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The heat transport within living biological tissue is a complicated process coupled with various physiological activities. The nonhomogeneous inner anatomical structure leads to an essential difference from classical heat transfer. The generalized model of bioheat transfer involving the relaxation mechanism as well as nonequilibrium heat transfer is first proposed to explore the heat transport properties within living biological tissues. Due to the volume averaging theory, the new local instantaneous energy equations of blood and tissue are constructed separately by introducing the phase lags, in which the delay effect between the heat flux and temperature gradient absent in existing generalized models is considered. The effective phase lags covering the delay effect and nonequilibrium effect are obtained on this basis. A detailed parametric study has been conducted to estimate the values of these effective phase lags and evaluate their contributions on heat transport within living biological tissues. The results state that the effective phase lags depend on the anatomical structure of tissues and its physical properties. The delay effect is dominated in general and has a higher temperature elevation than that induced by nonequilibrium effect only.

Thermo-mechanical properties of the functionally graded materials (FGMs) are the pivotal role to improve their service lives exposed to some extraordinary thermal circumstances. An analytical procedure to explore the thermo-mechanical interaction involving the micro-scale effect is proposed for the first time in this work. The governing equations are firstly constructed in a cylindrical coordinate in the context of the generalized Chandrasekharaiah–Tzou theory (C–T theory). An asymptotic approach, based on the Laplace transform technique and its limit theorem, is then employed to solve these equations analytically, in which a common linearization technique is prior to introduce to disperse the non-linear terms involving variable material properties with different gradient patterns. The layer-formed solutions of a typical FGM hollow cylindrical structure with its inner boundary subjected to a sudden temperature rise is finally obtained and validated. A detailed parametric study has been conducted to explore the effect of the micro-structure interaction, physical properties distribution patterns, and the structure size on the thermo-mechanical response. The results state that the effect of micro-structure interaction mainly focuses on the thermal wave propagation and is more significant for the ceramic-rich case. The delay effect on the heat transport induced by thermal inertia is also wakened significantly by the micro-structure interaction, which leads to a larger range of thermo-elastic response and smaller peak stress.

This paper is concerned with asymptotic solutions for the axisymmetric plane strain problem with variable material properties in the context of different generalized models of thermoelasticity. The unified forms of the governing equations for axisymmetric plane strain problem, involving the generalized theory with one thermal relaxation time (L-S theory), the generalized theory with two thermal relaxation time (G-L theory) and the generalized theory without energy dissipation (G-N theory), are presented by introducing the unifier parameters. The Laplace transform techniques and the Kirchhoff’s transformation are used to obtain the general solutions for any set of boundary conditions in the physical domain. The asymptotic solutions for a specific problem of an infinite cylinder, formed of an isotropic homogeneous material with variable thermal material properties, whose boundary is subjected to a sudden temperature rise, are derived by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, some generalized thermoelastic phenomena are obtained and illustrated, especially the jumps at the wavefronts, induced by the propagation of heat signal with a finite speed, are also observed clearly. By the comparison with the results obtained from the case of constant material properties, the effect of variable thermal material properties on the thermoelastic behavior is also discussed.

This paper is to investigate the thermoelastic response of an elastic medium with variable material properties under the transient thermal shock. The governing equations involving temperature-dependent properties are proposed by the Clausius inequality and generalized theory of thermoelasticity with one thermal relaxation time, where the higher order expansion with respect to increment temperature of the Helmholtz free energy is used to describe the relations of each material parameter with real temperature. The problem of a thin plate composed of titanium alloy, subjected to a sudden temperature rise at the boundary, is solved. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature and stresses, are obtained and discussed. The comparison of present results with those obtained from the case of constant material properties are conducted to reveal the effect of the temperature dependency of material properties on thermoelastic response. The comparison with the results obtained from the case that each material parameter is the function of fixed temperature is also conducted to explain the coupling effect between variable material properties and temperature distribution.

This paper is concerned with the thermoelastic behaviors of an elastic medium with variable thermal material properties. The problem is in the context of fractional order heat conduction. The governing equations with variable thermal properties were established by means of the fractional order calculus. The problem of a half-space formed of an elastic medium with variable thermal material properties was solved, and asymptotic solutions induced by a sudden temperature rise on the boundary were obtained by applying an asymptotic approach. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature and stresses were obtained and plotted. Variations in the distributions with different values of fractional order parameter were discussed. The results were compared with those obtained from the case of constant material properties to evaluate the effects of variable material properties on thermoelastic behaviors.

The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement, temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.

In this paper, a new formulation for the generalized thermoelasticity in an isotropic elastic medium with temperature-dependent material properties is established. The governing equations for the generalized axisymmetric plane strain problem are derived. The asymptotic solutions for an infinite cylinder with the boundary subjected to the thermal shock are obtained under the linear assumption. Numerical results for the propagation of the thermal and elastic waves and the distributions of the displacement, temperature and stresses are given and illustrated graphically. Using these solutions, some phenomenon involved in the generalized thermoelastic problem are obtained, and the jumps at the wavefronts are observed clearly. The comparison is made with results obtained in the temperature-independent case and the influence of the temperature dependency of material properties on the propagation of thermal and elastic waves are also discussed.