Transient buoyant convection in a 45°‐inclined enclosure heated and cooled on adjacent walls

Aydın, Orhan; Ünal, A. A.

doi:10.1108/09615530610653082

Cited by 4 publications

(1 citation statement)

References 34 publications

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“…Factorization error which arises due to the unknown pressure boundary conditions is avoided by using vorticitystreamfunction (V-SF) formulation. Many authors have previously used V-SF formulation (Rahimi et al, 2019;Balam and Gupta, 2019;Aydin and Ünal, 2006;Ingber, 2003; Natural convection flow in enclosures Miroshnichenko and Sheremet, 2015;Andreozzi et al, 2002;Sheremet et al, 2017;Garg, 1992;Aydin and Yang, 2000;Campo et al, 2005;Yoo, 2005) for solving natural convection flow in enclosures. Similarly, by using RK4 algorithm based on explicit formulation, the linearization error is also avoided.…”

Section: Governing Equationsmentioning

confidence: 99%

A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures

Balam

Gupta

2019

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Purpose Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving the higher order temporal accuracy. A fourth-order accurate finite difference method in both space and time is proposed to overcome these numerical errors and accurately model the transient behaviour of natural convection flow in enclosures using vorticity–streamfunction formulation. Design/methodology/approach Fourth-order wide stencil formula with appropriate one-sided difference extrapolation technique near the boundary is used for spatial discretisation, and classical fourth-order Runge–Kutta scheme is applied for transient term discretisation. The proposed method is applied on two transient case studies, i.e. convection–diffusion of a Gaussian Pulse and Taylor Vortex flow having analytical solution. Findings Error magnitude comparison and rate of convergence analysis of the proposed method with these analytical solutions establish fourth-order accuracy and prove the ability of the proposed method to truly capture the transient behaviour of incompressible flow. Also, to test the transient natural convection flow behaviour, the algorithm is tested on differentially heated square cavity at high Rayleigh number in the range of 103-108, followed by studying the transient periodic behaviour in a differentially heated vertical cavity of aspect ratio 8:1. An excellent comparison is obtained with standard benchmark results. Research limitations/implications The developed method is applied on 2D enclosures; however, the present methodology can be extended to 3D enclosures using velocity–vorticity formulations which shall be explored in future. Originality/value The proposed methodology to achieve fourth-order accurate transient simulation of natural convection flows is novel, to the best of the authors’ knowledge. Stable fourth-order vorticity boundary conditions are derived for boundary and external boundary regions. The selected case studies for comparison demonstrate not only the fourth-order accuracy but also the considerable reduction in error magnitude by increasing the temporal accuracy. Also, this study provides novel benchmark results at five different locations within the differentially heated vertical cavity of aspect ratio 8:1 for future comparison studies.

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Section: Governing Equationsmentioning

confidence: 99%

A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures

Balam

Gupta

2019

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Natural convection in an inclined quadrantal cavity heated and cooled on adjacent walls

Yesiloz

Aydın

2011

Experimental Thermal and Fluid Science

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Lattice Boltzmann simulation of transient natural convection of air in square cavity under a magnetic quadrupole field

Xie

Yao

et al. 2016

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Purpose The purpose of this paper is to apply the lattice Boltzmann method (LBM) with multiple distribution functions model, to simulate transient natural convection of air in a two-dimensional square cavity in the presence of a magnetic quadrupole field, under non-gravitational as well as gravitational conditions. Design/methodology/approach The density-temperature double distribution functions and D2Q9 model of LBM for the momentum and temperature equations are currently employed. Detailed transient structures of the flow and isotherms at unsteady state are obtained and compared for a range of magnetic force numbers from 1 to 100. Characteristics of the natural convection at initial moment, quasi-steady state and steady state are presented in present work. Findings At initial time, effects of the magnetic field and gravity are both relatively limited, but the effects become efficient as time evolves. Bi-cellular flow structures are obtained under non-gravitational condition, while the flow presents a single vortex structure at first under gravitational condition, and then emerges a bi-cellular structure with the increase of magnetic field force number. The average Nusselt number generally increases with the augment of magnetic field intensity. Practical implications This paper will be useful in the researches on crystal material and protein growth, oxygen concentration sensor, enhancement or suppression of the heat transfer in micro-electronics and micro-processing technology, etc. Originality/value The current study extended the application of LBM on the transient natural convective problem of paramagnetic fluids in the presence of an inhomogeneous magnetic field.

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Transient buoyant convection in a 45°‐inclined enclosure heated and cooled on adjacent walls

Cited by 4 publications

References 34 publications

A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures

A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures

Natural convection in an inclined quadrantal cavity heated and cooled on adjacent walls

Lattice Boltzmann simulation of transient natural convection of air in square cavity under a magnetic quadrupole field

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