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Journal articles on the topic 'Integral Transforms (GITT)'

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Published: 4 June 2021

Last updated: 9 February 2022

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1

Buligon, L., G. A. Degrazia, O. C. Acevedo, C. R. P. Szinvelski, and A. G. O. Goulart. "A semi-analytical solution for the mean wind profile in the Atmospheric Boundary Layer: the convective case." Atmospheric Chemistry and Physics Discussions 9, no. 5 (2009): 19817–44. http://dx.doi.org/10.5194/acpd-9-19817-2009.

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Abstract. A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT), which joints series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind

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2

Buligon, L., G. A. Degrazia, O. C. Acevedo, C. R. P. Szinvelski, and A. G. O. Goulart. "A semi-analytical solution for the mean wind profile in the Atmospheric Boundary Layer: the convective case." Atmospheric Chemistry and Physics 10, no. 5 (2010): 2227–36. http://dx.doi.org/10.5194/acp-10-2227-2010.

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Abstract. A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT), which combines series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wi

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3

Silva, Elizeu Melo da, João N. N. Quaresma, Emanuel N. Macêdo, and Renato M. Cotta. "Integral transforms for three-dimensional pumping in confined, leaky, and unconfined aquifers." Journal of Hydrology and Hydromechanics 69, no. 3 (2021): 319–31. http://dx.doi.org/10.2478/johh-2021-0020.

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Abstract Analytical or hybrid numerical-analytical solutions based on the Generalized Integral Transform Technique (GITT) are obtained for the transient three-dimensional pumping problem of aquifers with a fully penetrating vertical well between two parallel streams. The problem formulation for confined and leaky aquifers allows for achieving exact analytical solutions through integral transforms, while the unconfined aquifer case introduces a fourth kind boundary condition which leads to a coupled transformed head ordinary differential system, that can be solved either analytically or numeric

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4

Cotta, Renato M., Carolina Palma Naveira-Cotta, and Diego C. Knupp. "Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (2016): 767–89. http://dx.doi.org/10.1108/hff-08-2015-0309.

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Purpose – The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis. Design/methodology/approach – The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue proble

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5

Medeiros, Nielson Veloso, Emanuel Negrão Macêdo, Rui Nelson Otoni Magno, Claudio José Cavalcante Blanco, and João Nazareno Nonato Quaresma. "Integral transform solution for the analysis of hydrodynamic lubrication of thrust bearings." Industrial Lubrication and Tribology 69, no. 6 (2017): 1074–84. http://dx.doi.org/10.1108/ilt-08-2016-0187.

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Purpose The aim of this paper is related to an analysis of hydrodynamic lubrication of circular thrust bearings. Design/methodology/approach The modified Reynolds equation was treated to obtain a hybrid numerical-analytical solution through the generalized integral transform technique (GITT) for the problem. Findings Numerical results for the engineering parameters such as pressure field, load capacity and power consumption were thus produced as functions of the radial and circumferential directions. These parameters depend on the geometry of sector-shaped used: Rayleigh pad with 4, 8 and 16 s

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6

Fu, Guangming, Chen An, and Jian Su. "Integral transform solution of natural convection in a cylinder cavity with uniform internal heat generation." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 7 (2018): 1556–78. http://dx.doi.org/10.1108/hff-08-2017-0294.

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Purpose The purpose of this study is to propose the generalised integral transform technique to investigate the natural convection behaviour in a vertical cylinder under different boundary conditions, adiabatic and isothermal walls and various aspect ratios. Design/methodology/approach GITT was used to investigate the steady-state natural convection behaviour in a vertical cylinder with internal uniformed heat generation. The governing equations of natural convection were transferred to a set of ordinary differential equations by using the GITT methodology. The coefficients of the ODEs were de

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7

Machado, H. A., N. G. C. Leite, E. Nogueira, and H. Korzenowisk. "SOLUTION OF MULTIPHASE HEAT CONDUCTION PROBLEMS VIA THE GENERALIZED INTEGRAL TRANSFORM TECHNIQUE WITH DOMAIN CHARACTERIZATION THROUGH THE INDICATOR FUNCTION." Revista de Engenharia Térmica 15, no. 2 (2016): 53. http://dx.doi.org/10.5380/reterm.v15i2.62169.

