Enhanced lumped-differential formulations of diffusion problems

Corrêa, E.J.; Cotta, Renato M.

doi:10.1016/s0307-904x(98)00005-5

Cited by 37 publications

(24 citation statements)

References 8 publications

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“…Since its development, the CIEA has been applied to many problems. Among these studies, deserve mention the ones involving phase change [3], heat transfer in fins [4], heat exchangers [5,6], linear heat conduction [7], hyperbolic heat conduction [8], radiative cooling [9], ablation [10], drying [11], heat diffusion with temperaturedependent conductivity [12], and combined convectiveradiative cooling [13,14]. A very similar approach was also used in the work of Keshavarz and Taheri [15].…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical methodology for calculating friction factors in flow through polygonal cross section ducts

Reis

Sphaier

Alves

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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An approximate analytical methodology for calculating the friction factor within ducts of irregular cross-section is herein proposed. The approximations are developed by transforming the original governing PDEs into simpler ODEs, using approximation rules provided by the coupled integral equations approach. The transformed system is directly integrated and analytical solutions for the friction factor are readily obtained. Four different approximation cases are analyzed, which yield simple closed-form expressions for calculating the friction factor in terms of geometric parameters for rectangular, triangular, and trapezoidal ducts. The results of these expressions are compared with literature data, and very reasonable agreement is seen. After performing an error analysis of the results, regions for applicability of the methodology where accuracy requirements can be maintained are highlighted. Finally, enhanced approximation formulas yielding maximum errors as low as 3% are developed by using simple weighted averages of different approximation cases. Keywords Lumped-capacitance formulation Á Arbitrary geometry Á Friction factor Á Mathematical modeling List of symbols a, b, c Geometric parameters in cross-section domain D H Hydraulic diameter f Fanning's friction-factor G Ã Dimensionless pressure gradient H a;b Hermite approximation K Aspect ratio p Pressure u Axial velocity u Cross-sectional averaged velocity U Dimensionless axial velocity x Axial variable X Dimensionless function for left boundary y, z Cross-section variables Y, Z Dimensionless problem variables z 1 Function for left boundary Re Reynolds number Greek symbols a, b, m Hermite approximation parameters n, g Dimensionless left boundary function parameters l Dynamic viscosity f i Solution constants

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Section: Introductionmentioning

confidence: 99%

Approximate analytical methodology for calculating friction factors in flow through polygonal cross section ducts

Reis

Sphaier

Alves

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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show abstract

“…Due to the widespread availability of user-friendly and powerful numerical software, the method has lost its practical value for solving heat conduction problems in simple solid geometries. In the last decades some researchers have touched upon the subject again, unknowing the existence of the integral approximation method (Correa & Cotta, 1998;Sadat, 2005;van der Sman, 2003). These studies have rendered improved lumped models, frequently identical as the ones obtained by integral approximation.…”

Section: Integral Approximation To Heat Conduction Problemsmentioning

confidence: 99%

Scale analysis and integral approximation applied to heat and mass transfer in packed beds

Sman

2008

Journal of Food Engineering

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“…Hermite procedure allows the model order reduction by approaching an integral on the values of the integrating and their derivatives on the limits of the integration, as follow: (11) The technique makes use of H 0,0 , H 1,1 definitions and simultaneously of the spherical coordinates transformation, facilitating the generation of the radial medium variables (13,15,16).…”

Section: Reduction Technique Based On the Hermite Integrations Formulasmentioning

confidence: 99%

A new process for acrylic acid synthesis by fermentative process

Lunelli

Duarte

Toledo

et al. 2007

Appl Biochem Biotechnol

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With the synthesis of chemical products through biotechnological processes, it is possible to discover and to explore innumerable routes that can be used to obtain products of high added value. Each route may have particular advantages in obtaining a desired product, compared with others, especially in terms of yield, productivity, easiness to separate the product, economy, and environmental impact. The purpose of this work is the development of a deterministic model for the biochemical synthesis of acrylic acid in order to explore an alternative process. The model is built-up with the tubular reactor equations together with the kinetic representation based on the structured model. The proposed process makes possible to obtain acrylic acid continuously from the sugar cane fermentation.

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Enhanced lumped-differential formulations of diffusion problems

Cited by 37 publications

References 8 publications

Approximate analytical methodology for calculating friction factors in flow through polygonal cross section ducts

Approximate analytical methodology for calculating friction factors in flow through polygonal cross section ducts

Scale analysis and integral approximation applied to heat and mass transfer in packed beds

A new process for acrylic acid synthesis by fermentative process

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