Thermodiffusion, Marangoni and Gravity Driven Convections in a Liquid Layer Overlying a Porous Layer: Lateral Heating Conditions

2008 ◽  
Author(s):  
M. A. Rahman ◽  
M. Z. Saghir
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Microgravity Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Buoyancy Convection ◽  
Gravity Driven

In this paper, we study the onset of thermal convection in a liquid layer overlying a porous layer, where the whole system being laterally heated. The non-linear two-dimensional Navier Stokes equations, the energy equation and the mass transfer equation are solved for the liquid layer. Instead of Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. Three cases are presented in this paper. In the first case, the gravity driven buoyancy convection is studied. In the second case, the surface tension is assumed to vary linearly with temperature, therefore the existence of Marangoni convection. To analyze the Marangoni convection, we consider microgravity condition. Different aspect ratios as well as the thickness ratios are studied in detail for both the first and second cases. In the third case, diffusion and the thermodiffusion between two binary fluids with two different compositions in liquid and porous layer is studied.

scholarly journals Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

scholarly journals Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

2021 ◽  
Vol 17 ◽  
Author(s):  
B. Kanimozhi ◽  
M. Muthtamilselvan ◽  
Qasem M. Al-Mdallal ◽  
Bahaaeldin Abdalla
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Radial Magnetic Field ◽  
Navier Stokes Equations ◽  
Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Numerical Modeling of Si0.15Ge0.85 by the Traveling Solvent Method

2002 ◽  
Author(s):  
T. J. Makriyannis ◽  
M. Z. Saghir ◽  
D. Labrie
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Promising Technique ◽  
High Quality ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Buoyancy Convection ◽  
Strong Convection ◽  
Element Technique

The traveling solvent method (TSM) is a relatively new and promising technique for the production of high quality semiconductors. TSM has been tested on many alloys producing pure and homogeneous crystals. In the present study the effect of buoyancy convection on the growth of the Si0.15Ge0.85 crystal grown by the traveling solvent method is investigated under different heating conditions. The full Navier-Stokes equations together with the energy and solutal equations were solved numerically using the finite element technique. The model take into consideration the losses of heat by radiation and the use of the phase diagram to determine the silicon concentration at the growth interface. Results revealed a strong convection in the solvent, which in turn is detrimental to the growth uniformity in the crystal rod. Additional numerical results showed that the convective heat transfer significantly influences the solute distribution in the liquid zone and the growth rate increases substantially.

Centrifugal instabilities during spin-down to rest in finite cylinders. Numerical experiments

1981 ◽  
Vol 102 ◽  
pp. 329-352 ◽  
Author(s):  
G. P. Neitzel ◽  
Stephen H. Davis
Keyword(s):  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Onset Time ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Initial State ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Gradient Forces ◽  
Axis Of Symmetry

A cylinder filled with a viscous, incompressible fluid is in an initial state of rigid-body rotation about its axis of symmetry. If the container is brought to rest impulsively, the resulting unsteady spin-down flow may be subject to sidewall instabilities due to an imbalance between centrifugal and pressure gradient forces. These instabilities are examined numerically using a finite-difference simulation to integrate the axisymmetric Navier–Stokes equations for a variety of aspect ratios and Reynolds numbers. The Taylor–Görtler vortex-wavelength spectrum, the torque and the angular momentum histories are calculated. Criteria for the onset time for instability and the spin-down time are given. The effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed. The results are compared with experiment.

scholarly journals Instability of inclined fluid-film flow with substrate filtration

2021 ◽  
Author(s):  
Hom N. Kandel
Keyword(s):  
Stokes Equations ◽  
Nonlinear Effects ◽  
Fluid Film ◽  
Navier Stokes ◽  
Neutral Stability ◽  
Fluid Films ◽  
Navier Stokes Equations ◽  
Gravity Driven ◽  
The Stability ◽  
Natural Settings

Gravity-driven flows of thin fluid films with a free surface along a porous substrate occur in many important circumstances found in industry and natural settings. In this thesis a model for such flows is derived by coupling the Navier-Stokes equations governing the clear flow in the fluid film with Darcy's law for the filtration of fluid through the porous medium. A linear stability analysis is conducted and the effect of various parameters on the state of neutral stability is investigated. A simplified model is developed by reducing the dimensionality of the problem, which is then employed in order to determine the nonlinear effects on the stability of the equilibrium flow.

scholarly journals Study of the stability of a thin liquid layer in the Landau–Levich problem

2020 ◽  
pp. 48-55
Author(s):  
A. V. Lyushnin ◽  
◽  
K. A. Permyakova ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Liquid Layer ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landay–Levich problem is theoretically investigated. The free energy of this layer is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of two electric layers at both interphase boundaries. In the framework of long-wave approximation, the stability of such a system with respect to perturbations is studied in the system of Navier–Stokes equations. A stability map is provided for different layer thicknesses.

Numerical Investigation on the Effect of Marangoni Convection in an Industrial Czochralski Crucible

2002 ◽  
Author(s):  
V. Kumar ◽  
G. Brenner ◽  
F. Durst ◽  
G. Biswas
Keyword(s):  
Free Surface ◽  
Radial Velocity ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Crystalline Silicon ◽  
Marangoni Effect ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thermal Fields ◽  
Different Depths

The quasi direct numerical simulations (DNS) of the flow and the thermal fields in an industrial Czochralski crucible have been carried out in order to investigate the effect of thermocapillary or Marangoni convection employing an optimised parallel-vector block-structured Navier-Stokes equations solver. The simulations have been performed without and with the Marangoni effect at a specified rotation of the crucible during the synthesis of mono-crystalline Silicon (Pr=0.011). The time-averaged flow field reveals that the inward radial velocity at the free surface of the melt is quite high for the case with Marangoni convection. The flow is directed towards the solid crystal due to the presence of significant surface tension gradients at the free surface. A stronger downward flow has been observed at the center of the crucible owing to this strong radial velocity. Due to the superposition of the Marangoni convection, temperature fluctuations are reduced under the free surface and at the crystal interface. Thus the fluctuations in the growth rate are reduced. The turbulent kinetic energy, k is smaller below the crystal at different depths in the melt for the cases without any effect of the Marangoni convection as compared to the cases with Marangoni convection. The temperature along the free surface of the melt is increased when the thermocapillary effect is included.

Hydrodynamic Performance of Autonomous Underwater Gliders with Active Twin Undulatory Wings of Different Aspect Ratios

2020 ◽  
Vol 8 (7) ◽  
pp. 476 ◽  
Author(s):  
Yongcheng Li ◽  
Jianxin Hu ◽  
Qiuzhuo Zhao ◽  
Ziying Pan ◽  
Zheng Ma
Keyword(s):  
Linear Growth ◽  
Stokes Equations ◽  
Hydrodynamic Performance ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Underwater Glider ◽  
Navier Stokes Equations ◽  
Underwater Gliders ◽  
Aspect Ratios ◽  
Autonomous Underwater Glider

The propulsive performance of a bio-inspired autonomous underwater glider (AUG) with active twin undulatory wings undergoing undulatory motion was investigated by numerically solving the viscous incompressible Navier–Stokes equations, coupled with the immersed boundary method. The aspect ratio (AR) effects of the undulatory wings were studied. The simulation results showed that with the increase of AR, the thrust force generated by the active twin undulatory wings showed a linear growth, while the propulsion efficiency of the AUG increased to the peak and then decreased. The optimum magnitude of AR around 2 was obtained in the current study. The vortex structures in the wake of the active twin wings are also presented and discussed. The conclusions acquired here could provide guidance for the new conceptual design of bio-inspired AUGs.

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