scholarly journals The Coriolis Effect on Thermal Convection in a Rotating Sparsely Packed Porous Layer in Presence of Cross-Diffusion

Coatings ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Suman Shekhar ◽  
Ravi Ragoju ◽  
Gudala Janardhana Reddy ◽  
Mikhail A. Sheremet
Keyword(s):  
Rayleigh Number ◽  
Eigenvalue Problem ◽  
Porous Layer ◽  
Lewis Number ◽  
Darcy Number ◽  
Taylor Number ◽  
Wave Number ◽  
Physical Parameters ◽  
Critical Wave Number ◽  
Cross Diffusion

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number.

scholarly journals Influence of entropy on Brinkman–Forchheimer model of MHD hybrid nanofluid flowing in enclosure containing rotating cylinder and undulating porous stratum

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fares Redouane ◽  
Wasim Jamshed ◽  
S. Suriya Uma Devi ◽  
Belhadj M. Amine ◽  
Rabia Safdar ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Rotational Speed ◽  
Rotating Cylinder ◽  
Darcy Number ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Positive Direction ◽  
Medium Permeability

AbstractThe current article aims to discuss the natural convection heat transfer of Ag/Al2O3-water hybrid filled in an enclosure subjected to a uniform magnetic field and provided with a rotating cylinder and an inner undulated porous layer. The various thermo-physical parameters are investigated such as Rayleigh number ($$100 \le Ra \le 100000$$ 100 ≤ R a ≤ 100000 ), Hartmann number ($$0 \le Ha \le 100$$ 0 ≤ H a ≤ 100 ), and the nanoparticles concentration ($$0.02 \le \phi \le 0.08$$ 0.02 ≤ ϕ ≤ 0.08 ). Likewise, the rotational speed of the cylinder ($$- 4000 \le \omega \le + 4000$$ - 4000 ≤ ω ≤ + 4000 ), as well as several characteristics related to the porous layer, are examined li its porosity ($$0.2 \le \varepsilon \le 0.8$$ 0.2 ≤ ε ≤ 0.8 ), Darcy number ($$- 100000 \le Da \le - 100$$ - 100000 ≤ D a ≤ - 100 ) which indicates the porous medium permeability and the number of undulations ($$0 \le N \le 4$$ 0 ≤ N ≤ 4 ). The calculations are carried out based on the Galerkin Finite element method (GFEM) to present the streamlines, isotherms, entropy generation, and average Nusselt numbers in details. The main results proved that increment of Rayleigh number and Darcy number enhances heat transfer convection within the enclosure. Whilst, the porosity presents a minimal impact. Also, the rotational speed in a positive direction has a favorable influence on the heat transfer dispersion across the cavity.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

scholarly journals Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

2019 ◽  
pp. 1-13
Author(s):  
C. Israel-Cookey ◽  
L. Ebiwareme ◽  
E. Amos
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Internal Heat ◽  
Lewis Number ◽  
Mode Analysis ◽  
Internal Heating ◽  
Vadasz Number ◽  
The Stability ◽  
Solutal Rayleigh Number

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter,  and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number,  and solutal Rayleigh number,  delay the onset of instability.

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

Thermal Stability of Horizontally Superposed Porous and Fluid Layers

1989 ◽  
Vol 111 (2) ◽  
pp. 357-362 ◽  
Author(s):  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Darcy Number ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Porous Layers ◽  
Fluid Layers ◽  
Comprehensive Picture

The results of stability analyses for the onset of convective motion are reported for the following three horizontally superposed systems of porous and fluid layers: (a) a porous layer sandwiched between two fluid layers with rigid top and bottom boundaries, (b) a fluid layer overlying a layer of porous medium, and (c) a fluid layer sandwiched between two porous layers. By changing the depth ratio dˆ from zero to infinity, a set of stability criteria (i.e., the critical Rayleigh number Rac and the critical wave number ac) is obtained, ranging from the case of a fluid layer between two rigid boundaries to the case of a porous layer between two impermeable boundaries. The effects of k/km (the thermal conductivity ratio), δ (the square root of the Darcy number), and α (the nondimensional proportionality constant in the slip condition) on Rac and ac are also examined in detail. The results in this paper, combined with those reported previously for Case (a) (Pillatsis et al., 1987), will provide a comprehensive picture of the interaction between a porous and a fluid layer.

