Effect of Wall Conduction on the Stability of a Fluid in a Rectangular Region Heated from Below

1972 ◽  
Vol 94 (4) ◽  
pp. 446-452 ◽  
Author(s):  
Ivan Catton
Keyword(s):  
Lateral Wall ◽  
Rectangular Region ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Aspect Ratios ◽  
Usual Manner ◽  
Vertical Walls ◽  
The Stability ◽  
The Galerkin Method ◽  
Good Agreement

The initiation of natural convection in a fluid confined above and below by rigid, perfectly conducting surfaces and laterally by vertical walls of arbitrary thermal conductivity which form a rectangle is examined. The linearized perturbation equations are obtained in the usual manner and reduced to an eigenvalue problem. The Rayleigh number is the eigenvalue and is a function of the lateral-wall conductance and horizontal plan form (aspect ratios). The problem associated with satisfying the no-slip boundary conditions on all surfaces is surmounted by using the Galerkin method. Results are compared with experiments and shown to be in good agreement.

AN ELASTIC-COLLISION SCHEME FOR LATTICE BOLTZMANN METHODS

2001 ◽  
Vol 12 (03) ◽  
pp. 387-401 ◽  
Author(s):  
J. G. ZHOU
Keyword(s):  
Experimental Data ◽  
Lattice Boltzmann ◽  
Elastic Collision ◽  
Complex Geometries ◽  
Slip Boundary Conditions ◽  
Lattice Boltzmann Methods ◽  
Slip Boundary ◽  
Arbitrary Complex ◽  
Bounce Back ◽  
Good Agreement

An elastic-collision scheme is developed to achieve slip and semi-slip boundary conditions for lattice Boltzmann methods. Like the bounce-back scheme, the proposed scheme is efficient, robust and generally suitable for flows in arbitrary complex geometries. It involves an equivalent level of computation effort to the bounce-back scheme. The new scheme is verified by predicting wind-driven circulating flows in a dish-shaped basin and a flow in a strongly bent channel, showing good agreement with analytical solutions and experimental data. The capability of the scheme for simulating flows through multiple bodies has also been demonstrated.

Liquid Transport Properties in Sub-Micron Channel Flows

2001 ◽  
Author(s):  
K. Johan A. Westin ◽  
Kenneth S. Breuer ◽  
Chang-Hwan Choi ◽  
Peter Huang ◽  
Zhiqiang Cao ◽  
...  
Keyword(s):  
Flow Rate ◽  
Low Flow ◽  
Slip Boundary Conditions ◽  
Liquid Transport ◽  
Flow Rates ◽  
Slip Boundary ◽  
Laminar Channel Flow ◽  
Flow Through ◽  
Set Up ◽  
Good Agreement

Abstract An experimental set-up for pressure driven liquid flow through microchannels have been designed and tested. The flow rate is determined by tracking the free liquid surface in a precision bore hole using a laser distance meter. Measurements of the flow rate through silicon microchannels with a height of less than 0.9 μm show good results for Newtonian fluids (silicon oil, ethanol) at flow rates as low as 0.2 nl/s. The experimental results are also in very good agreement with predictions based on laminar channel flow using no-slip boundary conditions, indicating that standard macroscopic assumptions are still valid for these fluids under these conditions. However, experiments with aqueous solutions show anomalies in the form of unexpectedly low flow rates and time dependent variations. Possible explanations to these observations are discussed.

Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

2005 ◽  
Vol 128 (2) ◽  
pp. 176-182 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Heat Generation ◽  
Analytical Study ◽  
Vertical Component ◽  
Governing Equations ◽  
Biharmonic Equations ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Volumetric Heat Generation ◽  
Good Agreement

An analytical study has been conducted for natural convection in a cavity of different aspect ratios with uniform volumetric heat generation. Two different boundary conditions are investigated for the cavity, viz., all walls are isothermal; two horizontal walls are adiabatic and two vertical walls are isothermal. A stream function vorticity formulation is used where the variables are expanded in terms of Rayleigh number, defined as Ra=gβh5q‴∕ανk. The governing equations are reduced, to biharmonic equations, and these biharmonic equations are solved using one of the methods, available in the literature. It is observed that the horizontal component of velocity is smaller than the vertical component near the center and the vertical walls of the cavity. The results for velocity profiles are compared with the simulations obtained from Fluent and they are found to be in good agreement.

scholarly journals ON THE STABILITY OF SELF-PROPELLED BODIES WITH RESPECT TO THEIR SHAPE MOTION

2011 ◽  
Vol 21 (04) ◽  
pp. 667-691 ◽  
Author(s):  
MATTHIEU BONNIVARD
Keyword(s):  
System Analysis ◽  
Finite Dimension ◽  
Slip Boundary Conditions ◽  
Shape Stability ◽  
Slip Boundary ◽  
Moving Body ◽  
The Stability ◽  
Regularity Results ◽  
Perfect Slip Boundary Conditions ◽  
Dynamic Shape

This paper studies the stability of the trajectories of self-propelled bodies immersed in a fluid at low Reynolds number, with respect to their dynamic shape deformation. We consider both adherence and perfect slip boundary conditions on the moving body. Using shape derivative arguments in association with recent higher order regularity results for the Bogovskiĭ operator, we bring the shape stability question to a finite dimension dynamical system analysis.

