Nonlinear numerical analysis of convective-radiative fin using MLPG method

Garg, Rajul; Thakur, Harishchandra; Tripathi, Brajesh

doi:10.18280/ijht.350405

Cited by 6 publications

(2 citation statements)

References 27 publications

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“…Numerical simulation Garg et al (2015;2017a, 2017b have solved the nonlinear and transient heat transfer problem of fins; and Vyas et al (2018) have simulated the fins of three different profilesrectangular, triangular and concave by the MLPG method. In both the cases, the effect of radiation at the fin's surface has also been examined.…”

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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Section: Introductionmentioning

confidence: 99%

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

Garg¹,

Thakur²,

Tripathi³

2020

Self Cite

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show abstract

“…However, among all the meshfree methods, the MLPG method has become quite popular due to its successful acceptability in various fields of engineering [18][19][20][21][22][23]. In this method the domain discretization originates from a weak form over a local sub-domain of arbitrary shape which is located completely inside the global domain.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of two-dimensional fluid flow problem using truly meshfree method

Garg¹,

Thakur²,

Tripathi³

2018

MMEP

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The solution of two-dimensional steady and transient fluid flow problem by the truly meshless local Petrov-Galerkin (MLPG) method has been addressed in the present article. The unknown function of velocity u(x) is approximated by moving least square approximant u h (x). The essential boundary condition is imposed both by the direct and penalty function methods. Fourth order spline weight function, monomial basis function and a set of nonconstant coefficients are used to construct the approximants. The two-level  method is employed for temporal discretization. The results obtained by the MLPG method are compared with the analytical solution and also with the benchmark method results and found to be in the excellent agreement.

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Nonlinear heat transfer analysis of spines using MLPG method

Thakur

2021

Engineering Analysis with Boundary Elements

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Nonlinear numerical analysis of convective-radiative fin using MLPG method

Cited by 6 publications

References 27 publications

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

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

Numerical simulation of two-dimensional fluid flow problem using truly meshfree method

Nonlinear heat transfer analysis of spines using MLPG method

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