Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
2.6 Applications of the BEM to Heat Transfer and Inverse Problems
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In this chapter we will consider specialized applications of the BEM in heat transfer. Specifically, we will consider application of heat transfer for axisymmetric problems, that lays down the groundwork for a very useful result in certain cases of heat conduction in nonhomogeneous media with linearly varying thermal conductivity as well as heat transfer in thin plates and extended surfaces that utilizes a fundamental solution that can be utilized in treating linear heat diffusion problems by the Laplace transform method. This is followed by a discussion of practical applications of the BEM to large-scale three dimensional problems and detailed treatment of domain decomposition methods is provided along with some industrial applications. Finally, utilization of the BEM is presented as a suitable field solver for inverse problems problems, and consideration is given to the solution of the inverse geometric problem for the detection of subsurface flaw and cavities.