Generalized thermoviscoelastic novel model with different fractional derivatives and multi-phase-lags

• Published in: European physical journal plus Vol. 135; no. 10; p. 851
• Main Authors: Soleiman, A., Abouelregal, Ahmed E., Khalil, K. M., Nasr, M. E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Boundary conditions; Complex Systems; Condensed Matter Physics; Differential equations; Laplace transforms; Mathematical and Computational Physics; Mathematical functions; Mathematical models; Molecular; Multiphase; Numerical analysis; Optical and Plasma Physics; Physics; Physics and Astronomy; Propagation; Regular Article; Theoretical; Thermoelasticity; Thermoviscoelasticity; Viscoelasticity
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-020-00842-6

In the current investigation, we introduce a generalized modified model of thermoviscoelasticity with different fractional orders. Based on the Kelvin–Voigt model and generalized thermoelasticity theory with multi-phase-lags, the governing system equations are derived. In limited cases, the proposed model is reduced to several previous models in the presence and absence of fractional derivatives. The model is then adopted to investigate a problem of an isotropic spherical cavity, the inner surface of which is exposed to a time-dependent varying heat and constrained. The system of governing differential equations has been solved analytically by applying the technique of Laplace transform. To clarify the effects of the fractional-order and viscoelastic parameters, we depicted our numerical calculations in tables and figures. Finally, the results obtained are discussed in detail and also confirmed with those in the previous literature.