Heat transient response in the surfaces of an infinitely long annular cylinder with internal heat source

In this work, we present a solution to a problem for an infinitely long annular cylinder, for two cases. The first case is a whose internal heat source and the inner and outer surfaces are traction free. While the second case whose inner and outer surfaces are subjected to known surrounding temperatures, they are traction free. The problem is solved using the theory of generalized thermoelasticity with two relaxation times. The effect of heat sources and their relation to physical quantities has been studied. We also showed the effect of heat exchange between the surfaces of the annual cylinder and the surrounding media, at different times. The Laplace transform concerning time is used. The inversion process is carried out using a numerical method based on a Fourier series expansion. The temperature, displacement and stresses are calculated numerical and represent the results graphically. The results can be applied to laminated stiffeners used on piping that carries hot fluids.