Refined One Relaxation Time-Fractional Theory for the Thermoelastic Response of Circular Cylinders with Variable Thermal Conductivity

The fractional thermoelasticity theory is presented for the thermal response of a circular cylinder. The basic equations of the cylinder are derived from a fractional theory in the context of the generalized Lord and Shulman theory. It is taken into consideration the variable thermal conductivity of the circular cylinder. A temperature-mapping function is used for this purpose. The cylinder is subjected to an exponential decay of temperature mapping over time at its outer surface. The governing equations are solved by using the Laplace transform technique, and its inversion is carried out numerically. Numerical outcomes are computed and represented graphically for the field variables along the radial direction of the cylinder. The effects of many parameters on all thermoelastic fields are investigated. The analysis highlights the relationship between the field quantities and the radial direction of the circular cylinder, the impact of the exponential decay time, the impact of the thermal conductivity parameter, the inclusion of the fractional parameter, and the difference between the refined thermoelasticity theories.