Abstract
The theory of two-temperature generalized thermoelasticity, based on Youssef's theory, was used to solve boundary value problems of one-dimensional generalized thermoelasticity half-space by heating its boundary with different types of heating. The governing equations are solved using new mathematical methods within the purview of the Lord-Şhulman (L-S) theory and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating-thermal shock type. The separation of variables method is used to get the exact expressions for distributions of displacement, the stresses, and temperature distribution. Variations of the considered functions through the horizontal distance are illustrated graphically. Comparisons are made with results between the two theories. Numerical work is also performed for a suitable material and results are discussed, specifically the conductive temperature, the dynamical temperature, and the stress and strain distributions are shown graphically when discussed.