Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

Area of Science:

• Solid Mechanics
• Heat Transfer
• Continuum Mechanics

Background:

• Generalized thermoelasticity theories account for finite thermal wave propagation speeds.
• Dual-phase-lag heat conduction models capture micro-scale thermal effects.
• Fractional calculus offers a powerful framework for modeling complex material behaviors.

Purpose of the Study:

• To develop a novel two-temperature generalized thermoelasticity theory with fractional dual-phase-lag heat conduction.
• To investigate thermoelastic interactions in a semi-infinite solid with variable thermal conductivity.
• To analyze the influence of thermal and mechanical loading on the material response.

Main Methods:

• Formulation of basic equations in a vector-matrix differential equation in the Laplace transform domain.
• Solution using a state-space approach.
• Numerical inversion of Laplace transforms via Fourier series expansion.

Main Results:

• Numerical solutions obtained for thermoelastic quantities.
• Graphical representation of results to illustrate physical phenomena.
• Analysis of the impact of variable thermal conductivity, temperature discrepancy, and fractional order parameter.

Conclusions:

• The developed theory provides a comprehensive framework for analyzing complex thermoelastic phenomena.
• Variable thermal conductivity, temperature discrepancy, and fractional order significantly influence thermoelastic responses.
• The study offers insights into the behavior of advanced thermoelastic materials.