Convection in a viscoelastic fluid-saturated sparsely packed porous layer

1990 ◽  
Vol 68 (12) ◽  
pp. 1446-1453 ◽  
Author(s):  
N. Rudraiah ◽  
P. V. Radhadevi ◽  
P. N. Kaloni
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Critical Rayleigh Number ◽  
Maxwell Fluid ◽  
Wave Number ◽  
Jeffrey Fluid ◽  
Oscillatory Convection ◽  
Viscoelastic Parameters ◽  
Jeffreys Model

The linear stability of a viscoelastic fluid-saturated sparsely packed porous layer heated from below is studied analytically using the Darcy–Brinkman–Jeffreys model with different boundary combinations. The Galerkin technique is employed to determine the criterion for the onset of oscillatory convection. The effects of the viscoelastic parameters, the Prandtl number, and the porous parameter on the critical Rayleigh number, the wave number, and the frequency are analyzed. The results are compared with those obtained for both a Darcy–Jeffrey fluid and a Maxwell fluid. It is shown that under certain conditions for the viscoelastic parameters, the flow is overstable. The possibility of the occurrence of bifurcation is also discussed.

scholarly journals SIMILARITY SOLUTION OF HEAT AND MASS TRANSFER FOR LIQUID EVAPORATION ALONG A VERTICAL PLATE COVERED WITH A THIN POROUS LAYER

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Md Hasanuzzaman
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Porous Layer ◽  
Vertical Plate ◽  
Nonlinear Partial Differential Equations ◽  
Lewis Number ◽  
Darcy Number ◽  
Shooting Technique ◽  
Liquid Evaporation

In this paper, heat and mass transfer for liquid evaporation along a vertical plate covered with a thin porous layer has been investigated. The continuity, momentum, energy and mass balance equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations and solved analytically and numerically by using the shooting technique in MATLAB. The effect of various parameters like the Froude number, the porosity, the Darcy number, the Prandtl number, the Lewis number and the driving parameters on the temperature and concentration profiles are presented and discussed. It is viewed that the heat transfer performance is enhanced by the presence of a porous layer. The local Nusselt number and the local Sherwood numbers are computed and analyzed both numerically and graphically.

scholarly journals Effect of Centrifugal Force on a Porous Anisotropic Medium in Rotation, Saturated by a Non-Newtonian Fluid

2019 ◽  
pp. 1-10
Author(s):  
Vodounnou Edmond Claude ◽  
Ahouannou Clément ◽  
Semassou Guy Clarence ◽  
Sanya A. Emile ◽  
Dègan Gérard
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Linear Stability ◽  
Centrifugal Force ◽  
Newtonian Fluid ◽  
Critical Rayleigh Number ◽  
Wave Number ◽  
Marginal Stability ◽  
Critical Wave Number ◽  
Anisotropic Porous Medium

The present study deals with the linear stability of an anisotropic porous medium in rotation, saturated by a non-Newtonian fluid in a rectangular cavity heated on the side, subjected to the effect of the centrifugal force. The state of marginal stability is established by determining the critical Rayleigh number and the critical wave number. We have observed the effect of the parameters  and  of the anisotropy on the convection threshold.

Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
J. C. Umavathi ◽  
Ali J. Chamkha
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Fluid Model ◽  
Lewis Number ◽  
Double Fourier Series ◽  
Elastic Parameter ◽  
Cross Diffusion ◽  
Nusselt Numbers ◽  
Approach To Steady State ◽  
The Impact

Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

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.

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