Minimizing entransy dissipation for heat transfer processes with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo linebreak="goodbreak" linebreakstyle="after">∝</mml:mo> <mml:mi>Δ</mml:mi> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and heat leakage

Abstract

Heat transfer process with heat leakage and generalized radiative heat transfer law (HTL) [q∝Δ(Tn)] is investigated. Optimality condition for the minimum entransy dissipation (MED) is derived by applying average optimal control theory. On the basis of the general optimization result, the results for four special cases of Newtonian [q∝Δ(T)], linear phenomenological [q∝Δ(T−1)], radiative [q∝Δ(T4)], and mixed [q∝Δ(T4) with q∝Δ(T)] HTLs are further obtained. Optimal paths are compared with the common strategies of constant heat flux rate and constant hot fluid temperature operation. Numerical examples are presented, and influences of heat transferred amount and heat leakage on optimization performances are analyzed.

Topics & Concepts