Abstract
Based on the theoretical model of a heated ideal working fluid in the cylinder, the optimal motion path of the piston in this system, for the maximum work output, is re-studied by establishing the changed Lagrangian function and applying the elimination method when the initial internal energy, initial volume, finial volume and the process time are given and generalized radiative heat transfer law between the working fluid and heat bath is considered. The analytical solutions of the intermediate Euler-Lagrange arc with square, cubic and radiative heat transfer laws are taken as examples and obtained. The optimal motion path of the piston with cubic heat transfer law, which is obtained by applying the elimination method, is compared with that obtained by applying the Taylor formula expansion method through numerical example. The comparing result shows that the accuracy of the result which is obtained by applying the elimination method is not affected by the length of time of the expansion process of the working fluid, so this result is more universal.
Highlights
Finding the optimal configurations of thermodynamic processes and systems under different given optimal objectives is one of the most active research directions of the finite time thermodynamics (FTT) theory [1,2,3,4,5,6,7,8,9,10]
heat transfer law (HTL) is not always Newton’s HTL and obeys other laws, and HTLs will affect the optimal configurations of thermodynamic processes and systems
Based on the Refs. [11,12,17,20,21,22], using the elimination method to eliminate the variable V (t) by applying optimal control theory (OCT), the optimal motion path (MP) of the piston of a heated ideal working fluid (WF) in the cylinder is studied by the single variable E(t) when the HTL between the WF and heat bath is generalized radiative HTL
Summary
Finding the optimal configurations of thermodynamic processes and systems under different given optimal objectives is one of the most active research directions of the finite time thermodynamics (FTT) theory [1,2,3,4,5,6,7,8,9,10]. HTLs, respectively, and obtained the first-order approximate analytical solutions by using the Taylor formula expansion method. [20,21,22] applied the Taylor formula expansion method to simplify a Entropy 2020, 22, 720; doi:10.3390/e22070720 www.mdpi.com/journal/entropy the cylinder under generalized radiative [20], Dulong–Petit [21] and convective-radiative [22] HTLs, respectively, and obtained the first-order approximate analytical solutions by using the Taylor formula expansion method. [11,12,17,20,21,22], using the elimination method eliminate optimal MPs of the piston of a heated ideal WF in the cylinder under generalized convective HTL.
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