A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins

Safarpoor, Mansour; Shirzadi, Ahmad

doi:10.1016/j.enganabound.2018.09.016

Cited by 9 publications

(3 citation statements)

References 48 publications

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“…Radial basis functions (RBFs) have been widely used in solving ODEs and PDEs (see, for example, [5,6,7,8,9,10,11,12,13]). In the RBF collocation methods [14], the field variable, which is typically a nonlinear function, is expressed as a linear combination of RBFs, of which the accuracy can be enhanced quickly with an increase in the number of RBFs (i.e.…”

Section: Introductionmentioning

confidence: 99%

New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils

Mai‐Duy

Strunin

2021

Engineering Analysis with Boundary Elements

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Section: Introductionmentioning

confidence: 99%

New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils

Mai‐Duy

Strunin

2021

Engineering Analysis with Boundary Elements

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“…Multi-dimensional and complex problems have also been addressed by the MLPG method such as 3D thermo-elastoplastic analysis of thick functionally graded plate (Vaghefi et al, 2016), 2D fluid flow problems (Garg et al, 2018a), multi-dimensional nonlinear convection-diffusion equations based on least square radial basis function partition of unity method (Li et al, 2018), 2D complex Ginzburg-Landau equation (Shokri and Bahmani, 2019) and 2D and 3D steady-state heat conduction in regular and complex domains (Singh and Singh, 2019). Safarpoor and Shirzadi (2019) have applied the radial basis function-MLPG (RBF-MLPG) method for numerical study of heat and mass transfer equations in elliptic fins and observed that the method enjoys exponential convergence, stability and accuracy. They revealed that the proposed method can be used for solving the general differential equations (GDEs) of 2D temperature distribution under dry and fully wet conditions effectively.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of two-dimensional fins using the meshless local Petrov – Galerkin method

Garg¹,

Thakur²,

Tripathi³

2020

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Purpose The study aims to highlight the behaviour of one-dimensional and two-dimensional fin models under the natural room conditions, considering the different values of dimensionless Biot number (Bi). The effect of convection and radiation on the heat transfer process has also been demonstrated using the meshless local Petrov–Galerkin (MLPG) approach. Design/methodology/approach It is true that MLPG method is time-consuming and expensive in terms of man-hours, as it is in the developing stage, but with the advent of computationally fast new-generation computers, there is a big possibility of the development of MLPG software, which will not only reduce the computational time and cost but also enhance the accuracy and precision in the results. Bi values of 0.01 and 0.10 have been taken for the experimental investigation of one-dimensional and two-dimensional rectangular fin models. The numerical simulation results obtained by the analytical method, benchmark numerical method and the MLPG method for both the models have been compared with that of the experimental investigation results for validation and found to be in good agreement. Performance of the fin has also been demonstrated. Findings The experimental and numerical investigations have been conducted for one-dimensional and two-dimensional linear and nonlinear fin models of rectangular shape. MLPG is used as a potential numerical method. Effect of radiation is also, implemented successfully. Results are found to be in good agreement with analytical solution, when one-dimensional steady problem is solved; however, two-dimensional results obtained by the MLPG method are compared with that of the finite element method and found that the proposed method is as accurate as the established method. It is also found that for higher Bi, the one-dimensional model is not appropriate, as it does not demonstrate the appreciated error; hence, a two-dimensional model is required to predict the performance of a fin. Radiative fin illustrates more heat transfer than the pure convective fin. The performance parameters show that as the Bi increases, the performance of fin decreases because of high thermal resistance. Research limitations/implications Though, best of the efforts have been put to showcase the behaviour of one-dimensional and two-dimensional fins under nonlinear conditions, at different Bi values, yet lot more is to be demonstrated. Nonlinearity, in the present paper, is exhibited by using the thermal and material properties as the function of temperature, but can be further demonstrated with their dependency on the area. Additionally, this paper can be made more elaborative by extending the research for transient problems, with different fin profiles. Natural convection model is adopted in the present study but it can also be studied by using forced convection model. Practical implications Fins are the most commonly used medium to enhance heat transfer from a hot primary surface. Heat transfer in its natural condition is nonlinear and hence been demonstrated. The outcome is practically viable, as it is applicable at large to the broad areas like automobile, aerospace and electronic and electrical devices. Originality/value As per the literature survey, lot of work has been done on fins using different numerical methods; but to the best of authors’ knowledge, this study is first in the area of nonlinear heat transfer of fins using dimensionless Bi by the truly meshfree MLPG method.

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“…The idea of local Petrov–Galerkin method dates back to [11, 32] for solving problems in solid mechanics. The combination with RBFs in Euclidean spaces can be found in [33–35]. In this paper we extend the method of [29] for solving diffusion problems on the sphere.…”

Section: Introductionmentioning

confidence: 99%

A Petrov–Galerkin RBF method for diffusion equation on the unit sphere

Darani

Mirzaei

2020

Numerical Methods Partial

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This paper concerns a numerical solution for the diffusion equation on the unit sphere. The given method is based on the spherical basis function approximation and the Petrov-Galerkin test discretization. The method is meshless because spherical triangulation is not required neither for approximation nor for numerical integration. This feature is achieved through the spherical basis function approximation and the use of local weak forms instead of a global variational formulation. The local Petrov-Galerkin formulation allows to compute the integrals on small independent spherical caps without any dependence on a connected background mesh. Experimental results show the accuracy and the efficiency of the new method.

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A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins

Cited by 9 publications

References 48 publications

New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils

New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils

Numerical simulation of two-dimensional fins using the meshless local Petrov – Galerkin method

A Petrov–Galerkin RBF method for diffusion equation on the unit sphere

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