Thermodynamic effects of the thermal conductivity dependence upon temperature in one-dimensional hyperbolic heat conduction
For parabolic conduction systems with constant boundary temperatures, various authors have considered the possibility of obtaining functions which are always decreasing in time evolution and which have a minimum in the steady state. The case of hyperbolic one-dimensional heat conduction with constant boundary temperatures has been examined. The purposes are the same, but the approaches are somewhat different. In this case it is possible to demonstrate that the time change of the entropy production per unit flux is always negative in time evolutions and is zero in the steady state.