The present research deals with the study of transversely isotropic thermoelastic beam in the context of Green-Naghdi (GN) theory of thermoelasticity of Type-II and Type-III. The mathematical model is prepared for the thin beam in a closed form with the application of Euler Bernoulli beam theory. The Laplace Transform technique has been used to find the expressions for displacement component, lateral thermal moment, deflection and axial stress in transformed domain. The general algorithm of the inverse Laplace Transform is developed to compute the results numerically in physical domain. The effect of two theories of thermoelasticity Green-Naghdi-II and Green-Naghdi-III has been depicted on the various quantities. Some particular cases have also been deduced.

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