Effects of small boundary perturbation on flow of viscous fluid

Marušić–Paloka, Eduard

doi:10.1002/zamm.201500195

Cited by 11 publications

(26 citation statements)

References 10 publications

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“…We state that the procedures below are similar to the ones found in [], except for the estimate of temperature because the Stokes system does not depend on temperature. By denoting

{\overset{u}{true}}^{ε} = false⟨ {\tilde{u}}_{x}^{ε}, {\tilde{u}}_{y}^{ε} false⟩

, Marušić‐Paloka considered the Stokes system,

- Δ {\overset{u}{true}}^{ε} + \nabla {\overset{p}{true}}^{ε} = 0, div {\overset{u}{true}}^{ε} = 0 in {normalΩ}^{ε},

{\overset{u}{true}}^{ε} = 0, for y = 0, 1 - ε h false(x false), {\overset{u}{true}}_{y}^{ε} = 0 and {\overset{p}{true}}^{ε} = p_{k} for x = k, and k = 0, 1,

and derived an effective model and wall law (see Sections 2.1, 3.1, and –). Therefore, we simply recall the previous results for velocity and pressure but focus on the computations for temperature.…”

Section: Introductionmentioning

confidence: 90%

“…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%

“…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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“…We state that the procedures below are similar to the ones found in [], except for the estimate of temperature because the Stokes system does not depend on temperature. By denoting