(SI17-06) Green-Naghdi Theory of Two-Temperature Fractional Thermoelasticity under Thermal Shock and Ramp-Type Heating

Authors

• Sagar Sankeshwari, SVKM’s NMIMS Deemed to be University
• Vinayak Kulkarni, University of Mumbai

Abstract

The linear thermoelasticity theory without energy dissipation developed by Green-Naghdi has been reconstructed by using two temperature theory in the context of a time fractional derivative. In half-space, the mathematical model is discussed for one-dimensional wave propagation subject to two different problems, viz., thermal shock and ramp-type heating at the bounding surface. Assume the bounding surface is traction-free. The analytical solutions are obtained in the Laplace domain. The Gaver-Stehfest technique is numerically used to perform time domain inversion of the Laplace transform, satisfying Kuznetsov’s convergence condition. The impact of fractional order parameters on the variations of various fields inside the medium is addressed graphically. It is concluded the behavior of the thermophysical fields is significantly influenced by fractional order parameter, where this parameter becomes new indicator of its ability to conduct the thermal energy.

Recommended Citation

Sankeshwari, Sagar and Kulkarni, Vinayak (2026). (SI17-06) Green-Naghdi Theory of Two-Temperature Fractional Thermoelasticity under Thermal Shock and Ramp-Type Heating, Applications and Applied Mathematics: An International Journal (AAM), Vol. 21, Iss. 4, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol21/iss4/2