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The Generalized Integral Transform Technique (GITT) has appeared in the literature as an alternative to conventional discrete numerical methods for partial differential equations in heat transfer and fluid flow. This method permits the automatic control of the error and is easy to program, since there is no need for a discretization. The method has being constantly improved, but there still a vast number of practical problems that has not being solved satisfactory. In several brands of engineering, the transport equations have to be solved for a combination of different phases or materials or

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8

Guigon, J. M. B. S., J. S. Pérez Guerrero, and R. M. Cotta. "COMPUTATIONAL OPTIMIZATION FOR INTEGRAL TRANSFORM ALGORITHMS APPLIED TO THE LID-DRIVEN CAVITY FLOW PROBLEM." Revista de Engenharia Térmica 6, no. 1 (2007): 104. http://dx.doi.org/10.5380/reterm.v6i1.61824.

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An analysis is presented of the computational optimization for integral transform algorithms using the streamfunction only formulation of the Navier-Stokes equations, as applied to the steady incompressible laminar flow of a Newtonian fluid in two-dimensional formulation. The classical lid-driven rectangular cavity flow problem is considered in order to revise the conventional development of the Generalized Integral Transform Technique (GITT). The GITT is applied transforming the partial differential equation into a system of coupled ordinary differential equations, which is numerically solved

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9

Neto, Reynaldo D'Alessandro. "UMA CONSTRUÇÃO HISTÓRICA DAS TÉCNICAS DA TRANSFORMADA INTEGRAL CLÁSSICA (CITT) E GENERALIZADA (GITT)." Boletim Cearense de Educação e História da Matemática 7, no. 20 (2020): 80–92. http://dx.doi.org/10.30938/bocehm.v7i20.2613.

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Estes resultados parciais de uma pesquisa de doutorado do Programa de Pós-Graduação em Educação Matemática da UNESP – Rio Claro, insere-se na linha de pesquisa Relações entre História e Educação Matemática e tem como objetivo descrever a evolução histórica que culmina na concepção da Técnica da Transformada Integral Clássica, e as motivações que levaram a sistematização do seu modelo generalizado. As técnicas têm como foco resolver Equações Diferenciais Parciais (EDP) a princípio não tratáveis pelas teorias clássicas, como o conhecido método da separação de variáveis. Pretendemos fazer uma con

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10

de, B. "An integral transform solution for unsteady compressible heat transfer in fluids near their thermodynamic critical point." Thermal Science 17, no. 3 (2013): 673–86. http://dx.doi.org/10.2298/tsci120826068d.

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The classical thermodynamic model for near critical heat transfer is an integral-differential equation with constant coefficients. It is similar to the heat equation, except for a source term containing the time derivative of the bulk temperature. Despite its simple form, analytical methods required the use of approximations to generate solutions for it, such as an approximate Fourier transformation or a numerical Laplace inversion. Recently, the Generalized Integral Transform Technique or GITT has been successfully applied to this problem, providing a highly accurate analytical solution for i

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11

Maia, C. R. M., R. A. V. Ramos, M. F. Pelegrini, and T. A. Alves. "HEAT TRANSFER STUDY IN SLUG FLOW ON ELLIPTICAL DUCTS CROSS SECTIONS BY GENERALIZED INTEGRAL TRANSFORM TECHNIQUE." Revista de Engenharia Térmica 4, no. 2 (2005): 154. http://dx.doi.org/10.5380/reterm.v4i2.5414.

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This work shows the calculation of heat transfer parameters for slug flow in the thermal entrance region of elliptical section tubes submitted to a second kind boundary condition. The main difficulty in the application of the boundary conditions in problems with this kind of geometry has been removed by using a suitable coordinate change. The generalized integral transform technique (GITT) has been used to obtain the solution of the energy equation. The mixture temperature and the local and average Nusselt numbers have been calculated for several aspect ratios and the results have been compare

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12

Venezuela, A. L., R. F. Cantão, R. S. Ongaratto, and R. N. Haneda. "MODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION." Revista de Engenharia Térmica 17, no. 1 (2018): 94. http://dx.doi.org/10.5380/reterm.v17i1.62266.

