Analysis of Heat Conduction in a Quadratic Functionally Graded Plane by Boundary Element Method Based on the Variable Transmission Approach

AuthorsA Shaker, M. Khodadad, H Ashrafi
JournalJournal of Aerospace Mechanics
Presented byبلی
Page number77-89
Volume number15
Paper TypeOriginal Research
Published At2020
Journal GradeScientific - research
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of


In this research, the governing differential equation of heat conduction problem in a non-homogenous, functionally graded material (FGM) is solved using the boundary elements method (BEM). Except for some limited cases, there is not known Green function or fundamental singular solution for this kind of problems, which is necessary to have the boundary elements analysis. In this paper, the thermal conductivity of the functionally graded plate is considered as a quadratic function of one direction and then an auxiliary variable is introduced into the governing differential equation in order to simplify the problem to a kind with known fundamental singular solution and therefore, heat transfer is solved in a 2D functionally graded material by simple boundary elements method which is not possible by common methods. Based on the proposed approach, a computer code is developed using the MATLAB. The validity of this developed code is verified by solving and analyzing a number of heat transfer problems.

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