Numerical modeling of transient heat conduction and transient thermoelasticity in heterogeneous media

The dissertation develops an analytical and computational basis for modeling time-dependent effects due to heat conduction and thermoelasticity in heterogeneous media. Randomly distributed heterogeneities are modeled either as circular cylindrical or spherical inhomogeneities and cavities (pores) of arbitrary size.;The approach for the transient heat conduction problem is based on the use of the Laplace transform, superposition and addition theorems. The analytical series representation of the solution in the transform domain is obtained by using the orthogonal properties of the Fourier series or series of surface spherical harmonics to satisfy the boundary and interfacial conditions. The only error introduced in this process is due to the series truncation. The solution in the original time domain is obtained by performing the inversion of the Laplace transform. The numerical examples demonstrate the accuracy, computational efficiency and robustness of the method. The main advantage of the method, as opposed to general purpose numerical procedures, is its ability to efficiently and accurately solve problems with large numbers of heterogeneities. An additional advantage of the analytical nature of the solution in the transform domain is the possibility to derive closed-form asymptotic approximations that describe the behavior of the solution at large time.;An important potential application of the method is for the analysis of the time-dependent behavior of thermoelastic composite and porous materials, which may include nano-scale heterogeneities. The dissertation presents an investigation of the time-dependent thermoelastic effects in a material with a circular nano-scale cavity.