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There are several mathematical models that describe permeate flow in membrane separation processes. Among these, the series resistance model plays a prominent role. It takes into account membrane strength, concentration polarization, polarized layer and fouling to describe the permeate flow over time. In this work, an analysis of the modified series resistance model was performed, in which the resistance by polarization of the concentration is defined as being directly proportional to the transmembrane pressure. The proportionality constant is given by the product of a specific coefficient of

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13

An, Chen, and Jian Su. "Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6789634.

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Dynamic behavior of axially functionally graded (FG) pipes conveying fluid was investigated numerically by using the generalized integral transform technique (GITT). The transverse vibration equation was integral transformed into a coupled system of second-order differential equations in the temporal variable. The Mathematica’s built-in function, NDSolve, was employed to numerically solve the resulting transformed ODE system. Excellent convergence of the proposed eigenfunction expansions was demonstrated for calculating the transverse displacement at various points of axially FG pipes conveyin

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14

Fu, Guangming, Yudan Peng, Baojiang Sun, Chen An, and Jian Su. "An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic foundation." Engineering Computations 36, no. 6 (2019): 2034–47. http://dx.doi.org/10.1108/ec-12-2018-0582.

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Purpose The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation. Design/methodology/approach The GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solv

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15

Fávero, Camila, Glênio Aguiar Gonçalves, Daniela Buske, Régis Sperotto de Quadros, and Viliam Cardoso da Silveira. "Modelo de pluma segmento com velocidades estocásticas para dispersão atmosférica em condições de vento fraco." Ciência e Natura 42 (August 28, 2020): e11. http://dx.doi.org/10.5902/2179460x45353.

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This work presents an analytical solution for the transient three-dimensional advection-diffusion equation. This solution, obtained from a combination of the variable separation method and GILTT (Generalized Integral Laplace Transform Technique) is used to simulate the pollutant dispersion in the atmosphere. The new solution has the advantage of not requiring a numerical inversion performed in the temporal variable in works using only GILTT technique. The model was tested in low wind condition, with diffusion in transverse and longitudinal directions and stochastic speeds. Simulations were per

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16

Ferreira Pelegrini, Marcelo, Thiago Antonini Alves, Felipe Baptista Nishida, Ricardo A. Verdú Ramos, and Cassio R. Macedo Maia. "Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling." Advanced Materials Research 1082 (December 2014): 187–90. http://dx.doi.org/10.4028/www.scientific.net/amr.1082.187.

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In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The G

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17

Andrade, J. H., C. A. C. Santos, A. W. A. Cavalcante, and M. A. Rocha. "ANALYSIS OF TWO-DIMENSIONAL FLOW IN DUCTS WITH CIRCULAR SAW GITT FORMULATION IN PRIMITIVE VARIABLES." Revista de Engenharia Térmica 10, no. 1-2 (2011): 73. http://dx.doi.org/10.5380/reterm.v10i1-2.61966.

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In this paper the Generalized Integral Transform Technique is employed to produce hybrid solutions for the velocity and pressure fields of a newtonian fluid in two dimensional flow. The problem is formulated by using primitive variables and the necessary mathematical manipulations were used to obtain the Poisson equation for the pressure field. The momentum equations in the axial direction of flow and Poisson are transformed to remove the transversal dependency. The resulting transformed fields are solved with the IMSL numerical subroutine, DBVPFD. The obtained results for the longitudinal vel

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18

Trotta Matt, Carlos Frederico. "Combining integral transform and a generalized probabilistic approach of uncertainties to quantify model-parameter and model uncertainties in computational structural dynamics: The stochastic GITT method." Applied Mathematical Modelling 99 (November 2021): 673–703. http://dx.doi.org/10.1016/j.apm.2021.07.008.

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19

Silveira, Viliam Cardoso da, Daniela Buske, Régis Sperotto de Quadros, Glênio Aguiar Gonçalves, and Guilherme Jahnecke Weymar. "Fenômeno de meandro do vento e a função de autocorrelação calculada com base na concentração de poluentes simulada pelo modelo transiente 3D-GILTT." Ciência e Natura 42 (August 28, 2020): e28. http://dx.doi.org/10.5902/2179460x47026.

