More around Cattaneo equation to describe heat transfer processes

We revisit Cattaneo's derivation of the equation describing heat transfer and bearing his name, finding a more elaborated model equation, that we will compare with the time-lagged model. This equation does not comply with the second law of thermodynamics, as well as Cattaneo equation. The latter, however, is known to have provided meaningful results in certain experiments conducted in some liquids and solids at very low temperature. These experiments also match the results given by a nonlinear model proposed by A. Morro and T. Ruggeri in 1988, which instead does meet the laws of thermodynamics. A comparison is made with such a model too.