A GN model based upon two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity

•Two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity are presented.•The eigenvalue approach techniques are used to solve the non-dimensional coupled equations in the domain of Laplace.•The graphical results indicate that the two-temperature parameter has significant effects on all the physical quantities.

In this paper, a general solution to the field equations of two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity has been obtained in the context of Green and Naghdi model. The eigenvalue approach is adopted for the solution of application for unbounded medium with a spherical cavity. The medium is assumed to be initially quiescent. The inner surface of the cavity is taken traction free and subjected to a ramp-type heating. The Laplace transform technique is used. Some comparison have been shown in figures to estimate the effect of the ramp type and two-temperature parameters.