scholarly journals Effect of Rotation on Thermosolutal Convection in Visco-elastic Nanofluid with Porous Medium

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Sudhir Kumar Pundir ◽  
◽  
Mukul Kumar ◽  
Rimple Pundir ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Normal Mode ◽  
Lewis Number ◽  
Conservation Equation ◽  
Thermosolutal Convection ◽  
Stationary Convection ◽  
Rotation Effect ◽  
Weighted Residual Method ◽  
Mode Technique

In this paper, we studied the rotation effect on the thermosolutal convection in visco-elastic nanofluid in the presence of porous medium using Walters` (model B`). To solve the conservation equation, we used the normal mode technique and Galerkin weighted residual method. For stationary convection, the onset criterion derived analytically and experiential that visco-elastic nanofluid behaves as a regular Newtonian nanofluid. The effect of rotation, thermo-nanofluid Lewis number, thermosolutal Lewis number and solutal Rayleigh number analyze analytically and graphically.

scholarly journals On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

2018 ◽  
Vol 62 (3) ◽  
pp. 233-240
Author(s):  
Gian C. Rana ◽  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Stationary Convection ◽  
Stress Parameter ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Solutal Rayleigh Number

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.

scholarly journals Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

2018 ◽  
Vol 23 (4) ◽  
pp. 911-928
Author(s):  
R. Sekar ◽  
D. Murugan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Normal Mode ◽  
Coriolis Force ◽  
Linear Stability Analysis ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Stability Effect ◽  
Mode Technique

Abstract The effect of Coriolis force on the Soret driven ferrothermohaline convection in a densely packed porous medium has been studied. A linear stability analysis is carried out using normal mode technique. It is found that stationary convection is favorable for the Darcy model, therefore oscillatory instability is studied. A small thermal perturbation is applied to the basic state and linear stability analysis is used for which the normal mode technique is applied. It is found that the presence of a porous medium favours the onset of convection. The porous medium is assumed to be variable and the effect of the permeable parameter is to destabilize the system. The present work has been carried out both for oscillatory as well as stationary instabilities. The results are depicted graphically.

Stability of Hydromagnetic Thermoconvective Flow Through Porous Medium

1973 ◽  
Vol 40 (4) ◽  
pp. 879-884 ◽  
Author(s):  
Prabhamani R. Patil ◽  
N. Rudraiah
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Normal Mode ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Thermal Convection ◽  
Stability Region ◽  
Flow Through ◽  
The Stability ◽  
Mode Technique

The stability of the onset of thermal convection of a conducting viscous fluid in a porous medium has been investigated using the linear (normal mode technique) and the non-linear (energy) stability theories. Both the theories show that the stability region is increased to the maximum extent when the usual viscous dissipation is also present in addition to the dissipation due to Darcy’s resistance and Joule heating.

scholarly journals Effect of Suspended Particles on Thermosolutal Convection of Rivlin-Ericksen Fluid in Porous Medium with Variable Gravity

2018 ◽  
Vol 23 (3) ◽  
pp. 813-820 ◽  
Author(s):  
A.K. Aggarwal ◽  
D. Dixit
Keyword(s):  
Porous Medium ◽  
Suspended Particles ◽  
Thermosolutal Convection ◽  
Stationary Convection ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Variable Gravity ◽  
Solute Gradient

Abstract The thermosolutal stability of a layer of the Rivlin-Ericksen fluid in a porous medium is considered under varying gravity conditions. It is found that for stationary convection, medium permeability and suspended particles have a destabilizing/stabilizing effect when gravity increases/decreases. The stable solute gradient has a stabilizing effect on the system.

scholarly journals Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Viscoelastic Fluid ◽  
Fluid Layer ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Free Boundaries ◽  
Soret And Dufour Effects ◽  
Diffusive Convection ◽  
Double Diffusive

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

scholarly journals Hall Effect on Bénard Convection of Compressible Viscoelastic Fluid through Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mahinder Singh ◽  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Linear Stability Theory ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field ◽  
Mode Technique

An investigation made on the effect of Hall currents on thermal instability of a compressible Walter’s B′ elasticoviscous fluid through porous medium is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. For the case of stationary convection, Hall currents and compressibility have postponed the onset of convection through porous medium. Moreover, medium permeability hasten postpone the onset of convection, and magnetic field has duel character on the onset of convection. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection have been obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. The magnetic field, Hall currents found to introduce oscillatory modes, in the absence of these effects the principle of exchange of stabilities is valid.

Natural convection effects on thermal ignition in a porous medium. I. Semenov model

1990 ◽  
Vol 429 (1877) ◽  
pp. 533-554 ◽  
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Lewis Number ◽  
Reaction Model ◽  
Heat Of Reaction ◽  
Thermal Ignition ◽  
Lumped Model ◽  
Convection Problem ◽  
Diffusion Convection

A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number ( ψ c ) on the Rayleigh number ( R *). It is shown that for R * → 0, ψ c approaches the classical (conduction) limit e -1 , while for R * ≫ 1, the ignition locus is given by the convection asymptote ψ c / R * = 4 e -2 . Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S , isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.

scholarly journals Variable Gravity Effects on Thermal Instability of Nanofluid in Anisotropic Porous Medium

2013 ◽  
Vol 18 (3) ◽  
pp. 631-642 ◽  
Author(s):  
R. Chand ◽  
G.C. Rana ◽  
S. Kumar
Keyword(s):  
Porous Medium ◽  
Brownian Motion ◽  
Rayleigh Number ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Free Boundaries ◽  
Gravity Effects ◽  
Anisotropic Porous Medium ◽  
Variable Gravity ◽  
Mode Technique

Abstract In this paper, we study the effects of variable gravity on thermal instability in a horizontal layer of a nanofluid in an anisotropic porous medium. Darcy model been used for the porous medium. Also, it incorporates the effect of Brownian motion along with thermophoresis. The normal mode technique is used to find the confinement between two free boundaries. The expression of the Rayleigh number has been derived, and the effects of variable gravity and anisotropic parameters on the Rayleigh number have been presented graphically

scholarly journals Electrohydrodynamic Instability of a Rotating Walters’ (model B’) Fluid in a Porous Medium: Brinkman model

2019 ◽  
Vol 23 (1) ◽  
pp. 138-143
Author(s):  
G. C. Rana ◽  
R. Chand ◽  
Veena Sharma
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Dispersion Relation ◽  
Rayleigh Number ◽  
Normal Modes ◽  
Darcy Number ◽  
Taylor Number ◽  
Boussinesq System ◽  
Brinkman Model ◽  
Stationary Convection

Abstract In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relation accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.

scholarly journals Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

2017 ◽  
Vol 47 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana ◽  
Dhananjay Yadav
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Mode Analysis ◽  
Brownian Diffusion

Abstract Thermal instability in a horizontal layer of Couple-stress nanofluid in a porous medium is investigated. Darcy model is used for porous medium. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticle is taken to be zero on the isothermal boundaries. Normal mode analysis and perturbation method is employed to solve the eigenvalue problem with the Rayleigh number as eigenvalue. Oscillatory convection cannot occur for the problem. The effects of Couple-stress parameter, Lewis number, modified diffusivity ratio, concentration Rayleigh number and porosity on stationary convection are shown both analytically and graphically.

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