Improved lumped-differential formulations and hybrid solution methods for drying in porous media

Dantas, L.B.; Orlande, Helcio R. B.; Cotta, Renato M.

doi:10.1016/j.ijthermalsci.2006.11.019

Cited by 25 publications

(2 citation statements)

References 23 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.

View full text Add to dashboard Cite

show abstract

“…This method has been applied to different problems, where it has been shown to yield much superior results than those obtained by the classical lumped system analysis (CLSA) or has extended the range of applicability of lumped models. As a result, the formulations that use this approximation are called improved lumped formulations and can be found in a number of recent studies, such as ablation [29], drying [30], heat conduction with temperature-dependent conductivity [31], transient convective and radiative cooling [32], adsorbed gas storage [33], heat conduction with a melting of a phase change material [34], thermal modeling of building elements [35], multilayered composite pipeline with active heating [36], and friction factor in irregularly shaped ducts [37]. In spite of the number of studies that employ improved lumped formulations, there is no application of this technique for Graetz-type problems.…”

Section: Introductionmentioning

confidence: 99%

Improved lumped analysis of Graetz problems with axial diffusion

Barros

Sphaier

2019

J Braz. Soc. Mech. Sci. Eng.

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This paper proposes analytical approximations for solving extended Graetz problems with axial diffusion in infinite domains. A general formulation, valid for both parallel-plates channels and circular ducts, is employed, and a discontinuous Dirichlet condition is applied at the wall. The adopted methodology consists of transforming the 2D convection equation into simpler one-dimensional forms, using approximation rules provided by the Coupled Integral Equations Approach. This technique is employed for producing expressions for the bulk temperature, and different levels of approximations are analyzed. The results are compared with an exact analytical solution to the problem and an expression obtained with the classical lumped system analysis (CLSA). While the results obtained with the CLSA are demonstrated to be substantially discrepant compared to the exact solution, the proposed improved formulas are equivalently simple and are shown to provide very good estimates for calculating the bulk temperature distribution. In addition, estimates for the length through which heat is diffused backward are also calculated with the derived approximate formulations and a practically perfect agreement is obtained with the higher-order approximation and the exact solution data.

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Mass Transfer in a Porous Medium: Multicomponent and Multiphase Flows

Nield

Bejan

2012

Convection in Porous Media

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Improved lumped-differential formulations and hybrid solution methods for drying in porous media

Cited by 25 publications

References 23 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

Improved lumped analysis of Graetz problems with axial diffusion

Mass Transfer in a Porous Medium: Multicomponent and Multiphase Flows

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