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[Abstract = "In this paper, a general finite element model is proposed to analyze transient phenomena in thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time with variable thermal conductivity. An application of an infinitely long annular cylinder was studied, where the inner surface is traction free and subjected to thermal shock, while the outer surface istraction free and thermally isolated. The results for the temperature increment, the stress components and the displacement component are illustrated graphically."]