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The aim of this work is to present a pollutants dispersion transient model in low wind conditions to simulate the behavior of the pollutants plume in the atmosphere, considering in the model the u e v horizontal wind components simulated by the LES-PALM model. The dispersion model is based in the advection-diffusion equation and represent by this methodology the wind meandering phenomenon. The Generalized Integral Laplace Transform Technique in three dimensions (3D- GILTT) solves the transient advection-diffusion equation. The data utilized to initialize the simulations are data of the low win

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20

Gomes, F. A. A., J. B. C. Silva, and A. J. Diniz. "RADIATION HEAT TRANSFER WITH ABLATION IN A FINITE PLATE." Revista de Engenharia Térmica 4, no. 2 (2005): 190. http://dx.doi.org/10.5380/reterm.v4i2.5410.

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The phenomenon of ablation is a process of thermal protection with several applications, mainly, in mechanical and aerospace engineering. Ablative thermal protection is applied using special materials (named ablative materials) externally on the surface of a structure in order to isolate it against thermal effects. The ablative phenomenon is a complex process involving phase changes with partial or total loss of the material. So the position of the boundary is initially unknown. The governing equations of the process form a non-linear system of coupled partial differential equations. The one-d

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21

Sphaier, L. A., A. Barletta, and M. Celli. "Unstable mixed convection in a heated inclined porous channel." Journal of Fluid Mechanics 778 (August 6, 2015): 428–50. http://dx.doi.org/10.1017/jfm.2015.394.

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This paper presents a stability analysis of a mixed convection problem in an inclined parallel-plate channel with uniform heating (or cooling) from the top and bottom. The channel is filled with a saturated homogeneous porous medium and the momentum equation is given by Darcy’s model. A forced through-flow is prescribed across the channel. Linear stability analysis is thus employed to determine the onset of thermoconvective instability. The channel inclination is shown to play an important role in the stability of the problem, where two different regimes can be present: a buoyancy-assisted reg

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22

Naveira-Cotta, Carolina P., Helcio R. B. Orlande, and Renato M. Cotta. "Combining Integral Transforms and Bayesian Inference in the Simultaneous Identification of Variable Thermal Conductivity and Thermal Capacity in Heterogeneous Media." Journal of Heat Transfer 133, no. 11 (2011). http://dx.doi.org/10.1115/1.4004010.

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This work presents the combined use of the integral transform method, for the direct problem solution, and of Bayesian inference, for the inverse problem analysis, in the simultaneous estimation of spatially variable thermal conductivity and thermal capacity for one-dimensional heat conduction within heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the generalized integral transform technique (GITT), offering a fast, precise, and robust solution for the transient temperature field. The inverse prob

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23

Da Silveira, Viliam Cardoso, Daniela Buske, and Régis Sperotto De Quadros. "Simulation of three-dimensional transient pollutant dispersion in low wind conditions using the 3D-GILTT technique." Revista Mundi Engenharia, Tecnologia e Gestão (ISSN: 2525-4782) 5, no. 6 (2020). http://dx.doi.org/10.21575/25254782rmetg2020vol5n61314.

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The aim of this work is to present a transient model in low wind conditionsto simulate the pollutants dispersion in the atmosphere. The dispersion model is based in the advection-diffusion equation and it considers the zonal and meridional components of the wind. The transient advection-diffusion equation is solved using integral transform techniques. In this work, the generalized integral transform and Laplace techniques are used, known in the literature as GILTT and which applied to the three-dimensional problem is called 3D-GILTT (Three-dimensional Generalized Integral Laplace Transform Tec

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24

Maia, C. R. M., R. A. V. Ramos, M. F. Pelegrini, and T. A. Alves. "HEAT TRANSFER STUDY IN SLUG FLOW ON ELLIPTICAL DUCTS CROSS SECTIONS BY GENERALIZED INTEGRAL TRANSFORM TECHNIQUE." Revista de Engenharia Térmica 4, no. 2 (2005). http://dx.doi.org/10.5380/ret.v4i2.5414.

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This work shows the calculation of heat transfer parameters for slug flow in the thermal entrance region of elliptical section tubes submitted to a second kind boundary condition. The main difficulty in the application of the boundary conditions in problems with this kind of geometry has been removed by using a suitable coordinate change. The generalized integral transform technique (GITT) has been used to obtain the solution of the energy equation. The mixture temperature and the local and average Nusselt numbers have been calculated for several aspect ratios and the results have been compare

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25

Li, T. T., C. An, M. L. Duan, H. Huang, and W. Liang. "Effect of the Boundary Conditions on the Dynamic Behaviours of Subsea Free-Spanning Pipelines." International Journal of Maritime Engineering Vol 160 2018 A2 Vol 160, A2 (2018). http://dx.doi.org/10.3940/rina.ijme.2018.a2.467.

