New fractional order model of thermoporoelastic theory for a porous infinitely long cylinder saturated with fluid

Abstract

In this manuscript, the generalized thermoporoelasticity theory is modified by using fractional derivatives. The revised equation is used to study mathematical model for two-dimensional problem subjected to a known heat source among the context of the fractional order generalized thermo-poroelasticity theory. An analytical solution using Laplace transform is followed to address the governing equations. Problem for porous infinitely Cylinder for certain boundary conditions is solved by the resulting formulation. Numerical effects are represented graphically and discussed. Some comparisons are shown in figures to estimate the impact of porosity ( 0 ≤ β ≤ 1 ) and fractional parameter ( 0 ≤ α ≤ 1 ) . Porosity has a pronounced effect on the speed, the pressure but has a weak effect on the temperatures. Comparison is done with a porous infinitely long Cylinder with the identical configuration in case of the absence of the fluid. The presented results in this issue are of great important in many science and engineering applications. Issues in cylindrical regions are important because of their several applications in producing of machine components. The theory of fractional calculus has been used successfully to model polymers materials. The result provides a motivation to investigate thermoelastic materials as a new class of applicable materials.