Transient responses of two temperature, fractional thermo-diffusive-elastic half space with temperature dependent properties. (English) Zbl 1542.74014
Summary: In scientific disciplines such as control engineering, astrophysics, geomechanics, nuclear physics, etc., thermoelastic diffusion plays a crucial role. When physical processes involve high temperature, considering two temperature theories and temperature-dependent material properties contribute to more rational results. The inclusion of fractional calculus in such studies provides results with significant accuracy. In this light, a model is formulated under two temperatures, fractional order Lord Shulman and Green Lindsay’s theories of generalized thermo-diffusive-elasticity. The medium under consideration is a half space which is kept unstressed initially at a uniform temperature \(T_0\). The material properties are considered to be a function of temperature. Governing equations and constitutive relations of the model are non-dimensionalized and simplified using potential functions. The field variables are determined analytically in the closed form in Laplace-Fourier transformed domain. Numerical computations are conducted with the assistance of MATLAB software. The study aims to observe the behavior of physical quantities for different values of two temperature, temperature-dependent, and fractional order parameters. Graphical representation is displayed with respect to space variables \(x\) and \(z\). The results reveal that physical quantities express varying degrees of influence corresponding to different effects involved in the study.
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74B05 | Classical linear elasticity |
| 74S40 | Applications of fractional calculus in solid mechanics |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
Keywords:
Caputo fractional derivative; Lord-Shulman theory; Green-Lindsay theory; potential function; Laplace-Fourier transform; numerical inversionSoftware:
MatlabReferences:
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