Optimal piston motion paths for a light-driven engine with generalized radiative law and maximum ecological function

Abstract

Searching optimal piston motion path (OPMP) by using optimal control theory for various thermal cycles is an important task in finite time thermodynamics. Some optimization objectives have been used in this type of researches, including maximum work output (MWO) and minimum entropy generation (MEG). This paper introduces maximum ecological function (MEF) into OPMP problem for light-driven engine (LDE) with generalized radiative heat transfer law (HTL) [q∝Δ(Tn)]. The LDE is with working fluid of reacting system [A]⇌[B] and irreversibilities of piston friction and heat conduction. Numerical examples of OPMPs at MEF with Newtonian (n=1), linear phenomenological (n=−1) and radiative (n=4) HTLs are provided. The results are compared with those obtained by MWO and MEG objectives as well as different HTLs. Utilizing MEF as objective can effectively accomplish entropy generation reduction with a little decrease in work output. Time-parametrized piston velocity, working fluid temperature and piston position for MEF are situated between those for MEG and MWO. Moreover, OPMPs for MEF with different HTLs are also quite different. Although all of the values of ecological function are negative for three special HTLs, work output and ecological function decrease with the increase in n, and entropy generation increases when n increases.

Keywords

• Light-driven engine
• Ecological performance
• Generalized radiative heat transfer law
• Optimal control
• Finite time thermodynamics