scholarly journals Non-Darcian-Bènard Double Diffusive Magneto-Marangoni Convection in a Two Layer System with Constant Heat Source/Sink

2021 ◽  
pp. 4039-4055
Author(s):  
N. Manjunatha ◽  
R. Sumithra
Keyword(s):  
Porous Layer ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Type I ◽  
Layer System ◽  
Constant Heat ◽  
Double Diffusive

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection   is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field.   The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects.  The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal.  The corresponding two TMNs   are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail.

scholarly journals Darcy-Benard double diffusive Marangoni convection in a composite layer system with constant heat source along with non uniform temperature gradients

2021 ◽  
Vol 17 (1) ◽  
pp. 7-15
Author(s):  
N Manjunatha ◽  
R Sumithra ◽  
R K Vanishree
Keyword(s):  
Marangoni Number ◽  
Marangoni Convection ◽  
Composite Layer ◽  
Lower Boundary ◽  
Temperature Gradients ◽  
Layer System ◽  
Constant Heat ◽  
The Impact ◽  
Double Diffusive ◽  
Diffusivity Ratio

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system enclosed by adiabatic boundaries for Darcy model. This composite layer is subjected to three temperature gradients with constant heat sources in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The Eigenvalue problem of a system of ordinary differential equations is solved in closed form for the Thermal Marangoni number, which happens to be the Eigen value. The three different temperature profiles considered are linear, parabolic and inverted parabolic profiles with the corresponding thermal Marangoni numbers are obtained. The impact of the porous parameter, modified internal Rayleigh number, solute Marangoni number, solute diffusivity ratio and the diffusivity ratio on Darcy-Benard double diffusive Marangoni convection are investigated in detail.

Combined effects of nonuniform temperature gradients and heat source on double diffusive Benard-Marangoni convection in a porous-fluid system in the presence of vertical magnetic field

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
N. Manjunatha ◽  
R. Sumithra ◽  
R.K. Vanishree
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Temperature Gradients ◽  
Vertical Magnetic Field ◽  
Nonuniform Temperature ◽  
Fluid System ◽  
Double Diffusive

The physical configuration of the problem is a porous-fluid layer which is horizontally unbounded, in the presence of uniform heat source/sink in the layers enclosed by adiabatic and isothermal boundaries. The problem of double diffusive Bènard-Marangoni convection in the presence of vertical magnetic field is investigated on this porous-fluid system for non-Darcian case and is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary conditions. The influence of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer and the applied magnetic field play an important role in controlling Benard-Marangoni convection. The parameters which direct this convection are determined and the effect of porous parameter is relatively interesting.

scholarly journals THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A LAYER OF NANOFLUID UNDER ROTATION

2016 ◽  
Vol 15 (1) ◽  
pp. 88
Author(s):  
G. C. Rana ◽  
R. C. Thakur
Keyword(s):  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Brownian Diffusion ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Double-diffusive convection in a horizontal layer of nanofluid under rotation heated from below is studied. The nanofluid describes the effects of thermophoresis and Brownian diffusion. Based upon perturbations and linear stability theory, the normal mode analysis method is applied to obtain the dispersion relation characterizing the effect of different parameters when both the boundaries are free. Due to thermal expansion, the nanofluid at the bottom will be lighter than the fluid at the top. Thus, this is a top heavy arrangement which is potentially unstable. In this paper we discuss the influences of various non-dimensional parameters such as rotation, solute gradient, thermo- nanofluid Lewis number, thermo-solutal Lewis number, Soret and Dufour parameter on the stability of stationary convection for the case of free-free boundaries. It is observed that rotation and solute gradient have stabilizing influence on the system. Rotation and solute gradient play important role in the thermal convection of fluid layer and has applications in rotating machineries such as nuclear reactors, petroleum industry, biomechanics etc. and solute gradient finds applications in geophysics, food processing, soil sciences, oil reservoir modeling, oceanography etc. A very good agreement is found between the present paper and earlier published results.

