A study of biothermoelastic interaction in viscoelastic biological tissue using the eigenvalues method

Purpose A comprehensive insight into bioheat transfer and the coupled thermomechanical response within tissues is vital for the precise application of thermal medical interventions. In the proposed model, the tissue surface is assumed to be traction-free and subjected to a time-dependent, exponentially diminishing heat flux. Design/methodology/approach This study explores the thermoelastic behavior of viscoelastic biological tissues exposed to thermal stimuli, employing the Green and Naghdi framework both with and without including energy dissipation mechanisms, as relevant to hyperthermia therapy. This is the first application of the eigenvalue approach in GN-III modeling of viscoelastic tissues. Findings To obtain exact solutions to the governing field equations, the generalized biothermoelastic formulation is addressed using Laplace transformation techniques in conjunction with an eigenvalue-based approach. Originality/value Graphical results for displacement, temperature and stress distributions are presented and a subsequent parametric investigation is carried out to identify optimal design variables that enhance the precision and therapeutic effectiveness of thermal treatments.