A thermodynamic analysis of an enhanced theory of heat conduction model: Extended influence of finite strain and heat flux

Abstract An Eulerian form of thermodynamically consistent generalized thermoelastic model capable of accounting for thermal signals is proposed. The heat flux is assumed to consist of both energetic and dissipative components. The constitutive relations for the stress, entropy and the heat fluxes are derived in the spatial coordinate system. Later on, a domain of dependence inequality for the proposed hyperbolic type heat conduction model is proved. The linearised form of this improved thermoelasticity theory of finite deformation is employed to study the thermoelastic interactions due a continuous source of heat in isotropic elastic solids. This newly developed model is also applied in a thermoelastic saturated porous medium. In order to obtain the exact analytical expressions of the field functions, appropriate integral transformations are employed in a convenient way.