Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound

We study some spectral and numerical properties of the solutions to a thermoelastic problem with double porosity. The model includes Cattaneo-type evolution law for the heat flux to remove the physical paradox of infinite propagation speed of the classical Fourier’s law. Firstly, we prove that the operator determined by the considered problem has compact resolvent and generates a C 0 -semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum determined growth condition holds. Therefore we prove that the energy of the considered problem decays exponentially to a rate determined explicitly by the physical parameters. Finally, some numerical simulations based on Chebyshev spectral method for spatial discretization are given to confirm the exponential stability result and to show the distribution of the eigenvalues and the variables of the problem.

On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

Reduced Differential Transform Method for Thermoelastic Problem in Hyperbolic Heat Conduction Domain

In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.