The evaluation of the singular and hypersingular integrals that appear in three-dimensional boundary element formulations for heat diffusion, in the frequency domain, is presented in analytical form. This improves computational efficiency and accuracy. Numerical integrations using existing techniques based on standard Gaussian integration schemes that incorporate an enormous amount of sampling points are used to verify the solutions of singular integrals. For the hypersingular integrals the comparison is evaluated by making use of an analytical solution that is valid for circular domains, combined with a standard Gaussian integration scheme for the remaining boundary element domain. Closed form solutions for cylindrical inclusions with null temperatures and null heat fluxes prescribed on the boundary are then derived and used to validate the three-dimensional boundary element formulations.
This paper presents a 3D boundary element model (BEM), formulated in the frequency domain, to simulate heat diffusion by conduction in the vicinity of 3D cracks. The model intends to contribute to the interpretation of infrared thermography (IRT) data results and to explore the features of this nondestructive testing technique (NDT) when it is used to detect and characterize defects. The defect is assumed to be a null thickness crack embedded in an unbounded medium. The crack does not allow diffusion of energy, therefore null heat fluxes are prescribed along its boundary. The BEM is written in terms of normal-derivative integral equations (TBEM) in order to handle null thickness defects. The resulting hypersingular integrals are solved analytically.The applicability of the proposed methodology to defect detection tests is studied once the TBEM results have been verified by means of known analytical solutions. Heat diffusion generated by a 3D point heat source placed in the vicinity of a crack is modeled. The resulting thermal waves phase is compared with that obtained when the defect is absent, so as to understand the influence of crack characteristics on the IRT data results analysis, especially on the phase-contrast images. Parameters such as the size of the crack, its shape, its position (buried depth and inclination) and its distance from the heat source are analyzed. Some conclusions are drawn on the effects of varying those parameters.
This paper sets out a three-dimensional (3D) boundary element method (BEM) formulation in the frequency domain to simulate heat transfer through a point thermal bridge (PTB) at a corner in a building envelope. The main purpose was to quantify the dynamic effect of a geometrical PTB in terms of distribution of temperatures and heat fluxes, which is useful for evaluating moisture condensation risk. The numerical model is first validated experimentally using a hot box to measure the dynamic heat behavior of a 3D timber building corner. The proposed model is then used to study the dynamic thermal bridging effect in the vicinity of a 3D concrete corner. Given the importance of the risk of condensation, this study looks at the influence of an insulating material and its position on the temperature and heat flux distribution through the PTB under steady state and dynamic conditions.
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