Benchmark results for natural and mixed convection heat transfer in a cavity

Yapıcı, Kerim; Obut, Salih

doi:10.1108/hff-02-2014-0036

Cited by 13 publications

(11 citation statements)

References 36 publications

(32 reference statements)

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“…The thermal-driven cavity flow a classical fluid dynamics phenomenon and most literature (Sezai and Mohamad, 1998; Sheremet et al , 2017; Yapici and Obut, 2015) studies it. So, we consider 3D thermal-driven cavity flow problem which has no exact solution for testing the proposed methods.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Wang

Feng

2019

HFF

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Purpose The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem. Design/methodology/approach The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P2, P2, P1, P2) to approximate the density, velocity, pressure and temperature field. Findings The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well. Originality/value Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

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Section: Numerical Experimentsmentioning

confidence: 99%

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Wang

Feng

2019

HFF

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“…Later, Le Quéré [20] has extended the range of Rayleigh numbers from 10 6 to 10 8 which is also widely considered as the extended range of benchmark solutions for transitional to turbulent regime natural convection flow available for the above model problem. In the successive Tables 1 and 2, we compare the present steady state solutions with benchmark solutions obtained by De Vahl Davis [19] and Le Quéré [20] for Ra 10 6 -10 8 and some well-established numerical results available in the literature [20][21][22][23][24][25][26][27]. Grid independence tests have been carried out and it was found that for the case of Ra = 10 7 , the 2D grid configuration is 161 × 161 nodes, while for the case of Ra = 10 8 , the 2D grid configuration of 241 × 241 nodes gave optimum converged results.…”

Section: Governing Equations For Natural Convection Flow In Enclosuresmentioning

confidence: 95%

Higher Order Accurate Transient Numerical Model to Evaluate the Natural Convection Heat Transfer in Flat Plate Solar Collector

et al. 2021

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The natural convection flow in the air gap between the absorber plate and glass cover of the flat plate solar collectors is predominantly evaluated based on the lumped capacitance method, which does not consider the spatial temperature gradients. With the recent advancements in the field of computational fluid dynamics, it became possible to study the natural convection heat transfer in the air gap of solar collectors with spatially resolved temperature gradients in the laminar regime. However, due to the relatively large temperature gradient in this air gap, the natural convection heat transfer lies in either the transitional regime or in the turbulent regime. This requires a very high grid density and a large convergence time for existing CFD methods. Higher order numerical methods are found to be effective for resolving turbulent flow phenomenon. Here we develop a non-dimensional transient numerical model for resolving the turbulent natural convection heat transfer in the air gap of a flat plate solar collector, which is fourth order accurate in both spatial and temporal domains. The developed model is validated against benchmark results available in the literature. An error of less than 5% is observed for the top heat loss coefficient parameter of the flat plate solar collector. Transient flow characteristics and various stages of natural convection flow development have been discussed. In addition, it was observed that the occurrence of flow mode transitions have a significant effect on the overall natural convection heat transfer.

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“…The second-order central differencing scheme is utilized to approximate the diffusion terms in the governing equations. On the other hand, the non-uniform form of the four-point fourth-order interpolation scheme proposed by Yapici and Obut [25] is utilized to be able to approximate convective terms.…”

Section: Problem Statement and Mathematical Formulationmentioning

confidence: 99%

A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models

Çakmak¹,

Durmazuçar²,

Yapıcı³

2021

International Advanced Researches and Engineering Journal

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In the current study, heat transfer enhancement in an enclosure was investigated by utilizing Al2O3-EG nanofluid. In the numerical solutions, the solid-liquid mixture equations were applied for the enclosure that composed alumina-ethylene glycol nanofluid, in terms of the two-dimensional buoyancy-driven convection. Various viscosity and thermal conductivity models were utilized for the purpose of assessing heat transfer improvement. The purpose of this study was to reveal the impacts caused by uncertainties in the viscosity and thermal conductivity of the nanofluid on laminar natural convection heat transfer occurring in a square enclosure. The temperatures of the right and left vertical walls of the enclosure were kept constant as Tc and Th, respectively, whereas the thermal insulation of the other walls was performed. The discretization of the governing equations was performed by utilizing the finite volume method and the SIMPLE algorithm. Calculations were made for the Rayleigh number (10 3 -10 6 ) and the volume fraction of alumina nanoparticles, ϕ= 0-5%. In this study, many parameters affecting heat transfer by natural convection were investigated in the enclosure containing Al2O3-EG nanofluid, and it was found that nanofluid viscosity was the most efficient factor for heat transfer rate.

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Benchmark results for natural and mixed convection heat transfer in a cavity

Cited by 13 publications

References 36 publications

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Higher Order Accurate Transient Numerical Model to Evaluate the Natural Convection Heat Transfer in Flat Plate Solar Collector

A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models

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