scholarly journals The onset of Marangoni bio-thermal convection in a layer of fluid containing gyrotactic microorganisms

2021 ◽  
Vol 6 (12) ◽  
pp. 13552-13565
Author(s):  
Latifa I. Khayyat ◽  
◽  
Abdullah A. Abdullah ◽  
Keyword(s):  
Thermal Convection ◽  
Marangoni Number ◽  
Fluid Layer ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Stationary Mode ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms

<abstract><p>The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of fluid containing motile gyrotactic microorganisms. The fluid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Péclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. The results of this study showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover, the critical eigenvalues obtained were real-valued indicating that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values.</p></abstract>

scholarly journals Marangoni convection in layers of water-based nanofluids under the effect of rotation

2021 ◽  
Vol 19 (1) ◽  
pp. 1029-1046
Author(s):  
Abeer H. Bakhsh ◽  
Abdullah A. Abdullah
Keyword(s):  
Marangoni Convection ◽  
Volume Fraction ◽  
Steady State Solution ◽  
Horizontal Layer ◽  
Brownian Diffusion ◽  
Nanoparticle Volume Fraction ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Modified Model ◽  
Conservation Condition

Abstract A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.

scholarly journals Magneto Convection in a Layer of Nanofluid With Soret Effect

2015 ◽  
Vol 9 (2) ◽  
pp. 63-69 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Fluid Layer ◽  
Soret Effect ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Diffusive Convection ◽  
Mode Method ◽  
Double Diffusive

AbstractDouble diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.

Thermal convection in gas–droplet mixtures with phase transition

1975 ◽  
Vol 70 (1) ◽  
pp. 89-112
Author(s):  
T. Kambe ◽  
R. Takaki
Keyword(s):  
Water Vapour ◽  
Density Gradient ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Travelling Waves ◽  
Horizontal Layer ◽  
Phase Changes ◽  
Droplet Growth ◽  
The Stability ◽  
Droplet Density

Thermal convection in a three-component fluid consisting of an inert carrier gas, a condensable vapour and small liquid droplets dispersed throughout the gaseous components has been investigated both theoretically and experimentally. The theoretical study is concerned with the stability of a horizontal fluid layer subject to gradients of both temperature and droplet density. The stability is characterized by four parameters: two material constants, that is, a modified Prandtl number P and a constant Q proportional to Dm − κ (Dm is the mutual mass diffusivity of the two gaseous constituents, κ the thermometric conductivity of the gas phase), a modified Rayleigh number R and a parameter S defined as the ratio of the droplet density gradient to the gas density gradient. It is shown for positive R that, irrespective of the value of R, the system is stable for S > S∞ (S∞ is a constant dependent on P and Q) and unstable for S < Q (Q is normally less than S∞) and that for the intermediate range Q < S < S∞ a transition from stability to instability occurs via an oscillatory state as R is increased through a critical value depending on S. It is shown that the stability is governed largely by both vapour diffusion through the inert gas and droplet growth or decay due to phase changes.In the experiments, thermal convection in a three-component fluid consisting of air, water vapour and water droplets was investigated. The cloud of droplets was mainly formed by injecting cigarette smoke into a horizontal layer of air saturated with water vapour. After the injection several phases of motion were observed successively. Among them there were travelling waves and steady cellular convection. Measurements were made of the critical Rayleigh numbers for the onset of the phases, the scale of the steady convection cells and the speed of the travelling waves. It is found that all the qualitative features of the experiment are explained by the theory.

Dufour and Soret Effects on the Thermosolutal Instability of Rivlin– Ericksen Elastico–Viscous Fluid in Porous Medium

2012 ◽  
Vol 67 (12) ◽  
pp. 685-691 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
The Stability

Dufour and Soret effects on the convection in a horizontal layer of Rivlin-Ericksen elastico- viscous fluid in porous medium are considered. For the porous medium, the Darcy model is used. A linear stability analysis based upon normal mode analysis is employed to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection has been derived analytically, and graphs have been plotted, giving various numerical values to various parameters, to depict the stability characteristics. The effects of the Dufour parameter, Soret parameter, solutal Rayleigh number, and Lewis number on stationary convection have been investigated.

Onset of thermal convection in a horizontal fluid layer under ramp heating

2002 ◽  
Author(s):  
Dae Jun Yang ◽  
Jake Kim ◽  
Chang Kyun Choi ◽  
In Gook Hwang
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Horizontal Fluid Layer

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

Linear stability of rotating convection in an imposed shear flow

1997 ◽  
Vol 350 ◽  
pp. 271-293 ◽  
Author(s):  
PAUL MATTHEWS ◽  
STEPHEN COX
Keyword(s):  
Rayleigh Number ◽  
Shear Flow ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Thermal Convection ◽  
Critical Rayleigh Number ◽  
Rotation Vector ◽  
Linear Stability Theory ◽  
Fixed Temperature ◽  
Differential Motion

In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.

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