Two Temperature Dual-phase-lag Fractional Thermal Investigation of Heat Flow Inside a Uniform Rod

A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the last end. The State-space approach has been employed to solve the corresponding boundary value problem to obtain the conductive and thermomechanical temperature along with thermal displacement and stresses in the Laplace domain. The role of the time-fractional order and delay time in the heat flux and temperature gradient has been investigated through numerical results representing graphically along the length of the rod. The classical, fractional and generalized thermoelasticity theory have been recovered and the finite speed of thermal wave has been attained