Problem in Poroelastic Media for an Infinitely Long Solid Circular Cylinder with Thermal Relaxation

Abstract

In this study, we consider an infinitely long poroelastic circular cylinder saturated with a liquid, whose lateral surface is traction free, impermeable, and subject to a time-dependent thermal shock. The medium is assumed to be initially quiescent. The problem is in the context of the generalised thermo-poroelasticity theory with one relaxation time. The solution is obtained by a direct approach without the customary use of potential functions. Laplace transform technique is used to obtain the general solution for any set of boundary conditions. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical results for the temperature in the cylinder and fluid, displacement of the cylinder, velocity of the fluid, and stresses for both components are obtained and represented graphically. The problem is solved for the case of one phase only, namely when the solid has no cavities and there is no fluid inside. The solution in this case for the temperature, displacement, and stress distributions is obtained and represented graphically.