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.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

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.

scholarly journals Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Javier A. Dottori ◽  
Gustavo A. Boroni ◽  
Alejandro Clausse
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Entropy Method ◽  
Alternative Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary ◽  
Boltzmann Method

A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM) based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.

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.

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.

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