Fundamental solutions for transient heat transfer by conduction and convection in an unbounded, half-space, slab and layered media in the frequency domain

Department of Civil Engineering, University of Coimbra, Pinhal de Marrocos, 3030-290 Coimbra, Portugal
Engineering Analysis with Boundary Elements 01/2005; DOI: 10.1016/j.enganabound.2005.06.002

ABSTRACT Analytical Green's functions in the frequency domain are presented for the three-dimensional diffusion equation in an unbounded, half-space, slab and layered media. These proposed expressions take into account the conduction and convection phenomena, assuming that the system is subjected to spatially sinusoidal harmonic heat line sources and do not require any type of discretization of the space domain. The application of time and spatial Fourier transforms along the two horizontal directions allows the solution of the three-dimensional time convection-diffusion equation for a heat point source to be obtained as a summation of one-dimensional responses. The problem is recast in the time domain by means of inverse Fourier transforms using complex frequencies in order to avoid aliasing phenomenon. Further, no restriction is placed on the source time dependence, since the static response is obtained by limiting the frequency to zero and the high frequency contribution to the response is small.The proposed functions have been verified against analytical time domain solutions, known for the case of an unbounded medium, and the Boundary Element Method solutions for the case of the half-space, slab and layered media.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) is proposed for the transient analysis of conduction heat transfer in the presence of inclusions, thereby overcoming the limitations posed by each method. The full domain is divided into sub-domains, which are modeled using the BEM/TBEM and the MFS, and the coupling of the sub-domains is achieved by imposing the required boundary conditions.The accuracy of the proposed algorithms, using different combinations of BEM/TBEM and MFS formulations, is checked by comparing the resulting solutions against referenced solutions.The applicability of the proposed methodology is shown by simulating the thermal behavior of a solid ring incorporating a crack or a thin inclusion in its wall. The crack is assumed to have null thickness and does not allow diffusion of energy; hence, the heat fluxes are null along its boundary. The thin inclusion is modeled as filled with thermal insulating material. Copyright © 2010 John Wiley & Sons, Ltd.
    International Journal for Numerical Methods in Engineering 10/2010; 84(2):179 - 213. · 2.06 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a technique based on a new model from finite differences discretization of Fourier heat propagation in 3D, is presented in order to be applied on a sequence of infrared images to enhance contrast and automatically detect and characterize flaws in composite slabs. The performance of this technique is evaluated using artificial thermal sequences from a simulated CFRP slab generated by ThermoCalc6L software. Results show that this technique offers a better contrast between defect and background than other common techniques like modified differentiated absolute contrast, and it runs faster than the classic 3D thermal filtering method.
    11th Quantitative Infrared Thermography conference, Naples, Italy; 06/2012
  • [Show abstract] [Hide abstract]
    ABSTRACT: This article presents an experimental validation of 2D and 2.5D boundary element method (BEM) solutions for transient heat conduction in systems containing heterogeneities. The problem is formulated in the frequency domain. The responses in the time domain are obtained by means of an inverse Fourier transform. Complex frequencies with a small imaginary part are introduced to cope with aliasing. Their effect is taken into account by rescaling the results in the time domain.For validation purposes, the solutions provided by the proposed BEM formulation were first verified against analytical solutions and then compared with experimental results. In the laboratory tests a steel inclusion was embedded in a confined host medium and unsteady temperatures were applied to its boundary. Two host media were tested: molded expanded polystyrene and medium-density fiberboard. The systems were subjected to plane and point heat sources. The thermal properties of these materials have been previously defined experimentally. The results show that the BEM solutions agree well with the experimental results.
    Engineering Analysis with Boundary Elements 11/2012; 36(11):1686–1698. · 1.60 Impact Factor

Full-text (2 Sources)

Available from
Jun 4, 2014