In this paper, based on the generalized heat transfer law, an air conditioning system is analyzed with the entropy generation minimization and the entransy theory. Taking the coefficient of performance (denoted as COP) and heat flow rate Q _out which is released into the room as the optimization objectives, we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations. Five numerical cases are presented. Combining the numerical results and theoretical analyses, we can conclude that the optimization applicabilities of the two theories are conditional. If Q _out is the optimization objective, larger entransy increase rate always leads to larger Q _out, while smaller entropy generation rate does not. If we take COP as the optimization objective, neither the entropy generation minimization nor the concept of entransy increase is always applicable. Furthermore, we find that the concept of entransy dissipation is not applicable for the discussed cases.

The purpose of this paper is to calculate the minimal disk which contains all the eigenvalues of matrices. In order to obtain the minimal disk which contains all the eigenvalues of matrices, an algorithm is presented.