Onset of Triply Diffusive Convection in a Maxwell Fluid Saturated Porous Layer

2013 ◽  
Vol 353-356 ◽  
pp. 2580-2585 ◽  
Author(s):  
Mo Li Zhao ◽  
Shao Wei Wang ◽  
Qiang Yong Zhang
Keyword(s):  
Porous Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Maxwell Fluid ◽  
Maxwell Model ◽  
Mode Analysis ◽  
Analysis Model ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Triply Diffusive Convection

The linear stability of triply diffusive convection in a binary Maxwell fluid saturated porous layer is investigated. Applying normal mode analysis , the criterion for the onset of stationary and oscillatory convection is obtained. The modified Darcy-Maxwell model is used as the analysis model. This allows us to make a thorough investigation of the processes of viscoelasticity and diffusions that causes the convection to set in through oscillatory rather than stationary. The effects of the parameters of Vadasz number, normalized porosity parameter, relaxation parameter, Lewis number and solute Rayleigh number are presented.

The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Medium ◽  
Molecular Diffusion ◽  
Normal Mode Analysis ◽  
Finite Amplitude ◽  
Mode Analysis ◽  
Double Diffusive Convection ◽  
Amplitude Analysis ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

Stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous layer

2017 ◽  
Vol 826 ◽  
pp. 376-395 ◽  
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Couette Flow ◽  
Porous Layer ◽  
Poiseuille Flow ◽  
Fluid Layer ◽  
Maximum Velocity ◽  
Stability Characteristic ◽  
Layer System ◽  
Neutral Curves ◽  
Layer Mode ◽  
The Stability

This paper performs a linear stability analysis to investigate the stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous medium saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow may destabilize the Poiseuille flow at small depth ratio $\hat{d}$, defined by the ratio of the depth of the fluid layer to the depth of the porous layer, and induce a tri-modal structure to the neutral curves. At moderate $\hat{d}$, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal behaviour of the neutral curves appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Poiseuille–Couette flow in a single fluid layer in that the flow becomes absolutely stable when the wall velocity is over 70 % of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is the same as the stability characteristic of a single-layer plane Couette flow.

scholarly journals Effect of Magnetic Field on Thermosolutal Instability of Rotating Ferromagnetic Fluid Under Varying Gravity Field

2021 ◽  
Vol 26 (1) ◽  
pp. 201-214
Author(s):  
S. K. Pundir ◽  
P. K. Nadian ◽  
R. Pundir
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Magnetic Field Rotation ◽  
Stabilizing Effect ◽  
Ferromagnetic Fluid ◽  
Solute Gradient

AbstractThis paper deals with the theoretical investigation of the effect of a magnetic field, rotation and magnetization on a ferromagnetic fluid under varying gravity field. To find the exact solution for a ferromagnetic fluid layer contained between two free boundaries, we have used a linear stability analysis and normal mode analysis method. For the case of stationary convection, a stable solute gradient has a stabilizing effect, while rotation has a stabilizing effect if λ>0 and destabilizing effect if λ<0. Further, the magnetic field is discovered to have both a stabilizing and destabilizing effect for both λ>0 and λ<0. It is likewise discovered that magnetization has a stabilizing effect for both λ>0 and λ<0 in the absence of the stable solute gradient. Graphs have been plotted by giving numerical values of various parameters. In the absence of rotation, magnetic field and stable solute gradient, the principle of exchange of stabilities is found to hold true for certain conditions.

scholarly journals Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
I. K. Khalid ◽  
N. F. M. Mokhtar ◽  
I. Hashim ◽  
Z. B. Ibrahim ◽  
S. S. A. Gani
Keyword(s):  
Feedback Control ◽  
Heat Source ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Density Ratio ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Double Diffusive

A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system.

Effect of Rotation and Magnetic Field on Thermal Stability of Ferromagnetic Fluid

2013 ◽  
Author(s):  
Amrish K. Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Thermal Stability ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Linearized Stability ◽  
Ferromagnetic Fluid ◽  
Exchange Of Stability ◽  
Thermal Stability Of

In this paper, the effect of rotation and magnetic field on thermal stability of a layer of ferromagnetic fluid heated from below has been investigated. For a fluid layer between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis. For the case of stationary convection, it is found that magnetic field and rotation have stabilizing effect on the thermal stability of the system. The principle of exchange of stability is not valid for the problem under consideration, whereas in the absence of rotation and magnetic field, it is valid.

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