Analytical Methods in Heat Transfer

Cotta, Renato M.; Knupp, Diego C.; Quaresma, João Nazareno Nonato

doi:10.1007/978-3-319-26695-4_2

Cited by 11 publications

(6 citation statements)

References 35 publications

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“…The Generalized Integral Transform Technique (GITT) (Cotta 1990, 1994, 1998, Cotta & Mikhailov 1997, 2006, Cotta et al 2016, 2017, 2018) was adopted for solving the time-dependent partial differential equations governing both water flow and radionuclide transport, and subsequently used in a radiological impact assessment. The hybrid numerical-analytical GITT approach offers an accurate and robust combination of analytical eigenfunction expansions, which eliminates the spatial variables through integral transforms, and a numerical methodology with automatic error control adopted for solution of the resulting transformed ordinary differential system in the time variable.…”

Section: Solution Methodology and Problem Formulation Formal Solutionmentioning

confidence: 99%

“…We then describe the methodology used for estimating the source term, as well as for the simulations of water flow and radionuclide transport in the leached ore pile and nearby soil layers. The hybrid numerical-analytical methodology known as the Generalized Integral Transform Technique (GITT) (Cotta 1990, 1994, 1998, Cotta & Mikhailov 1997, 2006, Cotta et al 2016, 2017, 2018) was adopted for solution of the partial differential equations governing water flow and radionuclide transport. This hybrid method, which originates from classical integral transform methods (Mikhailov & Ozisik 1984), has been used extensively within thermal sciences and engineering, but more recently also in environmental engineering applications , 2003, Leal & Ruperti 2000, 2001, Liu et al 2000, Rocha & Cruz 2001, Heilbron Filho et al 2002, Barros et al 2006, Skaggs et al 2007, Barros & Cotta 2007, Almeida et al 2008, Perez Guerrero et al 2009, 2010, 2012, Perez Guerrero & Skaggs 2010, Rubol et al 2016.…”

Section: Introductionmentioning

confidence: 99%

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Integral transform analysis of radionuclide transport in variably saturated media using a physical non-equilibrium model: application to solid waste leaching at a uranium mining installation

Cotta

Naveira-Cotta

Genuchten

et al. 2020

An. Acad. Bras. Ciênc.

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The Generalized Integral Transform Technique (GITT) was employed to simulate transient one-dimensional flow in variably saturated porous media, as well as radioactive waste transport within different layers (a solid waste pile, nearby soil, and a granular aquifer) towards the edge of a uranium mining installation under institutional control.Computational codes, written using the Mathematica software system, were implemented and tested for solution of the coupled advection-dispersion equations for an arbitrary number of daughter products within a radioactive chain migrating in saturated and unsaturated soil layers. The computer simulations were verified in great detail against results obtained using the built-in routine NDSolve of the Mathematica platform and the HYDRUS-1D software system. The present work reports the main results for 238 U chain radionuclide transport using data extracted from a safety assessment of solid waste repositories at a uranium mining and milling installation in Caetité, state of Bahia, Brazil, operated by INB (Indústrias Nucleares do Brasil). Concentration evolutions of the various radionuclides obtained with the simulations were analyzed for five different cases to explore variations in the infiltration and recharge rates, the effect of assuming physical equilibrium or non-equilibrium transport conditions, and of different initial concentrations of some of the radionuclides.

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Section: Solution Methodology and Problem Formulation Formal Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integral transform analysis of radionuclide transport in variably saturated media using a physical non-equilibrium model: application to solid waste leaching at a uranium mining installation

Cotta

Naveira-Cotta

Genuchten

et al. 2020

An. Acad. Bras. Ciênc.

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“…Therefore, the GITT approach itself can be employed in transforming the original differential eigenvalue problems into algebraic ones, by proposing a simpler auxiliary eigenvalue problem to provide a base for the eigenfunction expansions, such as described in [16,23,25]. According to the more traditional approach in solving eigenvalue problems, a simpler self-adjoint auxiliary problem could be chosen to provide the base of the eigenfunction expansion in solving problems ( 2) and (3).…”

Section: • Gitt Solution Of Biorthogonal Eigenvalue Problemsmentioning

confidence: 99%

“…Along the years and most markedly after the unification of the integral transform method in seven different classes of linear problems in heat and mass diffusion [11], a hybrid numerical-analytical extension to the classical approach, known as the Generalized Integral Transform Technique (GITT) [14] has been progressively advanced, as reviewed in different sources [15][16][17][18][19][20][21][22][23][24], aimed at handling different classes of formulations that would not allow for an exact integral transformation in the sense of [11].…”

Section: Introductionmentioning

confidence: 99%

Integral Transform Solution of Heat Conduction in Anisotropic Heterogeneous Media

Cotta,

Lachi,

Naveira-Cotta

et al. 2024

Comput Thermal Scien

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The generalized integral transform technique (GITT) is advanced to deal with conduction heat transfer in anisotropic heterogeneous media. A formal solution for exact integral transformation of conduction in anisotropic media is extended to account for heterogeneities expressed as space variable equation coefficients and source terms. The proposed eigenfunction expansion is based on biorthogonal eigenvalue problems, which results in an exact integral transformation for a class of linear problems and in a coupled transformed ordinary differential system for nonlinear situations. An algorithm is proposed for the associated eigenvalue problems, also handled through the GITT, by considering simpler biorthogonal eigenvalue problems of known analytical solution, leading to transformed algebraic eigenvalue problems. A single domain reformulation strategy is adopted to merge the information from multiple regions and materials, either isotropic or anisotropic, into one single diffusion equation. A two-dimensional transient test case is considered that presents an abrupt transition between isotropic and anisotropic materials yielding a marked change in thermal behavior in a defined region of interest formed by the anisotropic inclusion. Convergence behavior of the integral transform solution is illustrated, and the fully converged results are employed as a benchmark to inspect the accuracy of a commercial finite element code for automatically defined mesh refinement levels.

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“…Transform Technique (GITT) is an example of a hybrid method that has been successfully applied in the solution of various flow, heat and mass transfer problems (Aparecido et al, 1989;Cotta, 1990Cotta, , 1993Cotta, , 1994Cotta, , 1998Mikhailov, 1997, 2006;2016a;2016b;2018a;2018b, Pontes et. al., 2018, Serfaty and Cotta, 1990.…”

Section: -Introductionmentioning

confidence: 99%

Approximation error model (AEM) approach with hybrid methods in the forward-inverse analysis of the transesterification reaction in 3D-microreactors

Pontes

Costa

Naveira-Cotta

et al. 2021

Inverse Problems in Science and Engineering

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Approximation error model (AEM) approach with hybrid methods in the forwardinverse analysis of the transesterification reaction in 3D-microreactorsThis work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3Dmicroreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction.For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection-diffusion-reaction problems.

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Analytical Methods in Heat Transfer

Cited by 11 publications

References 35 publications

Integral transform analysis of radionuclide transport in variably saturated media using a physical non-equilibrium model: application to solid waste leaching at a uranium mining installation

Integral transform analysis of radionuclide transport in variably saturated media using a physical non-equilibrium model: application to solid waste leaching at a uranium mining installation

Integral Transform Solution of Heat Conduction in Anisotropic Heterogeneous Media

Approximation error model (AEM) approach with hybrid methods in the forward-inverse analysis of the transesterification reaction in 3D-microreactors

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