Navier-Stokes-Brinkman system for interaction of viscous waves with a submerged porous structure

Guta, Lemi; Sundar, S.

doi:10.5556/j.tkjm.41.2010.722

Cited by 15 publications

(4 citation statements)

References 13 publications

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“…The basic governance equations of Brinkman fluid consist of continuity, momentum and energy equations. According to Guta and Sundar [14] and Nield and Bejan [15], the equations of an incompressible fluid in vectorial form are written as…”

Section: Fig 1 Two-dimensional Geometry Of the Flowmentioning

confidence: 99%

“…Employing the Brinkman model to the viscoelastic model, an additional viscoelastic term is incorporated in momentum equation to describe the fluid viscosity and elasticity. The modified Cauchy stress tensor for Brinkman-viscoelastic fluid based on Tonekaboni et al, [16] and Guta and Sundar [14] is…”

Section: Fig 1 Two-dimensional Geometry Of the Flowmentioning

confidence: 99%

“…Then, the non-similarity transformation is introduced to find the solutions of Eqs. ( 11) to (14) as below…”

Section: Non-similarity Transformationmentioning

confidence: 99%

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Free Convection Boundary Layer Flow of Brinkman-Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Wall Temperature

Kanafiah

Kasim²,

Zokri³

et al. 2023

CFDL

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The demand on the complex model on the study of fluid flow problem is crucial since the real fluid exist in industry applications cannot be presented by the conventional fluid anymore due to the complex properties of the materials. Since then, many mathematicians and scientist try to create the model that can be presented those fluids. Fluid which having characteristics viscous and elasticity can be categorized as non-Newtonian type of fluid due to its relations which against Newton’s Law of viscosity. The application of the fluid is widespread in industrial applications including oils and gas sectors, the automobile industry and manufacturing processes. Paints is one of the examples of viscoelastic fluid since almost wall is painted by the materials polymer and solvents. Therefore, this work is intended to investigate the viscoelastic fluid flow with the porosity condition which then called as Brinkman-viscoelastic model. The flow is presumed to transfer over a geometry horizontal circular cylinder (HCC). The thermal boundary condition is set to be constant wall temperature (CWT). The governing equations which based on Navier Stokes equations are first transformed to the less complex form by utilizing a non-dimensionless and a non-similarity variable. The resulting equations were obtained in the partial differential equations (PDEs) and at the lower stagnation point case, the model is reduced to the ordinary differential equations (ODEs). The Keller-box method (KBM) is applied to solved the final equations. The validation process is performed by direct comparing with the established output in literature and found to be in a very strong agreement. This process is valid since the present model can be reduced to the previous model at the limiting case where the identical equations were obtained. The results of the present model are then computed and presented in tabular form and also illustrated in graphical form. It is noticed that the viscoelastic parameter and Brinkman Parameter significantly affected the fluid flow characteristics.

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Section: Fig 1 Two-dimensional Geometry Of the Flowmentioning

confidence: 99%

Section: Fig 1 Two-dimensional Geometry Of the Flowmentioning

confidence: 99%

See 1 more Smart Citation

Free Convection Boundary Layer Flow of Brinkman-Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Wall Temperature

Kanafiah

Kasim²,

Zokri³

et al. 2023

CFDL

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“…B. Verleye et al [1] presented a mathematical model of the permeability of textile by using Navier-Stokes-Brinkman Equations and employed the finite difference method to find the numerical solutions. L. Guta and S. Sundar [13] presented the wave-porous structure interaction by using the Navier-Stokes-Brinkman system and applied the Finite Volume Method (FVM) to calculate the numerical results. O. Iliev et al [15] presented a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations for various scientific and industrial problems.…”

Section: Introductionmentioning

confidence: 99%

The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations

Wuttanachamsri

Oangwatcharaparkan

2021

Tamkang J. Math.

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In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.

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Sneak Flow Simulations in the IXV′s Windward TPS Assembly

Patrício

2012

Modelling and Simulation in Fluid Dynamics in Porous Media

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Navier-Stokes-Brinkman system for interaction of viscous waves with a submerged porous structure

Cited by 15 publications

References 13 publications

Free Convection Boundary Layer Flow of Brinkman-Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Wall Temperature

Free Convection Boundary Layer Flow of Brinkman-Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Wall Temperature

The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations

Sneak Flow Simulations in the IXV′s Windward TPS Assembly

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