Optimal expansion of a heated working fluid for maximum work output with time-dependent heat conductance and generalized radiative heat transfer law

Abstract

The optimal configuration of the expansion process of a heated working fluid inside a cylinder for maximum work output with a movable piston and time-dependent heat conductance is determined in this paper using finite-time thermodynamics. The heat transfer between the working fluid and the external heat bath is assumed to obey the generalized radiative heat transfer law (q ∝ Δ(Tⁿ)). The heat conductance (product of heat transfer coefficient and heat transfer surface area) of cylinder walls is assumed to depend on the time-dependent heat transfer surface area of the walls in contact with gas. Euler–Lagrange formalism is applied to obtain the optimal process that maximizes the work output of the working fluid with fixed initial energy, initial volume, final volume, and total time allowed for the expansion. The optimal initial value of internal energy of the Euler–Lagrange arc is determined by numerical techniques. Numerical examples for the optimal configurations with time-dependent heat conductance for the cases of five special heat transfer laws (n = –1, 1, 2, 3, and 4) are provided, and the obtained results are compared with those obtained for the cases of constant heat conductance. The optimal configurations with time-dependent heat conductance for the cases of five special heat transfer laws are also compared with each other. The optimization problems with the generalized radiative heat transfer law are helpful for the further understanding of the effect of heat transfer law on the general performance and the inherent character of thermodynamic processes and cycles. The results presented herein can provide the basis for both determining optimal operating conditions and designing real systems operating with the generalized radiative heat transfer law.