Effect of gravity and variable thermal conductivity in a thermoelastic half space with dual phase lag model

This work presents a novel analysis of nonlinear plane wave propagation in a transversely isotropic thermoelastic half-space under the influence of gravity. The proposed work lies in capturing the second harmonic amplitudes of the propagating heat wave, which may be of interest in practical applications involving nondestructive evaluation or thermal wave diagnostics. The study is formulated within the framework of dual-phase lag (DPL) thermoelasticity, incorporating a temperature-dependent thermal conductivity (TC) that introduces nonlinearity into the governing equations. A particular solution is obtained using a combination of normal mode analysis and a Poincaré-type perturbation expansion, where a small parameter represents fluctuations around a steady-state temperature. To demonstrate the effectiveness of the model, a representative case is solved under realistic boundary conditions and tentative material parameters. MATLAB software is used to visualize key physical quantities, with both two- and three-dimensional plots illustrating the thermal and mechanical responses. The role of nonlinear thermal responses and gravity-induced effects in wave propagation offers critical insights enabling applications in diagnostics and material evaluation.