Dynamical temperature and generalized heat-conduction equation

•A generalized heat-conduction equation which accounts for nonlocal, nonlinear,non-local, non-linear, and relaxation effects, is derived.•The heat flux is supposed to be proportional to the gradient of the dynamical temperature.•The material functions are allowed to depend on temperature.•Several enhanced heat equations proposed recently in literature are obtained.•Comparison is made with the heat equation of Thermomass Theory.•It is pointed out that the heat flux is limited from above by a maximum value.

By means of a dynamical non-equilibrium temperature we derive a generalized heat-conduction equation which accounts for non-local, non-linear, and relaxation effects. The dynamical temperature is also capable to reproduce several enhanced heat equations recently proposed in literature. The heat flux is supposed to be proportional to the gradient of the dynamical temperature, and the material functions are allowed to depend on temperature. It is also pointed out that the heat flux cannot assume arbitrary values, but it is limited from above by a maximum value which ensures that the thermal conductivity remains positive.