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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Meshless Local B-Spline Collocation Method for Two-Dimensional Heat Conduction Problems With Nonhomogenous and Time-Dependent Heat Sources
Mas Irfan P. Hidayat,
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
Metallurgical Engineering,
Institut Teknologi Sepuluh Nopember,
Kampus ITS Keputih Sukolilo,
Surabaya 60111, East Java, Indonesia
e-mail: irfan@mat-eng.its.ac.id
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Bambang Ariwahjoedi,
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
Universiti Teknologi Petronas,
Bandar Seri Iskandar,
Tronoh 31750, Perak Darul Ridzuan, Malaysia
e-mail: ariwahjoedi@gmail.com
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Setyamartana Parman,
Setyamartana Parman
Department of Mechanical Engineering,
Universiti Teknologi Petronas,
Bandar Seri Iskandar,
Tronoh 31750, Perak Darul Ridzuan, Malaysia
e-mail: setyamartana@petronas.com.my
Universiti Teknologi Petronas,
Bandar Seri Iskandar,
Tronoh 31750, Perak Darul Ridzuan, Malaysia
e-mail: setyamartana@petronas.com.my
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T. V. V. L. N. Rao
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
Mechatronics Engineering,
The LNM Institute of Information Technology,
Jaipur 302031, Rajasthan, India
e-mail: tvvlnrao@gmail.com
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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
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
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
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
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. Jul 2017, 139(7): 071302 (11 pages)
Published Online: April 4, 2017
Article history
Received:
January 24, 2015
Revised:
January 19, 2017
Citation
Hidayat, M. I. P., Ariwahjoedi, B., Parman, S., and Rao, T. V. V. L. N. (April 4, 2017). "Meshless Local B-Spline Collocation Method for Two-Dimensional Heat Conduction Problems With Nonhomogenous and Time-Dependent Heat Sources." ASME. J. Heat Transfer. July 2017; 139(7): 071302. https://doi.org/10.1115/1.4036003
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