Thermodynamic effects of the equivalent thermal conductivity dependence on temperature gradient in one-dimensional heat transfer

Previously, the general case of one-dimensional heat transfer characterised by time-independent boundary temperatures was examined with techniques from generalised thermodynamics, and various kinds of thermal conductivity dependence were considered. A study is made of the way in which the thermal conductivity dependence on temperature, on temperature gradient, and on the coordinate in the heat flux direction with a finite number of discontinuities influences the minimum states and the time evolution of the entropy production rate and of the thermokinetic potential in one-dimensional systems with time-independent boundary temperatures. In particular, the influence of the dependence of apparent conductivity on temperature gradient - for example, owing to an appreciable amount of radiation - is examined with the well-known methods and purposes of generalised thermodynamics.