and Applied Mechanics
56, 4, pp. 1123-1137, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.1123
An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media
-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.
References
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
Aliabadi M.H., 2002, The Boundary Element Method, Volume 2, Applications in Solids and
Structures, John Wiley & Sons
Atkinson K.E., 1985, The numerical evaluation of particular solutions for Poisson’s equation,
IMA Journal of Numerical Analysis, 5, 3, 319-338
Becker A.A., 1992, The Boundary Element Method in Engineering: A Complete Course,McGraw-
-Hill Book Company
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
Fairweather G., Karageorghis A., 1998, The method of fundamental solutions for elliptic
boundary value problems, Advances in Computational Mathematics, 9, 1-2, 69-95
Golberg M.A., 1995, The method of fundamental solutions for Poisson’s equation, Engineering
Analysis with Boundary Elements, 16, 3, 205-213
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
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
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
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
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
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
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
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
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
Le Niliot C., Lef`evre 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
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 Theore-
tical and Applied Mechanics, 50, 4, 1011-1023
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 Compu-
tational Mechanics, 25, 1-2, 147-164
Partridge P.W., Brebbia C.A.,Wrobel, L.C., 1992, The Dual Reciprocity Boundary Element
Method, Southampton, Computational Mechanics Publications
Poullikkas A., Karageorghis A., Georgiou G., 1998, The method of fundamental solutions
for inhomogeneous elliptic problems, Computational Mechanics, 22, 1, 100-107
Rogowski, B., 2016, Green’s function for a multifield material with a heat source, Journal of
Theoretical and Applied Mechanics, 54, 3, 743-755
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
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
Stroud A.H., Secrest D., 1966, Gaussian Quadrature Formulas, New York, Prentice-Hall
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