Solution of Darcy–Brinkman–Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach

Murali, K.; Naidu, V. Kesavulu; Venkatesh, B.

doi:10.1088/1742-6596/1172/1/012033

Cited by 7 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method of manufactured solutions is adopted [20,21,24,25]; hence, we consider the model equations with the functions f w (y, t), f ϕ (y, t) and f θ (y, t) added to the right hand side of (1), ( 2) and (3), respectively, where Further, we impose the initial and boundary conditions w(y, 0) = cos(πy), ϕ(y, 0) = e −y 2 , θ(y, 0) = 1 (14) and…”

Section: Numerical Verificationmentioning

confidence: 99%

“…Due to the various applications mentioned above, many researchers have studied related work in the field of porous media flow. The finite element method was used to obtain the solution of the Darcy-Brinkman-Forchheimer equation for an irregular channel flow [14] nonlinear Brinkman-Forchheimer-extended Darcy flow was investigated by an approximate analytical solution in [5]. Three different physical situations governed by the nonlinear Brinkman-Forchheimer-extended Darcy model were studied.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

Nwaigwe

Oahimire²,

Weli

2023

ACM

View full text Add to dashboard Cite

This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.

show abstract

Section: Numerical Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

Nwaigwe

Oahimire²,

Weli

2023

ACM

View full text Add to dashboard Cite

show abstract

“…Moreover, he discussed both linear and nonlinear stability. The role of the finite element method to find the solution of Darcy Brinkman Forchheimer's (DBF) equation of irregular flow has been investigated by Murali et al, [9] the solution of nonlinear PDEs is obtained from the finite element approach (Gauss seidel and quasi linearization method) and the corresponding method is equipped with the help of some programming packages moreover they get the 10 −5 accuracy in the final solution. The onset of Darcy-Rayleigh convection in a viscoelastic, doubly diffusive, binary fluid layer saturated in an anisotropic porous material with temperature-dependent viscosity is analyzed numerically.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Linear, Parabolic and Inverted Parabolic Salinity Gradients on The Onset of Darcy Brinkman Rayleigh Benard Two-Component Convection in a Two-Layered System with Dufour Effect

Sumithra¹,

Munikrishnappa²,

Thomaiyar³

2023

ARFMTS

View full text Add to dashboard Cite

The physical configuration of the problem of Darcy Brinkman (DB) Rayleigh Benard Two-Component (RBTC) Convection in a two-layered system has been investigated for linear, parabolic and inverted parabolic salinity gradients with the Dufour effect. For the fluid layer, the upper boundary is free with surface tension and for the porous layer, the lower boundary is rigid. At the interface, the normal velocity, normal stress, shear stress, mass, mass flux, heat, and heat flux are continuous. The regular perturbation method is used to solve the resulting ordinary differential equations obtained from normal mode expansion. The effect of different physical parameters on the Rayleigh number versus depth ratio is discussed and results are presented graphically.

show abstract

“…[14][15][16][17]), for the nonlinear Darcy-Brinkman-Forchheimer model, one can mostly find results based on numerical simulations (see, e.g. [18][19][20][21]). Analytical treatments are quite sparse and have been reported recently for simple fractures with smooth walls and with no error analysis provided (see [22]).…”

Section: Introductionmentioning

confidence: 99%

On the Forchheimer‐extended Darcy‐Brinkman flow through a thin fracture

Pažanin,

Radulović

2023

Z Angew Math Mech

View full text Add to dashboard Cite

In this paper, we study the flow through a thin fracture filled with fluid‐saturated sparsely packed porous medium. The problem is described by the Forchheimer extended Darcy‐Brinkman model incorporating the quadratic drag term as a result of the inertial effects. Employing asymptotic analysis with respect to the fracture's thickness, we derive the higher‐order approximation for the velocity and pressure distribution explicitly acknowledging the Forchheimer (inertial) term. We provide numerical example as well and perform a rigorous error analysis to indicate the order of accuracy of the proposed approximate solution.

show abstract

Solution of Darcy–Brinkman–Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach

Cited by 7 publications

References 19 publications

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

The Effect of Linear, Parabolic and Inverted Parabolic Salinity Gradients on The Onset of Darcy Brinkman Rayleigh Benard Two-Component Convection in a Two-Layered System with Dufour Effect

On the Forchheimer‐extended Darcy‐Brinkman flow through a thin fracture

Contact Info

Product

Resources

About