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Abstract A three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables. The Fourier law is replaced by an approximation to a modification of the Fourier law with three different translations for the heat flux vector, the temperature gradient and also for the thermal displacement gradient. The model formulated is an extension of the thermoelastic models proposed by Lord–Shulman, Green–Naghdi and Tzou. Keywords: Coupled thermoelasticityGreen-Lindsay modelGreen-Naghdi modelLord-Schulman modelTzou model Acknowledgments The author expresses deep gratitude and thanks to the respected reviewer for his valuable advice and suggestions for the improvement of the paper.
S. K. Roy Choudhuri (Tue,) studied this question.