IMPACT OF NANOFLUIDS ON EXTERNAL AND INTERNAL FLOW VIA NAVIER-STOKES AND CONVECTION-DIFFUSION EQUATIONS FOR PARALLEL PLATES WITH SLIP BOUNDARY CONDITIONS

2020 ◽  
Author(s):  
Ricardo Costa ◽  
Marcos Curi
Keyword(s):  
Boundary Conditions ◽  
Internal Flow ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Slip Boundary Conditions ◽  
Convection Diffusion ◽  
Slip Boundary

scholarly journals IMPACT OF NANOFLUIDS ON EXTERNAL AND INTERNAL FLOW VIA NAVIER-STOKES AND CONVECTIONDIFFUSION EQUATIONS FOR PARALLEL PLATES WITH SLIP BOUNDARY CONDITIONS

2021 ◽  
Vol 20 (1) ◽  
pp. 45
Author(s):  
R. C. S. M. Costa ◽  
M. F. Curi
Keyword(s):  
Boundary Conditions ◽  
Internal Flow ◽  
External Flow ◽  
Engine Oil ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Slip Boundary Conditions ◽  
Constant Heat ◽  
Slip Boundary ◽  
Overall Efficiency

With the modernization and miniaturization of equipment and systems toincrease the overall efficiency in smaller spaces, new cooling solutions needto be developed. Microfluidic in the last decades becomes a new way to getthis. Nanofluids are used to attend this demand to optimize efficiency, withtheir improved thermohydraulic properties, especially different thermalconductivities. To determine the advantages of using a nanofluid for thermalexchange, the properties, parameters and modelling will be presented, and thedifferential equations necessary to obtain the results. In that sense, the basictheory of fluid mechanics and heat transfer, through the Navier-Stokes andConvection-Diffusion equation, is used in the two-dimensional steady-stateformulation. Slip boundary conditions for the velocity field. Constant heat fluxand constant temperature at the surface are used for the temperature field,initially without the flow’s microscale effects. The external flow over a flatplate and internal flow between parallel plates will be studied. Considering alaminar flow, with the base fluid being water and engine oil, with variousvolumetric fractions of Single Wall and Multiple Wall Carbon Nanotubes. Todetermine the results and create the comparative graphs, the WolframMathematica v.11 software will be used for solving the remaining partialdifferential equations.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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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