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The equation of heat conduction for this virtual medium is solved by the alternating directions method. ... In this work, we investigate the transient thermal analysis of two-dimensional cylindrical anisotropic medium subjected to a prescribed temperature at the two end sections and to a heat flux over the whole ... Numerical solution and Validation The numerical method used to solve the above heat conduction equation is the alternating-direction implicit method (ADI). ...doi:10.1051/matecconf/201928608009 fatcat:nqv24cabdrgofi5tvsvmdnwev4
The mathematical formulation of this approach for two-dimensional problems is presented in detail. ... heat conduction in anisotropic solids. ... Formulations Governing differential equation We consider two-dimensional steady-state heat conduction in anisotropic solids. ...doi:10.1299/jcst.3.66 fatcat:uhvob6b4jzcq3j4nllth3saauq
This study makes the first attempt to apply the SBM to steady-state heat conduction in three-dimensional (3D) anisotropic materials. ... The singular boundary method (SBM) is a recent strong-form meshless boundary collocation method. ... Acknowledgements The work described in this paper was supported by the National ...doi:10.1016/j.ijheatmasstransfer.2012.04.054 fatcat:ybw7elov3nhyroa7p4bs26nhjq
The application of the method of fundamental solutions to the Cauchy problem for steady-state heat conduction in two-dimensional functionally graded materials (FGMs) is investigated. ... Numerical results are presented for both smooth and piecewise smooth geometries. ... Lesnic from the Department of Applied Mathematics at the University of Leeds for all their encouragement in performing this research work. ...doi:10.1016/j.ijsolstr.2005.01.005 fatcat:kldvjvjesjezzoe6wk5fdmxace
(English summary) Inverse Problems 15 (1999), no. 3, 659-667. Summary: “We study the determination of an unknown bound- ary function in an initial-boundary value problem for the heat equation. ... conductivity problem in a half space via integral geometry. ...
A three-dimensional boundary element solution for the seepage analysis in multi-domain general anisotropic media has been developed based on the transformation approach. ... of adjacent domains) on the corresponding nodes of interface between two neighbor domains are needed for boundary element method. ... A comparison of boundary element method formulations for steady state anisotropic heat conduction in two dimensions based on the fundamental solution has been given by Mera et.al.  . ...doi:10.1016/j.enganabound.2012.12.006 fatcat:bybqwnagfnebtehvms3hpgq42u
Galerkin and inertial manifold methods for finite-dimensional approximation of nonlocal equations of nonlinear optics. (English summary) Inverse problems of natural science. Comput. Math. ... For the first time, the method of images is used to generate the solution for an arbitrar- ily anisotropic three-dimensional half-space. ...
New Analytic and Geometric Methods in Inverse Problems
Alessandrini and Gaburro  have proved uniqueness results for a family of anisotropic conductivity inverse boundary value problems with one unknown function. ... In the two dimensional case, with sufficiently obtuse triangles, the finite element method gives the same equations as a planar resistor mesh. ...doi:10.1007/978-3-662-08966-8_12 fatcat:ib3jgsnfv5fenji6qlf7vaeeli
Summary: “A pseudoparabolic one-dimensional initial-boundary value problem arising in the theory of heat flow in materials with thermal memory is studied in which the boundary input is real- time-controlled ... The authors outline the formulation of uniqueness conditions in the inverse thermal conductivity problem pertaining to a slender 87c:80008 rod. ...
A spectral numerical method is presented for solving the heat equation in oblate or prolate spheroids. Cartesian coordinates are scaled to transform the spheroidal geometry into a spherical geometry. ... Without heat sources and with a homogeneous Dirichlet boundary condition the problem reduces to an eigenproblem for the decay rate. The results are compared to the separated ... The solution method for (1) presented herein reduces the heat conduction problem to an equivalent heat problem in a sphere, with anisotropic heat conduction which depends on the ellipticity of the spheroid ...doi:10.21914/anziamj.v46i0.994 fatcat:lztwehs3z5d6zld3unlyyxw6pm
My professional and close personal association with Frank for two decades was one of the great privileges and pleasures of my life. ... In addition, he was adept in communicating with others, such as colleagues and students, had a great capacity for hard work, and showed a remarkable willingness to plow through some of the less pleasant ... The method we had used for numerical transform inversion in those problems had been designed for such functions. However, we wondered whether that method could be used also for oscillatory functions. ...doi:10.14713/ejbe.v1i1.746 fatcat:ud3coktorfdwlb2sjd2safhxum
Considered are two methods for determining the direction cosines in this situation. ... Despite the frequent appearance in the radiation heat transfer literature of articles describing Monte Carlo ray-trace (MCRT) applications to two-dimensional enclosures, no formal verification may be found ... ACKNOWLEDGMENT The authors gratefully acknowledge NASA's Langley Research Center for its financial support for this effort under NASA Contract NNL16AA05C with Science Systems and Applications, Inc., and ...arXiv:1810.05204v2 fatcat:yeakoqeqzjcfrbpb56gigminre
The enclosure contains an absorbing, emitting and linear anisotropic scattering medium in radiative equilibrium. The discrete ordinate method is employed to solve the radiative transfer equation. ... The inverse problem is formulated as an optimization problem and is solved using a micro-genetic algorithm. ... Two-dimensional irregular enclosures are considered. The inverse problem is formulated as an optimization problem. ...doi:10.24200/sci.2016.3826 fatcat:l2qrminesjdjjo6m6jafijfony
geometry with unstructured mesh and the last one in a problem with a variable heat source and different kinds of boundary conditions. ... The FVMC method is tested for three problems to assess the robustness of the method, first one in a simple geometry for validation and evaluation of the predictive performance, the second one in a complex ... , one or two-dimensional geometries, no internal heat generation or simple functional forms of thermal conductivities that simplify considerably the analysis of the heat conduction [20, 21] . ...doi:10.1007/s40430-019-1762-3 fatcat:g2bqpdbqpjcyvhxefrcu3euvvy
One can consider the remainder as a body force and solve the equation using DRM. Mathematical formulations of this approach for two-dimensional problems are presented in detail. ... This paper is concerned with an application of the boundary element method (BEM) using the dual reciprocity method (DRM) to analyze nonlinear transient heat conduction in anisotropic solids. ... Formulation Governing differential equation We shall consider two-dimensional nonlinear transient heat conduction in anisotropic solids. ...doi:10.1299/jee.2.266 fatcat:4zgvg2h4anh6xp5vfkwmtnm4ka
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