Optimal paths for minimizing lost available work during heat transfer processes with a generalized heat transfer law

Abstract

A common of finite-time heat transfer processes between high-and low-temperature sides with a generalized heat transfer law [q ∝ (∆(T n )) m ] are studied in this paper. The optimal heating and cooling configurations for minimizing lost available work are derived for the fixed initial and final temperatures of the working fluid of the system (low-temperature side). Optimal paths are compared with the common strategies of constant heat flux, constant source (reservoir) temperature and the minimum entropy generation operation by numerical examples. The condition corresponding to the minimum lost available work strategy is that corresponding to a constant rate of lost available work, not only valid for Newton's heat transfer law [q ∝ ∆T ] but also valid for the generalized convective heat transfer law [q ∝ (∆T ) m ]. The obtained results are more general and can provide some theoretical guidelines for the designs and operations of practical heat exchangers.

Entransy dissipation minimization for liquid-solid phase change processes

“…Comparison between eqs. (24) and (31) shows that the entransy dissipation corresponding to the optimal heat exchange strategies of minimum entransy dissipation during the phase change processes is 8/9 of that corresponding to constant reservoir temperature operations, which is also independent of all system parameters. Combining eq.…”

“…Nummedal [28] and Johannessen [29] investigated a class of plug flow reactors including the irreversibilities of heat transfer, fluid flow pressure drop and various chemical reactions, and derived the optimal configuration of the external furnace gases temperature for minimizing entropy generation. Chen et al [30] and Xia et al [31] derived optimal paths of heat transfer processes with a generalized heat transfer law [ ( ) n m q T ∝ Δ ] [14] for minimizing entropy generation [30] and minimizing exergy loss [31], respectively. Gordon et al [32] derived the optimal external heat reservoir temperature profiles of liquid-solid phase change processes for minimizing entropy generation.…”

Endoreversible Modeling and Optimization of a Multistage Heat Engine System with a Generalized Heat Transfer Law via Hamilton-Jacobi-Bellman Equations and Dynamic Programming

“…Fixed T 1f (t 1 = 150 s) References [25,65,[69][70][71] showed that the difference of reciprocal temperatures of the heat reservoir and the working fluid for the maximum work output of the reciprocating endoreversible heat engine with the linear phenomenological heat transfer law is a constant, and the reservoir temperature decreases with the time linearly; Refs. [3,63,64,[72][73][74] also showed that the difference of reciprocal temperatures of the high-and low-temperature sides for the minimum entropy generation of heat transfer processes with the linear phenomenological heat transfer law is a constant, and the high-temperature reservoir temperature decreases with the time linearly.…”

Maximum Profit Configurations of Commercial Engines

“…], Chen et al [38] and Xia et al [39] derived the optimal temperature configurations of heat transfer processes for minimum entropy generation [38] and minimum lost available work [39]. Xia et al [40] further investigated the minimum entransy dissipation of heat transfer processes with the generalized radiative heat transfer law.…”