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This paper establishes a fast and accurate solution of the dynamic behaviours of subsea free-spanning pipelines under four different boundary conditions, based on GITT - the generalised integral transform technique. The fluid-structure interaction model is proposed by combining a linear structural equation and a non-linear distributed wake oscillator model, which simulates the effect of external current acting on the pipeline. The eigenvalue problems for the cross-flow vibration of the free-spanning submarine pipeline conveying internal fluid for four different boundary conditions are examined

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26

dos Anjos, Emerson B., Carolina P. Naveira-Cotta, Manish K. Tiwari, Renato M. Cotta, and Igor S. Carvalho. "An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream." Journal of Engineering Mathematics 130, no. 1 (2021). http://dx.doi.org/10.1007/s10665-021-10161-z.

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AbstractThis work deals with the mathematical modeling of the transient freezing process of a supercooled water droplet in a cold air stream. The aim is to develop a simple yet accurate lumped-differential model for the energy balance for a freely suspended water droplet undergoing solidification, that allows for cost effective computations of the temperatures and freezing front evolution along the whole process. The complete freezing process was described by four distinct stages, namely, supercooling, recalescence, solidification, and cooling. At each stage, the Coupled Integral Equations App

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27

Machado dos Santos, Beatriz, Ludimila Silva Salles de Sá, and Jian Su. "Natural convection in a horizontal annular sector containing heat-generating porous medium." International Journal of Numerical Methods for Heat & Fluid Flow ahead-of-print, ahead-of-print (2021). http://dx.doi.org/10.1108/hff-01-2021-0002.

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Purpose The purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. Design/methodology/approach GITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically so

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28

Knupp, Diego C., Carolina P. Naveira-Cotta, and Renato M. Cotta. "Conjugated Convection-Conduction Analysis in Microchannels With Axial Diffusion Effects and a Single Domain Formulation." Journal of Heat Transfer 135, no. 9 (2013). http://dx.doi.org/10.1115/1.4024425.

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An extension of a recently proposed single domain formulation of conjugated conduction–convection heat transfer problems is presented, taking into account the axial diffusion effects at both the walls and fluid regions, which are often of relevance in microchannels flows. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid stream and the channel walls, by making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface. The generalized integral transform technique (GITT) is then emplo

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Cotta, Renato M., Carolina P. Naveira-Cotta, and Diego C. Knupp. "Convective Eigenvalue Problems for Convergence Enhancement of Eigenfunction Expansions in Convection–Diffusion Problems." Journal of Thermal Science and Engineering Applications 10, no. 2 (2017). http://dx.doi.org/10.1115/1.4037576.

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The present work considers the application of the generalized integral transform technique (GITT) in the solution of a class of linear or nonlinear convection–diffusion problems, by fully or partially incorporating the convective effects into the chosen eigenvalue problem that forms the basis of the proposed eigenfunction expansion. The aim is to improve convergence behavior of the eigenfunction expansions, especially in the case of formulations with significant convective effects, by simultaneously accounting for the relative importance of convective and diffusive effects within the eigenfunc

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30

"Mathematical Model and Analytical Solution for the Vibration of Inclined Fluid-Transporting Submarine Pipelines." International Journal of Maritime Engineering 161, A4 (2019). http://dx.doi.org/10.3940/rina.ijme.2019.a4.524.

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Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differ

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31

Gomes, F. A. A., J. B. C. Silva, and A. J. Diniz. "RADIATION HEAT TRANSFER WITH ABLATION IN A FINITE PLATE." Revista de Engenharia Térmica 4, no. 2 (2005). http://dx.doi.org/10.5380/ret.v4i2.5410.

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Abstract:

The phenomenon of ablation is a process of thermal protection with several applications, mainly, in mechanical and aerospace engineering. Ablative thermal protection is applied using special materials (named ablative materials) externally on the surface of a structure in order to isolate it against thermal effects. The ablative phenomenon is a complex process involving phase changes with partial or total loss of the material. So the position of the boundary is initially unknown. The governing equations of the process form a non-linear system of coupled partial differential equations. The one-d

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