MOTION OF A SLIP SPHERE IN A NONCONCENTRIC FICTITIOUS SPHERICAL ENVELOPE OF MICROPOLAR FLUID

2014 ◽  
Vol 55 (4) ◽  
pp. 383-401
Author(s):  
E. I. SAAD
Keyword(s):  
Boundary Conditions ◽  
Drag Force ◽  
Volume Fraction ◽  
Cell Model ◽  
Translational Motion ◽  
Slip Boundary ◽  
Spherical Envelope ◽  
Spherical Fluid ◽  
Special Case ◽  
Slip Coefficients

AbstractStokes’ axisymmetrical translational motion of a slip sphere, located anywhere on the diameter of a virtual spherical fluid ‘cell’, is investigated. The fluid is micropolar and flows are parallel to the line connecting the two centres. An infinite-series solution is presented for the stream function, pressure field, vorticity, microrotation component, shear stress and couple stress of the flow. Basset-type slip boundary conditions on the sphere surface are used for velocity and microrotation. The Happel and Kuwabara boundary conditions are used on the fictitious surface of the cell model. Numerical results for the normalized drag force acting on the sphere are obtained with excellent convergence for various values of the volume fraction, the relative distance between the centre of the sphere and the virtual envelope, the vortex viscosity parameter and the slip coefficients of the sphere. In the special case when the spherical particle is in the concentric position with the cell surface, the numerical values of the normalized drag force agree with the available values in the literature.

scholarly journals Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quanrong Li ◽  
Shijin Ding
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Strip Domain ◽  
Navier Slip Boundary Conditions ◽  
Slip Coefficients

<p style='text-indent:20px;'>This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have defined sign. In the meantime, we also establish a number of Gagliardo-Nirenberg inequalities in the corresponding Sobolev spaces which will be applicable to other similar situations.</p>

scholarly journals Cell Models for Non-Newtonian Fluid Past a Semipermeable Sphere

2019 ◽  
Vol 4 (6) ◽  
pp. 1352-1361
Author(s):  
Madasu Krishna Prasad
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Micropolar Fluid ◽  
Stokes Equations ◽  
Translational Motion ◽  
Tangential Velocity ◽  
Solid Sphere ◽  
Normal Velocity ◽  
Cell Models ◽  
Spherical Envelope

This paper is focused on investigating the boundary effects of the steady translational motion of a semipermeable sphere located at the center of a spherical envelope filled with an incompressible micropolar fluid. Stokes equations of micropolar fluid are employed inside the spherical envelope and Darcy’s law governs in semipermeable region. On the surface of semipermeable sphere, the boundary conditions used are continuity of normal velocity, vanishing of tangential velocity of micropolar fluid, and continuity of pressure. On the surface of the spherical envelope, the Happel’s, Kuwabara’s, Kvashnin’s, and Cunningham’s boundary conditions, are used along with no spin boundary condition. The expression for the hydrodynamic normalized drag force acting on the semipermeable sphere is obtained. The limiting cases of drag expression exerted on the semipermeable sphere and impermeable solid sphere in cell models filled with Newtonian fluid are obtained. Also, in absence of envelope, the drag expression for the micropolar fluid past a semipermeable sphere is obtained.

Heat and Mass Transfer of MHD Dissipative Casson Nanofluid Flow over a Stretching or Shrinking Sheet with Multiple Slip Boundary Conditions

2019 ◽  
Vol 393 ◽  
pp. 103-120 ◽  
Author(s):  
Emmanuel O. Titiloye ◽  
Jacob A. Gbadeyan ◽  
A.T. Adeosun
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Shrinking Sheet ◽  
Nanoparticle Volume Fraction ◽  
Slip Boundary Conditions ◽  
Nanofluid Flow ◽  
Slip Boundary ◽  
Stretching Or Shrinking Sheet

The present study concerns steady two-dimensional laminar mixed convective boundary layer Casson nanofluid flow along a stretching or shrinking sheet with multiple slip boundary conditions in a non-Darcian porous medium. The effect of viscous dissipation and non-linear radiation are considered. The governing partial differential equations, together with boundary conditions are transformed into a system of dimensionless coupled ordinary differential equations. Galerkin weighted residual method is then employed to solve the transformed coupled ordinary differential equations. The effect of various controlling parameters on dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient and nanoparticle volume fraction gradient are presented graphically and discussed. The present approach is validated by comparing the result of this work and those available in the literature, and they are found to be in excellent agreement.

scholarly journals Thermal Radiation in Nanofluid Penetrable Flow Bounded with Partial Slip Condition

CFD letters ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 32-44
Author(s):  
Nadia Diana Mohd Rusdi ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan Md. Arifin ◽  
Norfifah Bachok
Keyword(s):  
Boundary Conditions ◽  
Thermal Radiation ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Slip Boundary ◽  
Exponentially Shrinking Sheet ◽  
Layer Flow

Thermal radiation enhances heat transfer, and it is used widely in manufacturing and materials processing applications. Thus, steady two-dimensional boundary layer flow over an exponentially porous shrinking sheet of nanofluids was considered in the influence of thermal radiation related to partial slip boundary conditions and suction. This paper aims to study the nanofluid penetrable flow over an exponentially shrinking sheet with thermal radiation and partial slip. The effects of silver (Ag) nanoparticles with two different types of base fluids named water and kerosene oil are investigated in this study. First, the governing equations and boundary conditions are transformed to a non-linear ordinary differential equation and then solved using bvp4c solver. Using Matlab software, it is found that the dual solution exists in some values from the suction parameter. Furthermore, we identified both nanoparticle volume fraction and suction parameter increase, leading to the rise in velocity profile. Moreover, the suction parameter increases both skin friction coefficient and Nusselt number increase.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

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.

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