◽  
Wave Number ◽  
Closed Form Expression ◽  
Effective Control ◽  
Regular Perturbation ◽  
Binary Fluid ◽  
Vertical Vibrations

Abstract 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

POROUS PENETRATIVE CONVECTION WITH A SALT FIELD AND INTERNAL HEAT SOURCE

1992 ◽  
Vol 02 (04) ◽  
pp. 407-421
Author(s):  
LORNA RICHARDSON
Keyword(s):  
Porous Medium ◽  
Temperature Gradient ◽  
Heat Source ◽  
Nonlinear Stability ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Penetrative Convection ◽  
Weighted Energy ◽  
The Stability ◽  
Unconditional Nonlinear Stability

We investigate the stability of convection in a porous medium containing a heat source in which a destabilizing salt field and stabilizing temperature gradient are present. Both conditional and unconditional nonlinear stability thresholds are calculated and we note that RaE(conditional)>RaE(unconditional). The unconditional nonlinear analysis requires the use of a “weighted” energy.

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