Thermomagnetic modeling of a nonlocal viscoelastic half-space exposed to an internal heat source through a two-phase delay model

Abstract

In this article, a thermomagnetic viscoelastic nonlocal model has been introduced that incorporating the nonlocal elasticity theory of Eringen and the Kelvin–Voigt type. In the heat conductivity equation, the dual-phase-lag thermoelastic model (DPL) has been used to account for microstructural effects caused by high-rate heat transfer processes. The proposed DPL thermoelastic model illustrates the effects of material deficiencies and the thermomechanical relationship due to the extremely rapid heating. Within the framework of the nonlocal DPL model, a one-dimensional magneto-thermoelastic problem of half-space whose surface is exposed to an instantaneous heat source and magnetic field has been studied. With the eigenvalue approach technique and Laplace transform method, analytical solutions for the studied physical fields are provided. The transformed expressions to the field quantities are reversed into the physical domain by applying Zakian's algorithm. The effects of the nonlocal parameter, the viscosity and the applied heat source have been shown graphically on the differences in the fields within the medium.

KEYWORDS:

• Thermo-magneto-viscoelastic
• nonlocal theory
• half-space
• DPL model
• heat source
• eigenvalue approach

Acknowledgments

The author (Y. Elmasry) extends his appreciation to the Deanship of Scientific Research at King Khalid University for the financial support through research groups program under grant number (RGP.1/231/42).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by King Khalid University: [grant number RGP.1/231/42].