Hamilton-Jacobi-Bellman analysis of irreversible thermal exergy (Q1287817)

We analyze a dissipative extension of the classical Carnot problem of maximum work extracted from a system of two bodies with different temperatures. In the classical problem the instantaneous rates do vanish due to a reversibility requirement imposed on the process; in the extended problem some inevitable, rate-related irreversibilities are allowed, in particular those occurring in boundary layers. In our analysis, nonlinear thermodynamic modeling is inherently linked with ideas and methods of the optimal control. The applications refer, in particular, to the extension of the classical thermodynamic problem of maximum work (exergy) delivered from the system of a finite exchange area or of a finite contact time. The dissipative exergy is discussed in terms of the finite process intensity and finite duration. An analytical formalism, strongly analogous to those in analytical mechanics and optimal control theory, is an effective tool in the thermodynamic optimization. In this paper, a novel approach is worked out which is based on the Hamilton-Jacobi-Bellman equation for the dissipative exergy and related work functionals.