Meshless modeling of natural convection problems in non-rectangular cavity using the variational multiscale element free Galerkin method

Zhang, Xiaohua; Zhang, Ping

doi:10.1016/j.enganabound.2015.08.005

Cited by 32 publications

(7 citation statements)

References 31 publications

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“…Recently, Petrov-Galerkin local meshless method was used to study natural convection in a porous medium [16], Wijayanta et al [17] analyzed a local radial basis function method to obtain numerical solutions of the conjugate natural convection heat transfer problem for square cavity. Zhang et al [18] tested the robustness and accuracy of the variational multiscale element free Galerkin method, another meshless method, on several cases of natural convection, including a semicircular cavity, a triangular cavity with a flat wall, and a zigzag shape. The results obtained in these studies clearly showed that meshless methods are stable, accurate, and efficient.…”

Section: Ramentioning

confidence: 99%

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

Nuwairan¹,

Chaabelasri²

2023

Computer Modeling in Engineering &Amp; Sciences

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In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or Al 2 O 3 -water mixture with nanoparticle volume fractions range of 0 ≤ φ ≤ 0.2. A system of continuity, momentum, and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids. Partial derivatives in the governing equations were approximated using the RBF method. The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations. The main goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions. To assess the accuracy of the proposed method, several test cases of natural convection in square and triangular cavities were selected. For Rayleigh numbers ranging from 10 3 to 10 5 , a validation test of natural convection of Cu-water in a square cavity was used. The numerical investigation was then extended to Rayleigh number 10 6 , as well as Al 2 O 3 -water nanofluid with a volume fraction range of 0 ≤ φ ≤ 0.2. In a second investigation, the same nanofluids were used in a triangular cavity with varying volume fractions to test the proposed meshless approach on non-rectangular geometries. The numerical results appear to be in agreement with those from earlier investigations. Furthermore, the suggested meshless method was found to be stable and accurate, demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries. KEYWORDSNatural heat convection; nanofluids; cavities; meshless method; radial basis function Abbreviations N Number of nodes Cp Specific heat, J/kg/K g Acceleration due to gravity, m/s 2 k Thermal conductivity, W /mK Nu Nusselt number Pr Prandtl number

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Section: Ramentioning

confidence: 99%

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

Nuwairan¹,

Chaabelasri²

2023

Computer Modeling in Engineering &Amp; Sciences

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“…Currently, numerical methods for solving transient heat conduction equations are broadly classified into two categories: mesh-based methods, including finite difference method (FDM) [1,2], finite element method (FEM) [3,4], Finite Volume Method [5,6], and Boundary Element Method (BEM) [7]; and meshless methods, such as the generalized finite difference method [8,9], smoothed particle hydrodynamics method (SPH) [10], meshless local Petrov-Galerkin method (MLPG) [11][12][13][14], meshless local radial basis function-based differential quadrature (RBF-DQ) [15], peridynamics (PD) [16,17], and peridynamic differential operator (PDDO) [18,19]. Based on time discretization, these methods can be divided into explicit and implicit schemes.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Ruan,

Dong,

Zhang

et al. 2024

CMES

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Transient heat conduction problems widely exist in engineering. In previous work on the peridynamic differential operator (PDDO) method for solving such problems, both time and spatial derivatives were discretized using the PDDO method, resulting in increased complexity and programming difficulty. In this work, the forward difference formula, the backward difference formula, and the centered difference formula are used to discretize the time derivative, while the PDDO method is used to discretize the spatial derivative. Three new schemes for solving transient heat conduction equations have been developed, namely, the forward-in-time and PDDO in space (FT-PDDO) scheme, the backward-in-time and PDDO in space (BT-PDDO) scheme, and the central-in-time and PDDO in space (CT-PDDO) scheme. The stability and convergence of these schemes are analyzed using the Fourier method and Taylor's theorem. Results show that the FT-PDDO scheme is conditionally stable, whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable. The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method. The convergence rate in space for these three methods is two. These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems. The accuracy and validity of the schemes are verified by comparison with analytical solutions.

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“…The advent of meshless methods has expanded the spectrum of numerical methods available, offering high flexibility in handling complex geometries (Sophy et al 2002 ;Zhang et al 2015 ;Jeyar et al 2022 ;Luo et al 2015 ;Najafi etal. 2014 ;Pranowo et al 2021 ;Sheikhi et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Numerical assessment of meshless method for studying nanofluid natural convection in a corrugated wall square cavity

Es-Sabry

Jeyar

Chaabelasri

et al. 2023

Int. J. Renew. Energy Dev.

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This study aims to investigate the impact of various factors, such as wall shape, Rayleigh number, and volume fraction of nanoparticles, on natural convection in a square cavity that is filled with a mixture of Al2O3 solid particles and liquid water. The research employs numerical simulations based on the radial basis function meshless method and the artificial compressibility technique. The results of the study showed that the temperature distribution in the cavity was mostly uniform, except in the vicinity of the hot wall, while the flow was primarily dominated by convection as the Rayleigh number increased. Furthermore, the heat transfer rate increased with the volume fraction of nanoparticles, indicating the significance of nanoparticles in improving the thermal performance of the system. Additionally, the study found that the average Nusselt number, which characterizes the heat transfer efficiency, was highest when the cavity had a wavy wall. For single and double wavy walls, there were respective enhancements of 32% and 6% compared to a regular wall. Additionally, the Nusselt number increased as the volume fraction of nanoparticles, indicating a significant influence of nanoparticle concentration and wall geometry on the fluid flow and heat transfer characteristics in the square cavity. Consequently, this study's outcomes provide crucial insights into designing and optimizing thermal management systems, particularly those utilizing nanofluids.

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Meshless modeling of natural convection problems in non-rectangular cavity using the variational multiscale element free Galerkin method

Cited by 32 publications

References 31 publications

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Numerical assessment of meshless method for studying nanofluid natural convection in a corrugated wall square cavity

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