Convection-Free Thermodiffusion in a Water-Ethanol Mixture Subject to Varying Thermal Boundary Conditions

2005 ◽  
Author(s):  
M. Chacha ◽  
M. Z. Saghir
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Thermal Control ◽  
Boussinesq Approximation ◽  
Transport Processes ◽  
Navier Stokes ◽  
Soret Coefficient ◽  
Navier Stokes Equations ◽  
Ethanol Mixture ◽  
Thermal Boundary Conditions

The paper presents a precise numerical simulation of the transport processes in a rectangular cavity saturated with a water-ethanol mixture. The full transient Navier-Stokes equations coupled with the heat and mass transfer equations are solved by the means of the finite volume method. The mixture properties are drawn from the recent work by Dutrieux et al. [1]. The density is assumed to vary linearly with temperature and concentration (Boussinesq approximation) in the working temperature range while other thermo physical properties are held constant. After validation the present code is used for a series of numerical experiments. Thermodiffusion in a liquid-mixture of Ethanol and Water is analyzed under zero gravity condition. Different thermal boundary conditions scenarios are considered to simulate possible thermal control system shortcomings. Results of investigations might help in the preparation and monitoring of the heat sources control systems during the direct Soret coefficient measurement experiments.

Gyrotactic bioconvection at pycnoclines

2013 ◽  
Vol 733 ◽  
pp. 245-267 ◽  
Author(s):  
A. Karimi ◽  
A. M. Ardekani
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Lewis Number ◽  
Boussinesq Approximation ◽  
Dynamical Behaviour ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Micro Organisms

AbstractBioconvection is an important phenomenon in aquatic environments, affecting the spatial distribution of motile micro-organisms and enhancing mixing within the fluid. However, stratification arising from thermal or solutal gradients can play a pivotal role in suppressing the bioconvective flows, leading to the aggregation of micro-organisms and growth of their patchiness. We investigate the combined effects by considering gyrotactic motility where the up-swimming cells are directed by the balance of the viscous and gravitational torques. To study this system, we employ a continuum model consisting of Navier–Stokes equations with the Boussinesq approximation coupled with two conservation equations for the concentration of cells and stratification agent. We present a linear stability analysis to determine the onset of bioconvection for different flow parameters. Also, using large-scale numerical simulations, we explore different regimes of the flow by varying the corresponding boundary conditions and dimensionless variables such as Rayleigh number and Lewis number ($\mathit{Le}$) and we show that the cell distribution can be characterized using the ratio of the buoyancy forces as the determinant parameter when $\mathit{Le}\lt 1$ and the boundaries are insulated. But, in thermally stratified fluids corresponding to $\mathit{Le}\gt 1$, temperature gradients are demonstrated to have little impact on the bioconvective plumes provided that the walls are thermally insulated. In addition, we analyse the dynamical behaviour of the system in the case of persistent pycnoclines corresponding to constant salinity boundary conditions and we discuss the associated inhibition threshold of bioconvection in the light of the stability of linearized solutions.

scholarly journals Convection Inside Nanofluid Cavity with Mixed Partially Boundary Conditions

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6448
Author(s):  
Raoudha Chaabane ◽  
Annunziata D’Orazio ◽  
Abdelmajid Jemni ◽  
Arash Karimipour ◽  
Ramin Ranjbarzadeh
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Square Enclosure ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Boltzmann Method

In recent decades, research utilizing numerical schemes dealing with fluid and nanoparticle interaction has been relatively intensive. It is known that CuO nanofluid with a volume fraction of 0.1 and a special thermal boundary condition with heat supplied to part of the wall increases the average Nusselt number for different aspect ratios ranges and for high Rayleigh numbers. Due to its simplicity, stability, accuracy, efficiency, and ease of parallelization, we use the thermal single relaxation time Bhatnagar-Gross-Krook (SRT BGK) mesoscopic approach D2Q9 scheme lattice Boltzmann method in order to solve the coupled Navier–Stokes equations. Convection of CuO nanofluid in a square enclosure with a moderate Rayleigh number of 105 and with new boundary conditions is highlighted. After a successful validation with a simple partial Dirichlet boundary condition, this paper extends the study to deal with linear and sinusoidal thermal boundary conditions applied to part of the wall.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

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