On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary

Marušić–Paloka, Eduard; Pažanin, Igor

doi:10.1007/s11242-016-0818-4

Cited by 14 publications

(18 citation statements)

References 21 publications

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“…In this section, we formally derive the effective solution of – via Taylor series expansion under the assumption,

h (x) < 0 for 0 < x < 1,

so that the solution

(u^{ε}, p^{ε}, θ^{ε})

of – is defined in the unit square domain

Ω : = {normalΩ}^{0} = \{(x, y) \in R^{2} | 0 < x < 1, 0 < y < 1\} .

We can directly expand the solutions in a Taylor series with respect to y near the rough boundary

y = 1 - ε h (x)

. Note that the assumption

h < 0

is only a technical assumption, and the results obtained below are valid for a general smooth function h as in [].…”

Section: Derivation Of Effective Modelmentioning

confidence: 99%

“…Adopting the idea in [, Section 4.2], we estimate the differences between

(U^{ε}, P^{ε}, {normalΘ}^{ε})

and

(U_{app}^{ε}, P_{app}^{ε}, {normalΘ}_{app}^{ε})

. The convection term in the temperature equation induces a computational complexity in the estimation.…”

Section: Justification Of Effective Modelmentioning

confidence: 99%

“…Effective models have been developed for fluid flows only from various perspectives . Broadly, effective models have been proposed by imposing wall laws on an artificial smooth boundary, such as the Navier‐slip wall law ,

u^{1} = C_{N} \frac{\partial u^{1}}{\partial y} on artificial interface,

to represent flow modulations owing to a rough boundary.…”

Section: Introductionmentioning

confidence: 99%

“…Note that

(V_{app}^{ε}, Q_{app}^{ε}, T_{app}^{ε})

is defined in rectangular domain

{normalΩ}^{0} = false(0, 1 false) \times false(0, 1 false)

. Using the concept in [], we derive the approximate solutions by implementing the Taylor series expansion to the original solutions with respect to y near a rough boundary to determine the PDE systems in the

x y

‐coordinates for zeroth–order approximations and next–order correctors. Solving the corresponding PDE system of the zeroth–order approximations provides exact solutions, which do not contain the impact of a rough boundary.…”

Section: Introductionmentioning

confidence: 99%

“…To estimate the error between the proposed effective model and original model for

ε h ≢ 0

, we transform the system of equations in in

Ω^{ε}

into a system in Ω 0 by introducing a new variable

z = y / (1 - ε h (x))

(see also []). Using the solutions

(U^{ε}, P^{ε}, {normalΘ}^{ε})

of the transformed system and their approximated solutions

(U_{app}^{ε}, P_{app}^{ε}, {normalΘ}_{app}^{ε})

, we find PDE systems in

x z

‐coordinates for the zeroth–order approximations and next–order correctors via asymptotic analysis.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of convective heat transfer in channel flow with arbitrary rough surface

2018

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We consider forced convective heat transfer in a channel flow with a rough boundary. The roughness of the domain is expressed as the product of length scale ε and arbitrary smooth function h. The boundaries of the channel are assumed as hot (top) and cold (bottom) walls. We derive an effective model reflecting the rough boundary effects, and analyze the average Nusselt number and wall laws (effective boundary conditions). Consequently, we provide the criterion for the shape of the rough boundary to enhance the heat transfer. We further confirm that the Robin–type effective boundary condition is sufficient to describe the effect of the rough layer on the heat transfer.

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“…In this section, we formally derive the effective solution of – via Taylor series expansion under the assumption,

h (x) < 0 for 0 < x < 1,

so that the solution

(u^{ε}, p^{ε}, θ^{ε})

of – is defined in the unit square domain

Ω : = {normalΩ}^{0} = \{(x, y) \in R^{2} | 0 < x < 1, 0 < y < 1\} .

We can directly expand the solutions in a Taylor series with respect to y near the rough boundary

y = 1 - ε h (x)

. Note that the assumption

h < 0

is only a technical assumption, and the results obtained below are valid for a general smooth function h as in [].…”

Section: Derivation Of Effective Modelmentioning

confidence: 99%

“…Adopting the idea in [, Section 4.2], we estimate the differences between

(U^{ε}, P^{ε}, {normalΘ}^{ε})

and

(U_{app}^{ε}, P_{app}^{ε}, {normalΘ}_{app}^{ε})

. The convection term in the temperature equation induces a computational complexity in the estimation.…”

Section: Justification Of Effective Modelmentioning

confidence: 99%

u^{1} = C_{N} \frac{\partial u^{1}}{\partial y} on artificial interface,

to represent flow modulations owing to a rough boundary.…”

Section: Introductionmentioning

confidence: 99%

“…Note that

(V_{app}^{ε}, Q_{app}^{ε}, T_{app}^{ε})

is defined in rectangular domain

{normalΩ}^{0} = false(0, 1 false) \times false(0, 1 false)

x y

Section: Introductionmentioning

confidence: 99%

“…To estimate the error between the proposed effective model and original model for

ε h ≢ 0

, we transform the system of equations in in

Ω^{ε}

into a system in Ω 0 by introducing a new variable

z = y / (1 - ε h (x))

(see also []). Using the solutions

(U^{ε}, P^{ε}, {normalΘ}^{ε})

of the transformed system and their approximated solutions

(U_{app}^{ε}, P_{app}^{ε}, {normalΘ}_{app}^{ε})

, we find PDE systems in

x z

‐coordinates for the zeroth–order approximations and next–order correctors via asymptotic analysis.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of convective heat transfer in channel flow with arbitrary rough surface

2018

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

Pažanin,

Radulović

2023

Z Angew Math Mech

Self Cite

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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.

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Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

Beneš

Pažanin

2017

Continuum Mech. Thermodyn.

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On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary

Cited by 14 publications

References 21 publications

Analysis of convective heat transfer in channel flow with arbitrary rough surface

Analysis of convective heat transfer in channel flow with arbitrary rough surface

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

Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

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