Hybrid solution for transient internal convection with axial diffusion

Gondim, R.R.; Macêdo, Emanuel Negrão; Cotta, Renato M.

doi:10.1108/09615530710739176

Cited by 7 publications

(10 citation statements)

References 11 publications

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“…Also, more elaborate filtering schemes could provide a substantial enhancement in convergence behavior to further improve the computational performance of either of the algorithms here implemented, such as the local instantaneous filtering strategy discussed in Gondim et al [9]. Processing Time (sec) R Fig.…”

Section: Discussionmentioning

confidence: 95%

Integral transform solutions for atmospheric pollutant dispersion

Almeida

Pimentel

Cotta

2007

Environ Model Assess

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A transient two-dimensional advection-diffusion model describing the turbulent dispersion of pollutants in the atmosphere has been solved via the Generalized Integral Transform Technique (GITT), by two different schemes. The first approach performs numerical integration of the transformed system using available routines for initial value problems with automatic error control. In spite of the timeconsuming character of such a scheme, its flexibility allows the handling of problems involving time-dependent meteorological parameters such as wind speed and eddy diffusivities. The second approach works fully analytically being thus intrinsically more robust and economic, although not directly applicable in dealing with time-dependent parameters. For the test problem used in this work, both methods agree very well with each other, as well as with a known analytical solution for a simpler formulation used as benchmark. The impact of the longitudinal diffusivity on the stiffness of the ordinary differential equation (ODE) system arising from the integral transformation has been assessed through the processing time demanded to solve it when the numerical approach is used. The observed CPU times show that the analytical approach is clearly preferable unless the problem involves time-dependent parameters.

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Section: Discussionmentioning

confidence: 95%

Integral transform solutions for atmospheric pollutant dispersion

Almeida

Pimentel

Cotta

2007

Environ Model Assess

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“…Transient evolution of dimensionless average temperature and verification withGondim et al (2003Gondim et al ( , 2007 for parallel-plates channel and step change in inlet temperature, Kn = 0, Br = 0, and S = 15. In(a) Pe = 1, in (b) Pe = 10 typical parameter values, Kn = 0.01 and Pe = 10, with b t ¼ 1:957 and b m ¼ 1:0.…”

mentioning

confidence: 80%

“…Therefore, the test case by Gondim et al (2003Gondim et al ( , 2007 for a regular parallel-plate channel (Kn = 0), with steady velocity profile, is here considered for different and representative values of the Péclet number. Therefore, the test case by Gondim et al (2003Gondim et al ( , 2007 for a regular parallel-plate channel (Kn = 0), with steady velocity profile, is here considered for different and representative values of the Péclet number.…”

Section: Steady Transient and Periodic Convection With Slip Flowmentioning

confidence: 99%

“…Therefore, the test case by Gondim et al (2003Gondim et al ( , 2007 for a regular parallel-plate channel (Kn = 0), with steady velocity profile, is here considered for different and representative values of the Péclet number. A truncation order of just N = 15 terms was considered sufficient for convergence in the present verification, as will be examined in what follows, since we are dealing with a single integral transformation, which is performed along the most diffusive direction (η) and exactly transforming the transversal convection term, as opposed to the double transformation in Gondim et al (2003Gondim et al ( , 2007, which requires larger truncation orders. Therefore, Fig.…”

Section: Steady Transient and Periodic Convection With Slip Flowmentioning

confidence: 99%

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Analytical Heat and Fluid Flow in Microchannels and Microsystems

Cotta

Knupp

Naveira-Cotta

2016

Mechanical Engineering Series

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the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.More information about this series at

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“…(41) and (42). The general analytical solution given by formulae (28) is still under investigation and it may require additional mathematical development such as eigenvalue ordering 24 and/or local filtering [25][26][27] . 54 and 55).…”

Section: Test Case 2: Tank Model In a Homogeneous And Isotropic Mediumentioning

confidence: 99%

A General Analytical Solution for the Multidimensional Transient Linear Hydraulic Diffusivity Equation in Heterogeneous and Anisotropic Porous Media

Couto

Moreira²,

Marsili

2011

All Days

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A general analytical solution for the multidimensional transient linear hydraulic diffusivity equation is presented and its application is discussed in this work. The analytical solution is valid for heterogeneous and anisotropic porous media in any orthogonal coordinate system within a regular boundary domain. A source term, dependent on position and time, was included in the partial differential equation to represent production and/or injection wells. A general boundary condition is considered to account for a constant pressure boundary, a no-flow boundary (symmetry or impermeable boundary) or any prescribed flow boundary. The Generalized Integral Transform Technique (GITT) was used to obtain the analytical solution of the proposed problem. This technique transforms a complex partial differential equation into a system of simpler ordinary differential equations that can be solved by analytical, numerical or hybrid methods. Here, we consider a fully analytical solution to the problem. The general solution is then applied to a one-phase tank model in a homogeneous and isotropic porous medium for validation and analysis. A wide variety of applications can be envisioned and discussed for the proposed general solution: well testing in regular and irregular domains, analysis of local reservoir heterogeneities, analysis of reservoir anisotropy degree, analysis of stream lines in naturally fractured and hydraulic fractured reservoirs, formation damage quantification, reservoir shape factor calculations, oil recovery in different waterflood patterns, amongst many others. These applications are discussed and analyzed in the light of the presented general analytical solution.

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Hybrid solution for transient internal convection with axial diffusion

Cited by 7 publications

References 11 publications

Integral transform solutions for atmospheric pollutant dispersion

Integral transform solutions for atmospheric pollutant dispersion

Analytical Heat and Fluid Flow in Microchannels and Microsystems

A General Analytical Solution for the Multidimensional Transient Linear Hydraulic Diffusivity Equation in Heterogeneous and Anisotropic Porous Media

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