Laminar thermally developing flow inside right-angularly triangular ducts

Aparecido, J. B.; Cotta, Renato M.

doi:10.1007/bf00419981

Cited by 14 publications

(20 citation statements)

References 9 publications

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“…Therefore, the present work complements the ideas previously advanced in the hybrid solution of diffusiontype problems of irregular domains of Aparecido and Cotta [12][13][14], Aparecido et al [15], Barbuto and Cotta [16] for Newtonian fluids, and Lima et al [17] for nonNewtonian fluids. …”

Section: Introductionsupporting

confidence: 70%

“…(12), an ordering procedure for the expansions is employed according to Corrêa et al [24]. This is described as follows: indices i and m related to the temperature field are reorganized into the single index p, while the indices j and n are collapsed into the new index q.…”

Section: Mathematical Analysismentioning

confidence: 99%

“…An analysis of convergence is made and a set of benchmark results is established for quantities of practical interest, such as dimensionless average temperature and Nusselt numbers, within a wide range of the dimensionless axial coordinate, different power-law indices and apex angles. Also, comparisons are critically performed with the previously reported results by Shah and London [1] and Etemad et al [9], from direct numerical approaches, by Haji-Sheikh et al [8], from Galerkin-type functions, and by Aparecido and Cotta [12], from a hybrid analytical-numerical approach.…”

Section: Introductionmentioning

confidence: 97%

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Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

Chaves

Quaresma

Macêdo

et al. 2004

Heat Transfer Engineering

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A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches.

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Section: Introductionsupporting

confidence: 70%

Section: Mathematical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

Chaves

Quaresma

Macêdo

et al. 2004

Heat Transfer Engineering

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“…The reordering scheme adopted in this work is explained with details in [21]. Once the matrix assembly is completed, the transformed coefficients W W h ¼ W W j;m are obtained through the solution of the algebraic system (17). Note that (17) will provide eigenvectors f W Wg, each one associated with an eigenvalue l i , to be employed in the reconstruction of the respective eigenfunction W i ðx; yÞ, by means of the inversion formula:…”

Section: Computational Solution Proceduresmentioning

confidence: 99%

“…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.…”

mentioning

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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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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Laminar thermally developing flow inside right-angularly triangular ducts

Cited by 14 publications

References 9 publications

Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

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

Analytical Heat and Fluid Flow in Microchannels and Microsystems

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