Gaseous Slip Flow in a Micro-Channel

2003 ◽  
Author(s):  
Shou-Shing Hsieh ◽  
Huang-Hsiu Tsai ◽  
Chih-Yi Lin ◽  
Ching-Fang Huang ◽  
Cheng-Ming Chien
Keyword(s):  
Gas Flow ◽  
Perturbation Methods ◽  
Flow Model ◽  
Slip Flow ◽  
Micro Channel ◽  
Slip Boundary Conditions ◽  
Nitrogen Gas ◽  
Slip Boundary ◽  
Mass Flow Rates ◽  
Good Agreement

An experimental and theoretical study of low Reynolds number compressible gas flow in a micro channel is presented. Nitrogen gas was used. The channel was microfabricated on silicon wafers and were 50 μm deep, 200 μm wide and 24000 μm long. The Knudsen number ranged from 0.001 to 0.02. Pressure drop were measured at different mass flow rates in terms of Re and found in good agreement with those predicted by analytical solutions in which a 2-D continuous flow model with first slip boundary conditions are employed and solved by perturbation methods.

Microstructure in the Sedimentation of Anisotropic and Deformable Particles

2005 ◽  
Author(s):  
David Saintillan ◽  
Eric Darve ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Large Scale ◽  
Point Particle ◽  
Particle Interactions ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Deformable Particles ◽  
Orientation Distributions ◽  
Viscous Droplets ◽  
Large Scale Simulations ◽  
Good Agreement

We use large-scale simulations to study the microstructure and concentration fluctuations in sedimenting suspensions of anisotropic particles such as spheroids, and deformable particles such as viscous droplets in the Stokes flow regime. An efficient method based on point-particle interactions is used allowing the simulation of full-scale suspensions with both periodic and slip boundary conditions, where the latter are used to qualitatively reproduce the effects of container walls. The concentration instability occurring in such systems is adequately captured, and we show that the formation of inhomogeneities is closely linked to the large-scale fluctuations of the disturbance flow. In particular, our simulations suggest that the presence of walls is important for a wavenumber selection to be observed, as they lead to a decay of the initial large-scale recirculation that otherwise dominates the flow in periodic systems. Results for the sedimentation rates and orientation distributions are also presented, and show good agreement with published experimental results.

scholarly journals A SUBGRID STABILIZED METHOD FOR NAVIER-STOKES EQUATIONS WITH NONLINEAR SLIP BOUNDARY CONDITIONS

2021 ◽  
Vol 26 (4) ◽  
pp. 528-547
Author(s):  
Xiaoxia Dai ◽  
Chengwei Zhang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Fine Mesh ◽  
High Reynolds ◽  
The Stability ◽  
Nonlinear Slip Boundary Conditions

In this paper, we consider a subgrid stabilized Oseen iterative method for the Navier-Stokes equations with nonlinear slip boundary conditions and high Reynolds number. We provide one-level and two-level schemes based on this stability algorithm. The two-level schemes involve solving a subgrid stabilized nonlinear coarse mesh inequality system by applying m Oseen iterations, and a standard one-step Newton linearization problems without stabilization on the fine mesh. We analyze the stability of the proposed algorithm and provide error estimates and parameter scalings. Numerical examples are given to confirm our theoretical findings.

The Effect of Wall Conduction on the Stability of a Fluid in a Right Circular Cylinder Heated From Below

1983 ◽  
Vol 105 (2) ◽  
pp. 255-260 ◽  
Author(s):  
J. C. Buell ◽  
I. Catton
Keyword(s):  
Critical Rayleigh Number ◽  
Slip Boundary Condition ◽  
Dimensionless Temperature ◽  
Axisymmetric Mode ◽  
Slip Boundary ◽  
Wall Conductivity ◽  
Stream Functions ◽  
Cylindrical Volume ◽  
The Stability ◽  
The Galerkin Method

The onset of natural convection in a cylindrical volume of fluid bounded above and below by rigid, perfectly conducting surfaces and laterally by a wall of arbitrary thermal conductivity is examined. The critical Rayleigh number (dimensionless temperature difference) is determined as a function of aspect (radius to height) ratio and wall conductivity. The first three asymmetric modes as well as the axisymmetric mode are considered. Two sets of stream functions are employed to represent a velocity field that satisfies the no-slip boundary condition on all surfaces and conservation of mass everywhere. The Galerkin method is then used to reduce the linearized perturbation equations to an eigenvalue problem. The results for perfectly insulating and conducting walls are compared with the work of Charlson and Sani[9].

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