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Research Papers: Conduction

Meshless Local B-Spline Collocation Method for Two-Dimensional Heat Conduction Problems With Nonhomogenous and Time-Dependent Heat Sources

[+] Author and Article Information
Mas Irfan P. Hidayat

Department of Materials and
Metallurgical Engineering,
Institut Teknologi Sepuluh Nopember,
Kampus ITS Keputih Sukolilo,
Surabaya 60111, East Java, Indonesia
e-mail: irfan@mat-eng.its.ac.id

Bambang Ariwahjoedi

Department of Fundamental and Applied Science,
Universiti Teknologi Petronas,
Bandar Seri Iskandar,
Tronoh 31750, Perak Darul Ridzuan, Malaysia
e-mail: ariwahjoedi@gmail.com

Setyamartana Parman

Department of Mechanical Engineering,
Universiti Teknologi Petronas,
Bandar Seri Iskandar,
Tronoh 31750, Perak Darul Ridzuan, Malaysia
e-mail: setyamartana@petronas.com.my

T. V. V. L. N. Rao

Department of Mechanical-
Mechatronics Engineering,
The LNM Institute of Information Technology,
Jaipur 302031, Rajasthan, India
e-mail: tvvlnrao@gmail.com

1Corresponding author.

2Not affiliated with Universiti Petronas as of September 2016.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 24, 2015; final manuscript received January 19, 2017; published online April 4, 2017. Assoc. Editor: P. K. Das.

J. Heat Transfer 139(7), 071302 (Apr 04, 2017) (11 pages) Paper No: HT-15-1067; doi: 10.1115/1.4036003 History: Received January 24, 2015; Revised January 19, 2017

This paper presents a new approach of meshless local B-spline based finite difference (FD) method for transient 2D heat conduction problems with nonhomogenous and time-dependent heat sources. In this method, any governing equations are discretized by B-spline approximation which is implemented as a generalized FD technique using local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighboring nodal values based on B-spline interpolants. The set of neighboring nodes is allowed to be randomly distributed. This allows enhanced flexibility to be obtained in the simulation. The method is truly meshless as no mesh connectivity is required for field variable approximation or integration. Galerkin implicit scheme is employed for time integration. Several transient 2D heat conduction problems with nonuniform heat sources in arbitrary complex geometries are examined to show the efficacy of the method. Comparison of the simulation results with solutions from other numerical methods in the literature is given. Good agreement with reference numerical methods is obtained. The method is shown to be simple and accurate for the time-dependent problems.

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References

Figures

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Fig. 1

Classical spline to draw a smooth curve through a set of points before computer modeling

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Fig. 2

A global domain and nodes of subset in the support domain of center point

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Fig. 3

Geometry and boundary conditions for transient heat conduction of case I

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Fig. 4

Simulation results of temperature histories at points A and B for thermal problem of case I with respect to (a) B-spline order and (b) number of supporting nodes

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Fig. 5

Simulation results of temperature histories at points A and B for thermal problem of case I with respect to (a) number of collocation points and (b) time-steps

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Fig. 6

Geometry and boundary conditions for transient heat conduction of case II

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Fig. 7

Simulation results of temperature histories at points A and B for thermal problem of case II for several time-steps

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Fig. 8

Temperature profiles through the points: (a) A (line y = 0.1) and (b) B (line x = 0) with respect to number of nodes (μ = 5, ns = 10, and Δt = 25 s)

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Fig. 9

Domain of FGM made of ZrO2 and Ti–6Al–4V and its boundary conditions of case III

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Fig. 10

Simulation results of: (a) temperature histories at points A and B and (b) temperature profiles for thermal problem of case III with respect to number of nodes (μ = 5, ns = 7, and Δt = 20 s)

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Fig. 11

Simulation results of (a) temperature histories at points A and B and (b) temperature profiles for thermal problem of case III with respect to time-steps (μ = 5, ns = 7971 nodes)

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