Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

Abstract

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [ q ∝ Δ( T n )] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law ( n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law ( n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law ( n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.