Constant Heat Flux Solutions for Natural Convection Between Concentric and Eccentric Horizontal Cylinders

Glakpe, Emmanuel; Watkins, C. B.; Cannon, Joseph N.

doi:10.1080/10407788608913520

Cited by 49 publications

(19 citation statements)

References 12 publications

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“…In what follows, the proposed method is presented in detail for the energy equation (4) and the momentum equation (5). Special attention is given to the implementation of boundary conditions.…”

Section: Simulation Of Buoyancy-driven Flowmentioning

confidence: 99%

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A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Mai‐Duy

Le-Cao

Tran-Cong

2007

Numerical Methods in Fluids

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This paper reports a radial-basis-function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of high-order derivatives. The method is applied to simulate thermally-driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleighnumber solutions are achieved and they are in good agreement with previously published numerical data.

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Section: Simulation Of Buoyancy-driven Flowmentioning

confidence: 99%

“…[3,4]), finite-volume methods (FVMs) (e.g. [5,6]), boundary-element methods (BEMs) (e.g. [7][8][9]) and spectral techniques (e.g.…”

Section: Introductionmentioning

confidence: 99%

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Mai‐Duy

Le-Cao

Tran-Cong

2007

Numerical Methods in Fluids

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“…In 1986, Glakpe et al [6], considering a constant heat ux, presented a numerical solution to the steady laminar two-dimensional free convection in horizontal eccentric and concentric cylinders. Their results show that the temperature distribution on the outer heat ux boundary is similar to the local heat ux variation for isothermal cylinders.…”

Section: Literature Surveymentioning

confidence: 99%

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Zendehbudi

2017

Scientia Iranica

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Abstract. In the present work, a numerical method for solving the problem of free convection in enclosures with complex geometries is developed. This development is executed by the combination of projection and Galerkin nite-element methods. Ninenode (quadratic) quadrilateral elements are used to generate the grid for the eld of the problem. The results show that the convergence of this method is acceptable while there is no necessity to use upwind schemes. Increasing the numbers of nodes and decreasing the time increment yield a more accurate solution. The advantages of this numerical method are the ability to model any complex geometry and no necessity to use upwind schemes.

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“…[21,22]), finite-volume methods (FVMs) (e.g. [23,24]), boundary-element methods (BEMs) (e.g. [25,26]) and spectral methods (e.g.…”

Section: Example 2: Natural Convection In An Eccentric Annulus Betweementioning

confidence: 99%

Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids

Le-Cao¹,

Mai‐Duy²,

Tran³

et al. 2011

Computers & Fluids

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Constant Heat Flux Solutions for Natural Convection Between Concentric and Eccentric Horizontal Cylinders

Cited by 49 publications

References 12 publications

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

A Cartesian grid technique based on one‐dimensional integrated radial basis function networks for natural convection in concentric annuli

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids

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