北京师范大学学报（自然科学版）2016，Vol.52Issue(5)：550-555,6.DOI:10.16360/j.cnki.jbnuns.2016.05.003
非同型热机的非线性响应关系及其最大功率对应的效率∗
Nonlinear constitutive relation and efficiency at maximum power for nonhomotypic heat engine
摘要
Abstract
Typical heat engine exhibits a kind of homotypy:heat exchanges between the cyclic heat engine and the two reservoirs abide by the same function type.The forward and backward flows for an autonomous heat engine also conform to the same function type.These heat engines are named homotypic heat engines. Nonhomotypic cyclic heat engine,with heat exchange between the engine and the two reservoirs not conforming to the same function type,is considered in the present paper.Nonlinear constitutive relation for nonhomotypic cyclic heat engine is derived:J m =LA [1+ΛλA-δ(1+λ2 )2 A]+O(A3 ), where Jm and A are flux related to mechanical movement and affinity of the heat engine,respectively.L andΛare related to the first and the second order Onsager coefficients,respectively.λandδrepresent asymmetric parameter and nonhomotypic degree of the heat engine,respectively.A model of nonhomotypic endoreversible heat engine is constructed to confirm the above nonlinear constitutive relation.Efficiency at maximum power for nonhomotypic cyclic heat engine is:ηmaxP =ηC2 +η2C8 +2λ(1-Λβξ)+δ(1+λ2 )βξ1 6 η2C+O(η3C ), whereηC represents Carnot efficiency.Factorβis weighted reciprocal of temperature of the heat engine.Factorξis energy scale of the heat flowing through the heat engine in each cycle.From the above equation,it is found that sufficient condition to achieve universal efficiency (ηC/2+η2C/8)at maximum power is:2λ(1-Λβξ)+δ(1+λ2 )βξ=0.For nonhomotypic cyclic heat engine,this condition challenges symmetric coupling and energy-matching condition found in the literature .关键词
非同型热机/非线性响应/功率/效率Key words
nonhomotypic heat engine/nonlinear constitutive relation/efficiency/power分类
自科综合引用本文复制引用
赵凌飞,涂展春..非同型热机的非线性响应关系及其最大功率对应的效率∗[J].北京师范大学学报（自然科学版）,2016,52(5):550-555,6.基金项目
中央高校基本科研业务费专项资金资助项目(2015KJJCB01) （2015KJJCB01）
