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.

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.

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 Convection regimes induced by local boundary heating in a liquid–gas system

2019 ◽  
Vol 873 ◽  
pp. 441-458 ◽  
Author(s):  
Victoria B. Bekezhanova ◽  
A. S. Ovcharova
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Local Heating ◽  
Fluid Motion ◽  
Lower Boundary ◽  
Conjugate Problem ◽  
Temperature Fields ◽  
Layer System ◽  
Local Boundary ◽  
The Impact

In the framework of the complete formulation of the conjugate problem, the liquid–gas flow structure arising upon local heating using thermal sources is investigated numerically. The two-layer system is confined by solid impermeable walls. The Navier–Stokes equations in the Boussinesq approximation in the ‘streamfunction–vorticity’ variables are used to describe the media motion. The dynamic conditions at the interface are formulated in terms of the tangential and normal velocities, while the temperature conditions at the external boundaries of the system take into account the presence of local heaters. The influence of the number of heaters and heating modes on the dynamics and character of the appearing convective regimes is analysed. The steady and commutated heating modes for one and two heaters arranged at the lower boundary are investigated. The heating initiates convective and thermocapillary mechanisms causing the fluid motion. Transient regimes with the successive formation of two-vortex, quadruple-vortex and two-vortex flows are observed before the stabilization of the system in the uniform heating mode. A stable thermocapillary deflection appears at the interface above the heater. The commutated mode of heating entails oscillations of the interface with a change in the deflection form and the formation of travelling vortices in the fluids. The impact of particular mechanisms on the flow patterns is analysed. The paper presents typical distributions of the velocity and temperature fields in the system and the position of the interface for the considered cases.

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