An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

• Autorzy: Mohammadi M. , Hematiyan M. R. , Shiah Y. C.

Identyfikatory

DOI

10.15632/jtam-pl.56.4.1123

• Języki publikacji: EN

Abstrakty

EN

In this paper, a new formulation based on the method of fundamental solutions for two/three- -dimensional steady-state heat conduction problems involving internal curved line/surface heat sources is presented. Arbitrary shapes and non-uniform intensities of the curved heat sources can be modeled by an assemblage of several parts with quadratic variations. The presented mesh-free modeling does not require any internal points as in domain methods. Four numerical examples are studied to verify the validity and efficiency of the proposed method. Our analyses have shown that the presented mesh-free formulation is very efficient in comparison with conventional boundary or domain solution techniques.

Słowa kluczowe

EN

heat conduction; concentrated heat source; curved heat source; mesh-free method

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2018
• Tom: Vol. 56 nr 4
• Strony: 1123--1137
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Mohammadi M.

• Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

autor

Hematiyan M. R.

• Department of Mechanical Engineering, Shiraz University, Shiraz, Iran

autor

Shiah Y. C.

• Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan, R.O.C.

Bibliografia

• 1. Ahmadabadi M.N., Arab M., Ghaini F.M., 2009, The method of fundamental solutions for the inverse space-dependent heat source problem, Engineering Analysis with Boundary Elements, 33, 10, 1231-1235
• 2. Aliabadi M.H., 2002, The Boundary Element Method, Volume 2, Applications in Solids and Structures, John Wiley & Sons
• 3. Atkinson K.E., 1985, The numerical evaluation of particular solutions for Poisson’s equation, IMA Journal of Numerical Analysis, 5, 3, 319-338
• 4. Becker A.A., 1992, The Boundary Element Method in Engineering: A Complete Course, McGraw- -Hill Book Company
• 5. Chao C.K., Tan C.J., 2000, On the general solutions for annular problems with a point heat source, Journal of Applied Mechanical, 67, 3, 511-518
• 6. Fairweather G., Karageorghis A., 1998, The method of fundamental solutions for elliptic boundary value problems, Advances in Computational Mathematics, 9, 1-2, 69-95
• 7. Golberg M.A., 1995, The method of fundamental solutions for Poisson’s equation, Engineering Analysis with Boundary Elements, 16, 3, 205-213
• 8. Gu Y., Chen W., He X.Q., 2012, Singular boundary method for steady-state heat conduction in three dimensional general anisotropic media, International Journal of Heat and Mass Transfer, 55, 17, 4837-4848
• 9. Han J.J., Hasebe N., 2002, Green’s functions of point heat source in various thermoelastic boundary value problems, Journal of Thermal Stresses, 25, 2, 153-167
• 10. Hematiyan M.R., Haghighi A., Khosravifard A., 2018, A two-constrained method for appropriate determination of the configuration of source and collocation points in the method of fundamental solutions for 2D Laplace equation, Advances in Applied Mathematics and Mechanics, 10, 3, 554-580
• 11. Hematiyan M.R., Mohammadi M., Aliabadi M.H., 2011, Boundary element analysis of twoand three-dimensional thermo-elastic problems with various concentrated heat sources, Journal of Strain Analysis for Engineering Design, 46, 3, 227-242
• 12. Hidayat M.I.P., Ariwahjoedi B., Parman S., Rao, T.V.V.L., 2017, Meshless local B-spline collocation method for two-dimensional heat conduction problems with nonhomogenous and timedependent heat sources, Journal of Heat Transfer, 139, 7, 071302
• 13. Karami G., Hematiyan M.R., 2000a, A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources, International Journal for Numerical Methods in Biomedical Engineering, 16, 3, 191-203
• 14. Karami G., Hematiyan M.R., 2000b, Accurate implementation of line and distributed sources in heat conduction problems by the boundary-element method, Numerical Heat Transfer, Part B, 38, 4, 423-447
• 15. Kołodziej J.A., Mierzwiczak M., Ciałkowski M., 2010, Application of the method of fundamental solutions and radial basis functions for inverse heat source problem in case of steady-state, International Communications in Heat and Mass Transfer, 37, 2, 121-124
• 16. Le Niliot C., 1998, The boundary element method for the time varying strength estimation of point heat sources: Application to a two dimensional diffusion system, Numerical Heat Transfer, Part B, 33, 3, 301-321
• 17. Le Niliot C., Lefevre F., 2001, Multiple transient point heat sources identification in heat diffusion: Application to numerical two- and three-dimensional problems, Numerical Heat Transfer, Part B, 39, 3, 277-301
• 18. Mierzwiczak M., Kołodziej J.A., 2012, Application of the method of fundamental solutions with the Laplace transformation for the inverse transient heat source problem, Journal of Theoretical and Applied Mechanics, 50, 4, 1011-1023
• 19. Mohammadi M., Hematiyan M.R., Khosravifard A., 2016, Boundary element analysis of 2D and 3D thermoelastic problems containing curved line heat sources, European Journal of Computational Mechanics, 25, 1-2, 147-164
• 20. Partridge P.W., Brebbia C.A., Wrobel, L.C., 1992, The Dual Reciprocity Boundary Element Method, Southampton, Computational Mechanics Publications
• 21. Poullikkas A., Karageorghis A., Georgiou G., 1998, The method of fundamental solutions for inhomogeneous elliptic problems, Computational Mechanics, 22, 1, 100-107
• 22. Rogowski, B., 2016, Green’s function for a multifield material with a heat source, Journal of Theoretical and Applied Mechanics, 54, 3, 743-755
• 23. Shiah Y.C., Guao T.L., Tan C.L., 2005, Two-dimensional BEM thermoelastic analysis of anisotropic media with concentrated heat sources, Computer Modeling in Engineering and Sciences, 7, 3, 321-338
• 24. Shiah Y.C., Hwang P.W., Yang R.B., 2006, Heat conduction in multiply adjoined anisotropic media with embedded point heat sources, Journal of Heat Transfer, 128, 2, 207-214
• 25. Stroud A.H., Secrest D., 1966, Gaussian Quadrature Formulas, New York, Prentice-Hall
• 26. Telles J.C.F., 1987, A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals, International Journal for Numerical Methods in Engineering, 24, 5, 959-973

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).