Abstract
The theory of two-temperature generalized thermoelasticity is used to solve boundary value problems of two dimensional half-space with heating its boundary with different types of heating. The governing equations are solved using new mathematical methods under the purview of the Lord-Shulman and the classical dynamical coupled theory. The general solution obtained is applied to a specific problem of a half-space and the interaction with each other under the influence of gravity subjected to one type of heating, the thermal shock type. The normal mode method is used to obtain the exact expressions for the physical quantities. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the two theories. The physical quantities distributions are shown graphically with some comparisons in the presence and absence of the influence of gravity.