Dynamical converters with power-producing relaxation of solar radiation

Abstract

Thermodynamics is applied in mathematical simulation and optimization of nonlinear energy converters, in particular radiation engines, in steady and dynamical situations. Power is a cumulative effect maximized in a system with a nonlinear fluid, an engine or a sequence of engines, and an infinite bath. Dynamical state equations are applied to describe the resource temperature and work output in terms of a process control. Recent expressions for efficiency of imperfect converters are used to derive and solve Hamilton–Jacobi equations describing resource upgrading and downgrading. Various mathematical tools are applied in trajectory optimization with special attention given to the relaxing radiation. The radiation relaxation curve is non-exponential, characteristic of a nonlinear system. Power optimization algorithms in the form of Hamilton–Jacobi–Bellman equations lead to work limits and generalized availabilities. Converter's performance functions depend on end thermodynamic coordinates and a process intensity index, h, in fact, the Hamiltonian of power optimization problem. As an example of limiting work from radiation, a finite rate exergy of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian h.