Three-dimensional propagation of hyperbolic thermal waves in a solid bar with rectangular cross-section

The hyperbolic heat conduction in a solid bar with a rectangular section is analyzed. Each surface of the bar is subjected to a uniform and time varying heat flux. It is shown that, according to the heat-flux formulation of hyperbolic heat conduction, the heat flux density field can be determined by employing the analytical solution of a one-dimensional problem. The distributions of the heat flux density and the temperature are obtained for a bar with a finite length and with arbitrary time-evolutions of the heat flux on its surfaces. Special attention is devoted to a two-dimensional case, i.e. that of a bar with insulated ends. In this case, plots of the temperature field at given instants of time are reported and compared with those which correspond to a vanishing relaxation time.