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Volumn 80, Issue 6, 2009, Pages

Spectral analysis of the weighted Laplacian in slip and no-slip flows

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION - DIFFUSION; DENSITY OF STATE; EIGEN FUNCTION; HERMITIAN OPERATORS; LAPLACIANS; NO-SLIP BOUNDARY CONDITIONS; PARALLEL FLOWS; SCALAR FIELDS; SCALING BEHAVIOR; SLIP BOUNDARY CONDITIONS; SLIP CONDITION; SLIP FLOW; SPECTRAL ANALYSIS; SPECTRAL PROPERTIES; VELOCITY FIELD;

EID: 72449148186     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.066302     Document Type: Article
Times cited : (4)

References (31)
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    • This result stems from a detailed numerical analysis of the advection-diffusion problem for channel possessing aspect ratio α>5, by solving the complete advection-diffusion equation Eq., enforcing both the infinite-column approximation and the Danckwerts condition. For fixed Peeff, the accuracy of the approximation in which axial diffusion is neglected improves as the aspect ratio α increases.
    • This result stems from a detailed numerical analysis of the advection-diffusion problem for channel possessing aspect ratio α>5, by solving the complete advection-diffusion equation Eq., enforcing both the infinite-column approximation and the Danckwerts condition. For fixed Peeff, the accuracy of the approximation in which axial diffusion is neglected improves as the aspect ratio α increases.
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    • The integrals Eq. converge for any finite value of Peeff. For 2D straight channels, and 3D circular channels in the presence of no-slip boundary conditions (Poiseuille flow), it can be proved that, for n>2, m out (n) ∼ Pe eff (n-1) /3, while m out (1) ∼log Peeff, as discussed in Sec. . In the presence of slip boundaries, the nth moment for any n>1 converges for Peeff →∞ towards a constant value corresponding to the nth moment of the purely kinematic residence-time distribution.
    • The integrals Eq. converge for any finite value of Peeff. For 2D straight channels, and 3D circular channels in the presence of no-slip boundary conditions (Poiseuille flow), it can be proved that, for n>2, m out (n) ∼ Pe eff (n-1) /3, while m out (1) ∼log Peeff, as discussed in Sec.. In the presence of slip boundaries, the nth moment for any n>1 converges for Peeff →∞ towards a constant value corresponding to the nth moment of the purely kinematic residence-time distribution.
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    • The eigenvalues/eigenfunctions have been obtained numerically by expanding ψ (y) in cosines, ψ (y) = σ k=0 N xk cos (kπy), and by solving the generalized eigenvalue problem -λBx=Ax, where x= (x0, x1,..., xN), A= (Ah,k =- (πh) 2 sh δh,k), s0 =1, sh =1/2, h>1, B= (Bh,k = i;y) dy).
    • The eigenvalues/eigenfunctions have been obtained numerically by expanding ψ (y) in cosines, ψ (y) = σ k=0 N xk cos (kπy), and by solving the generalized eigenvalue problem -λBx=Ax, where x= (x0, x1,..., xN), A= (Ah,k =- (πh) 2 sh δh,k), s0 =1, sh =1/2, h>1, B= (Bh,k = ∫01 u (y) cos (hπy) cos (kπy) dy).
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    • The fact that limε→0 (ε) = r0 approaches a constant value derives from the most critical situation for the c spectrum expressed by Eq. The observation r0 ∼O (10-1) for no-slip Poiseuille flow is numerical.
    • The fact that limε→0 (ε) = r0 approaches a constant value derives from the most critical situation for the c spectrum expressed by Eq.. The observation r0 ∼O (10-1) for no-slip Poiseuille flow is numerical.
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.