[...]... by considering a reversible heating process of an object with temperature of T For a reversible heating process, the temperature difference between the object and the heat source and the heat added are infinitesimal, as shown in Fig 8 Continuous heating of the object implies an infinite number of heat sources that heat the object in turn The temperature of these heat sources increases infinitesimally... a fixed flow rate in the duct flow, for example, by introducing vortices in a specially designed tube [19] The second one is to improve the uniformity of the temperature profiles by the inserts composed of sparse metal filaments in circular tube [21] The filaments are normal to the tube wall and thin enough to produce a slight additional increase in the pressure drop Such kind of fins is neither for... rate with low increased flow resistance Finally, both the field synergy principle and the EED principle are extended to be applied for the heat exchanger optimization and mass convection optimization 1 Introduction At present, human being faces two key problems: world-wide energy shortage and global climate worming Since the utilization of about 80% various kinds of energy are involved in heat transfer... can be seen that there are two ways to enhance heat transfer: (a) increasing Reynolds or/and Prandtl number; which is well known in the literatures; (b) increasing the value of the dimensionless integration The vector dot product in the dimensionless integration in Eq (9) can be expressed as U ⋅ ∇T = U ⋅ ∇T cos β (10) where β is the included angle, or called the synergy angle, between the velocity... highest temperature in the domain The material allocation in the volume-to-point conduction problem can also be optimized by using the extremum entransy dissipation principle to minimize the average temperature in the domain Xia et al.[30], Cheng [29] and Cheng et al [31] reported the bionic optimization of volume-to-point conduction based on the extremum entransy dissipation principle Uniform heat source... problem is to find the optimal thermal conductivity distribution which leads to a lowest average temperature in the domain The total heat flow rate through the two outlets is equal to the heat delivered from a uniform heat source in the domain per unit time, Qt = ∫∫∫ ΦdV (34) V The average temperature in the domain is, Tm = 1 Qt ∫∫∫ ΦTdV (35) V According to the minimum entransy dissipation principle, Eq.(32)... volume-to-point problem 4.3 Comparison between EED Principle and MEG Principle To further understand the difference between the extremum entransy dissipation (EED) principle and the minimum entropy generation (MEG) principle the optimization effects of heat conduction based on these two different principles are compared For the symmetric volume-to-point problem shown in Fig 11, the entropy generation rate during... equal to the total heat source in the domain, the outlet temperature is fixed, we want to find the minimum average temperature of the domain, so as to obtain the minimum temperature difference for heat conduction), we have, 1 2 δ ∫∫∫ ΦTdV = Qtδ Tm = δ ∫∫∫ k ( ∇T ) dV = 0 V V 2 (36) with the constraint, ∫∫∫ kdV = Const (37) V For the above optimization problem, the following functional can be constructed,... statement of the heat conduction using the method of weighted residuals They derived a minimum entransy dissipation principle for prescribed heat flux boundary conditions and a maximum entransy dissipation principle for prescribed temperature boundary conditions that are referred to as the extremum entransy dissipation principle (EED principle) The minimum entransy dissipation principle states that for the... conditions, the minimum entransy dissipation rate in the domain leads to the minimum difference between the two boundary temperatures This principle can be expressed as 1 2 QtδΔT = δ ∫∫∫ k ( ∇T ) dV = 0 2 V (32) where δ denotes the variation, ΔT is the temperature difference, and Qt is the heat flow The maximum entransy dissipation principle states that the largest entransy dissipation rate in a domain with . Liqiu Wang (Ed.) A dvances in Transport Phenomena 2010 Liqiu Wang (Ed.) Advances in Transport Phenomena 2010 123 Prof. L iqiu Wang Department of Mechanical Engineering The University of Hong. Wang (Ed.): Advances in Transport Phenomena, ADVTRANS 2, pp. 1–91. springerlink.com © Springer-Verlag Berlin Heidelberg 2011 Optimization Principles for Heat Convection Zhi-Xin Li and Zeng-Yuan. Power Engineering of Ministry of Education, Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China e-mail: lizhx@tsinghua.edu.cn, demgzy@tsinghua.edu.cn