ISSN Online: 2377-424X
ISBN Print: 1-56032-797-9
International Heat Transfer Conference 11
LYAPOUNOV FUNCTIONS IN PARABOLIC ONE-DIMENSIONAL HEAT CONDUCTION WITH CONSTANT BOUNDARY TEMPERATURES AND WITH THERMAL CONDUCTIVITY AS A FUNCTION OF TEMPERATURE, OF THE COORDINATE IN THE HEAT FLUX DIRECTION AND OF TIME
Abstract
For heat conduction systems with constant boundary temperatures or with adiabatic boundary conditions, various authors considered the possibility of attaining functions which are always decreasing in a time evolution and are minimum at the steady state. Several kinds of thermal conductivity dependence were studied with techniques from generalized thermodynamics.
The aim of this paper is that of examining the case of parabolic one-dimensional heat conduction with constant boundary temperatures and thermal conductivity as a function of temperature, of the coordinate in the heat flux direction and, in an asymptotically vanishing way, of time. First of all entropy production rate and its differentials are considered. Afterwards, a new parameter named "generalized thermokinetic potential" is dealt with; this parameter is always decreasing in any time evolution and is minimum at the steady state.
The aim of this paper is that of examining the case of parabolic one-dimensional heat conduction with constant boundary temperatures and thermal conductivity as a function of temperature, of the coordinate in the heat flux direction and, in an asymptotically vanishing way, of time. First of all entropy production rate and its differentials are considered. Afterwards, a new parameter named "generalized thermokinetic potential" is dealt with; this parameter is always decreasing in any time evolution and is minimum at the steady state.