Laminar flow inside hexagonal ducts

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

doi:10.1007/bf00350515

Cited by 18 publications

(18 citation statements)

References 6 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: 71%

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: 71%

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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“…In more complex ducts, e.g hexagonal ones [27], the longitudinal velocity v(ξ) is the solution of the following Poisson problem forced by the uniform longitudinal pressure gradient div(∇v) = C, where C = ∂ z p/µ. In what follows, we consider laminar fully developed longitudinally invariant flow profiles, and we suppose that v(ξ) is known.…”

Section: State Of the Art Problem Formulation And Notationsmentioning

confidence: 99%

Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes

Pierre

Bouyssier

Gournay

et al. 2014

Journal of Computational Physics

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We propose and develop a variational formulation dedicated to the simulation of parallel convective heat exchangers that handles possibly complex input/output conditions as well as connection between pipes. It is based on a spectral method that allows to re-cast three-dimensional heat exchangers into a two-dimensional eigenvalue problem, named the generalized Graetz problem. Our formulation handles either convective, adiabatic, or prescribed temperature at the entrance or at the exit of the exchanger. This formulation is robust to mode truncation, offering a huge reduction in computational cost, and providing insights into the most contributing structure to exchanges and transfers. Several examples of heat exchangers are analyzed, their numerical convergence is tested and the numerical efficiency of the approach is illustrated in the case of Poiseuille flow in tubes.

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“…This hybrid approach kept along the years the same name of Generalized Integral Transform Technique (GITT), first proposed in [11], and involved the complete solution of the coupled transformed problem, based on the numerical solution of a truncated version of the transformed system of ordinary differential equations. In a relatively short period of time it was extended to different classes of problems, including nonlinear diffusion and convection-diffusion [16][17][18][19] and irregular domains in parabolic and elliptic formulations [20][21][22][23]. It would not take long for the GITT to be challenged by the solution of fluid flow problems governed either by the boundary layer equations or the Navier-Stokes equations [24,25].…”

Section: Introductionmentioning

confidence: 99%

A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

Cotta

Lisbôa

Curi

et al. 2019

Numerical Heat Transfer, Part B: Fundamentals

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The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numericalanalytical approach for fluid flow problems, with or without heat and mass transfer, here with emphasis on the literature related to flow problems formulated through the full Navier-Stokes equations. A brief overview of the integral transform methodology is first provided for a general nonlinear convection-diffusion problem. Then, different alternatives of eigenfunction expansion strategies are discussed in the integral transformation of problems for which the fluid flow model is either based on the primitive variables or the streamfunction-only formulations, as applied to both steady and transient states. Representative test cases are selected to illustrate the different eigenfunction expansion approaches, with convergence being analyzed for each situation. In addition, fully converged integral transform results are critically compared to previously reported simulations obtained from traditional purely discrete methods.

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Laminar flow inside hexagonal ducts

Cited by 18 publications

References 6 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

Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes

A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

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