Optimization Principles for Heat Convection

Abstract

Human being faces two key problems: world-wide energy shortage and global climate worming. To reduce energy consumption and carbon emission, it needs to develop high efficiency heat transfer devices. In view of the fact that the existing enhanced technologies are mostly developed according to the experiences on the one hand, and the heat transfer enhancement is normally accompanied by large additional pumping power induced by flow resistances on the other hand, in this chapter, the field synergy principle for convective heat transfer optimization is presented based on the revisit of physical mechanism of convective heat transfer. This principle indicates that the improvement of the synergy of velocity and temperature gradient fields will raise the convective heat transfer rate under the same other conditions. To describe the degree of the synergy between velocity and temperature gradient fields a non-dimensional parameter, named as synergy number, is defined, which represents the thermal performance of convective heat transfer. In order to explore the physical essence of the field synergy principle a new quantity of entransy is introduced, which describes the heat transfer ability of a body and dissipates during hear transfer. Since the entransy dissipation is the measure of the irreversibility of heat transfer process for the purpose of object heating the extremum entransy dissipation (EED) principle for heat transfer optimization is proposed, which states: for the prescribed heat flux boundary conditions, the least entransy dissipation rate in the domain leads to the minimum boundary temperature difference, or the largest entransy dissipation rate leads to the maximum heat flux with a prescribed boundary temperature difference. For volume-to-point problem optimization, the results indicate that the optimal distribution of thermal conductivity according to the EED principle leads to the lowest average domain temperature, which is lower than that with the minimum entropy generation (MEG) as the optimization criterion. This indicates that the EED principle is more preferable than the MEG principle for heat conduction optimization with the purpose of the domain temperature reduction. For convective heat transfer optimization, the field synergy equations for both laminar and turbulent convective heat transfer are derived by variational analysis for a given viscous dissipation (pumping power). The optimal flow fields for several tube flows were obtained by solving the field synergy equation. Consequently, some enhanced tubes, such as, alternation elliptical axis tube, discrete double inclined ribs tube, are developed, which may generate a velocity field close to the optimal one. Experimental and numerical studies of heat transfer performances for such enhanced tubes show that they have high heat transfer 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.