In this study, we aim to compare the optimal homotopy analysis solution with the exact solution of the thermoelastic interactions problem in an isotropic hollow cylinder. The thermoelastic interactions in a hollow cylinder in the context of the theory of generalized thermoelasticity with one relaxation time (Lord and Shulman’s theory) are considered. An application of a hollow cylinder is investigated where the inner surface is traction-free and subjected to a decaying-with-time thermal field, while the outer surface is traction-free and thermally isolated. The mathematical model is solved by analytical method and optimal homotopy analysis method (OHAM). In addition, the convergence of the obtained homotopy analysis method solution is discussed explicitly. Numerical results for the temperature distribution, displacement and radial stress are represented graphically. The accuracy of the optimal homotopy analysis method …