الفهرس | Only 14 pages are availabe for public view |
Abstract In this perspective, the aim of thesis presents several applications of fractional calculus (FC) in the theories of thermo-elastic, thermo-viscoelastic and thermo-viscoelastic diffusion. A new mathematical model for the governing equations in these fields has been derived using the methodology of fractional calculus. The effects of time fractional derivative parameters have been studied on the thermo-mechanical variables fields.a review of some background material is presented. We start with a brief review of the basic concepts and definitions of fractional calculus and the linear theory of elasticity. Next, a review of the theory of thermodynamics including the statement of the first and second laws is presented. After that, we present the subject of thermoelasticity and give a derivation of the equations of uncoupled, coupled and generalized thermoelasticity theories, respectively. Finally, we present the linear theory of viscoelasticity including the constitutive models of it. We follow with the effect of heat on viscoelastic material known as thermoviscoelasticity |