Thermo-mechanical memory responses of biological viscoelastic tissue with variable thermal material properties

Abstract

<jats:sec> <jats:title content-type="abstract-subheading">Purpose</jats:title> <jats:p>In the present paper, the new concept of “memory dependent derivative” in the Pennes’ bioheat transfer and heat-induced mechanical response in human living tissue with variable thermal conductivity and rheological properties of the volume is considered.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title> <jats:p>A problem of cancerous layered with arbitrary thickness is considered and solved analytically by Kirchhoff and Laplace transformation. The analytical expressions for temperature, displacement and stress are obtained in the Laplace transform domain. The inversion technique for Laplace transforms is carried out using a numerical technique based on Fourier series expansions.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Findings</jats:title> <jats:p>Comparisons are made with the results anticipated through the coupled and generalized theories. The influence of variable thermal, volume materials properties and time-delay parameters for all the regarded fields for different forms of kernel functions is examined.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Originality/value</jats:title> <jats:p>The results indicate that the thermal conductivity and volume relaxation parameters and MDD parameter play a major role in all considered distributions. This dissertation is an attempt to provide a theoretical thermo-viscoelastic structure to help researchers understand the complex thermo-mechanical processes present in thermal therapies.</jats:p> </jats:sec>

Mathematical Modelling with the Exact Solution of Three Different Bioheat Conduction Models of a Skin Tissue Shocked by Thermoelectrical Effect

“…Ezzat constructed the model of the thermoviscoelasticity theory of fractional dual-phase-lag heat conduction law with rheological properties of the volume to investigate one-dimensional bioheat transfer and heatinduced mechanical response in human skin tissue [26]. In Pennes's bioheat transmission and heat-induced mechanical response in human living tissue with variable thermal conductivity based on rheological parameters of the volume, Ezzat presented a novel notion of memorydependent derivative [27]. Many applications of analytical analysis of the dual-phase-lag model of bioheat transfer have been constructed and solved [28][29][30][31][32].…”

On the memory-dependent derivative electric-thermoelastic wave characteristics in the presence of a continuous line heat source

“…Parallel to fractional ordered derivatives, memory-dependent derivatives serve as an important mathematical tool in describing many real world phenomena. One can refer to Yu et al (2014), Ezzat et al (2014;2016a;2016b), , and Ezzat (2020) for an overview of utilizations of memory-dependent derivative analytics.…”

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

“…Li et al (2020) have researched heat and mechanical behavior of biological tissue based on viscoelastic theory. Ezzat (2020aEzzat ( , 2020bEzzat ( , 2020c suggested a one-dimensional thermoviscoelasticity model theory with variable thermal conductivity and rheological volume features to explore bio-thermo-mechanical behaviors in living tissue.…”