Non-Fourier fractional thermoelastic two dimensional model of a hollow
sphere
- Vinayak Kulkarni,
- Gaurav Mittal
Abstract
Assuming non-Fourier thermal effects, Tzou's dual-phase-lag model has
been applied to introduce the governing heat conduction equation in the
presented mathematical model. Moreover, in order to design a well-posed
stable dual-phase-lag model, the governing time fractional
dual-phase-lag heat equation has been established by introducing
conductive temperature and thermodynamical temperature, satisfying the
two-temperature theory. Due to the application of phase-lags the heat
conduction equation became hyperbolic. The corresponding governing
equations of motion and stresses have been considered in two-dimensional
bounded spherical domain. The spherical boundaries are assumed to be
traction free. The Laplace and the Legendre integral transforms have
been applied to obtain the analytical solutions of conductive and
thermodynamical temperatures, displacement components and thermal
stresses. The Gaver-Stehfest algorithm has been employed to achieve the
time domain inversions of Laplace transforms numerically, satisfying the
Kuznetsov convergence criteria. Classical, fractional and generalized
thermoelasticity theories has been recovered theoretically and
numerically as well for various fractional orders and phase-lags values.09 Apr 2020Submitted to Mathematical Methods in the Applied Sciences 12 Apr 2020Assigned to Editor
12 Apr 2020Submission Checks Completed
13 Apr 2020Reviewer(s) Assigned
18 Dec 2020Review(s) Completed, Editorial Evaluation Pending
18 Dec 2020Editorial Decision: Revise Minor
20 Dec 20201st Revision Received
20 Dec 2020Submission Checks Completed
20 Dec 2020Assigned to Editor
20 Dec 2020Editorial Decision: Accept