Simulation of laminar flow inside ducts of irregular geometry using integral transforms

Guerrero, J.S. Pérez; Quaresma, João Nazareno Nonato; Cotta, Renato M.

doi:10.1007/s004660050488

Cited by 38 publications

(32 citation statements)

References 8 publications

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“…Para os resultados apresentados a seguir, foram considerados casos de escoamento laminar deágua (ρ = 1000.52 kg/m 3 , µ = 0.001 kg/ms, k = 0.597 W/m, C p = 4.1818 · 10 3 J/kg • C) dentro de um canal com expansão gradual, tal como ilustrado na figura 3.3 [69,70]. A geometria do canal depende do número de Reynolds, de tal forma que a expansão diminui a medida que o número de Reynolds aumenta.…”

Section: Resultsunclassified

Problemas Inversos em Transferência de Calor

2011

Notas Em Matemática Aplicada

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A Sociedade Brasileira de Matemática Aplicada e Computacional -SBMAC publica, desde as primeiras edições do evento, monografias dos cursos que são ministrados nos CNMAC.Para a comemoração dos 25 anos da SBMAC, que ocorreu durante o XXVI CNMAC, foi criada a série Notas em Matemática Aplicada para publicar as monografias dos minicursos ministrados nos CNMAC, o que permaneceu até o XXXIII CNMAC em 2010.A partir de 2011, a série passa, também, a publicar livros nasáreas de interesse da SBMAC. Os autores que submeterem textosà série Notas em Matemática Aplicada devem estar cientes de que poderão ser convidados a ministrarem minicursos nos eventos patrocinados pela SBMAC, em especial nos CNMAC, sobre assunto a que se refere o texto.O livro deve ser preparado em Latex (compatível com o Miktex versão 2.7), as figuras em eps e deve ter entre 80 e 150 páginas. O texto deve ser redigido de forma clara, acompanhado de uma excelente revisão bibliográfica e de exercícios de verificação de aprendizagem ao final de cada capítulo.Veja outros títulos publicados em formato e-book na página

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Section: Resultsunclassified

Problemas Inversos em Transferência de Calor

2011

Notas Em Matemática Aplicada

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“…Benchmark solutions for this problem were established in the past by using purely numerical methods, such as ¢nite differences and ¢nite elements [38]. Recently, this problem was revisited by utilizing the hybrid numerical-analytical method of solution of the generalized integral transform technique [39].…”

Section: R Esults and Discussionsmentioning

confidence: 99%

“…For the results presented below, we considered as an example of the application of the current solution approach test cases involving the laminar £ow of water (rˆ1000:52 kg=m 3 , mˆ0:001 kg=m s, kˆ0:597 W=m¯C, C pˆ4 :1818£ 10 3 J=kg¯C) inside a channel with a smooth expansion, as illustrated in Figure 3 [38,39]. The geometry of the channel depends on the Reynolds number, so that it becomes straighter as the Reynolds number increases.…”

Section: R Esults and Discussionsmentioning

confidence: 99%

Inverse Forced Convection Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Irregularly Shaped Channels

Colaço¹,

Orlande²

2001

Numerical Heat Transfer: Applications

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This article deals with the use of the conjugate gradient method of function estimation for the simultaneous identi cation of two unknown boundary heat uxes in channels with laminar ows. The irregularly shaped channel in the phy sical domain is transformed into a parallel plate channel in the computational domain by using an elliptic scheme of numerical grid generation. The direct problem, as well as the auxiliary problems and the gradient equations, required for the solution of the inverse problem with the conjugate gradient method are formulated in terms of generalized boundary-tted coordinates. Therefore, the solution approach presented here can be readily applied to forced convection boundary inverse problems in channels of any shape. Direct and auxiliary problems are solved with nite volumes. The numerical solution for the direct problem is validated by comparing the results obtained here with benchmark solutions for smoothly expanding channels. Simulated temperature measurement s containing random errors are used in the inverse analysis for strict cases involving functional forms with discontinuities and sharp corners for the unknown functions. The estimation of three different types of inverse problems are addressed in the paper: ( i) time-dependent heat uxes; ( ii) spatially dependent heat uxes; and ( iii) time and spatially dependent heat uxes.

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“…The extension of this analysis to the computation of the potential field itself, is now a straightforward task and particularly computationally effective for linear problems, when the integral transformation procedure yields decoupled ordinary differential equations for the transformed potentials, and the inversion formula provides a fully analytical solution for the original potential in all independent variables. Nevertheless, the approach is similarly applicable to nonlinear situations, as previously considered [19,20].…”

mentioning

confidence: 83%

“…Since 1989, a number of contributions have appeared in the integral transform solution of elliptic and parabolic diffusion problems within irregularly shaped domains [14][15][16][17][18][19][20]. All these contributions have in common the procedure of directly integral transforming the original partial differential system, starting from chosen one-dimensional eigenvalue problems which carry the information on the irregular shape through their own domain bounds, written as functions of the coordinate variables.…”

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confidence: 99%

Analytical and hybrid solutions of diffusion problems within arbitrarily shaped regions via integral transforms

Sphaier¹,

Cotta²

2002

Computational Mechanics

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Linear diffusion problems defined within irregular multidimensional regions are analytically solved through integral transforms, requiring numerical routines only for integration purposes, when a general functional boundary representation is considered. Auxiliary one-dimensional eigenvalue problems mapping the irregular region are applied with an integral transformation procedure so that the original differential SturmLiouville system gives place to an algebraic eigenvalue problem. The exact analytical inversion formula is then employed to yield the desired potential, explicitly, at any point within the domain. To allow for improved flexibility and further applicability, the related integration is simplified through an approximate boundary representation using lines connecting user provided points instead of the former exact representation of the irregular bounds, which is particularly advantageous when a functional description of the boundaries is not available. A cylindrical region test case with known exact solution is considered, and treated as an irregular region in the Cartesian coordinates system. Convergence behavior and error analysis are carefully undertaken and illustrated.

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Simulation of laminar flow inside ducts of irregular geometry using integral transforms

Cited by 38 publications

References 8 publications

Problemas Inversos em Transferência de Calor

Problemas Inversos em Transferência de Calor

Inverse Forced Convection Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Irregularly Shaped Channels

Analytical and hybrid solutions of diffusion problems within arbitrarily shaped regions via integral transforms

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