Fractional Cattaneo equation with a harmonic source and associated thermal stresses in axisymmetric and central symmetric cases

Abstract

Integer and fractional order Cattaneo equations with a source varying harmonically in time under zero initial conditions are studied in the axisymmetric case and the central symmetric case. The integral transform techniques are used to find the fundamental solutions. The displacement potential is used to find the associated thermal stresses in both cases. The impact of the fractional order parameters and time-harmonic source on the temperature as well as stress distributions has been examined. The outcomes of numerical computations are represented graphically for various values of the order of fractional derivatives. The main objective of the article is to examine the role of the order of the fractional derivatives in the rate of heat transfer and related thermal stresses. Moreover, it has been observed that the angular frequency controls the oscillatory behavior of solutions and also affects the amplitude of the oscillations. This analysis has a wide scope of applications in the study of viscoelastic materials, thermal energy storage systems, biological systems, etc.