Thermal-wave heat conduction in a solid cylinder which undergoes a change of boundary temperature

The propagation of thermal waves in a solid cylinder which undergoes a change of its boundary temperature is studied by assuming the validity of Cattaneo-Vernotte's constitutive equation for the heat flux. The hyperbolic energy equation, together with its boundary and initial conditions, is written in a dimensionless form and solved analytically by the Laplace transform method. It is shown that, if the boundary temperature undergoes a step change, the temperature field presents singularities. On the other hand, no singularity is present if the temperature change is achieved by a continuous monotonic evolution of the boundary temperature. However, even in this case, the absolute value of the temperature change in internal points of the cylinder can be greater than that prescribed at the boundary.