Generalized constructal optimization of strip laminar cooling process based on entransy theory

A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The "generalized optimal construct" derived by minimum complex function shows a compromise between the energy retention and quality of the strip.

Thermal performance analysis of non-uniform height rectangular fin based on constructal theory and entransy theory

A model of non-uniform height rectangular fin, in which the variation of base's thickness and width are taken into account, is established in this paper. The dimensionless maximum thermal resistance(DMTR) and the dimensionless equivalent thermal resistance(DETR) defined based on the entransy dissipation rate(EDR) are taken as performance evaluation indexes. According to constructal theory, the variations of the two indexes with the geometric parameters of the fin are analyzed by using a finite-volume computational fluid dynamics code, the effects of the fin-material fraction on the two indexes are analyzed. It is found that the two indexes decrease monotonically as the ratio between the front height and the back height of the fin increases subjected to the non-uniform height rectangular fin. When the model is reduced to the uniform height fin, the two indexes increase first and then decrease with increase in the ratio between the height of the fin and the fin space. The fin-material fraction has no effect on the change rule of the two indexes with the ratio between the height of the fin and the fin space. The sensitivity of the DETR to the geometric parameters of the fin is higher than that of the DMTR to the geometric parameters. The results obtained herein can provide some theoretical support for the thermal design of rectangular fins.

Optimization of combined endoreversible Carnot heat engines with different objectives

Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.

Constructal entransy dissipation rate minimization for helm-shaped fin with inner heat sources

A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of the body with single and multiple inner heat sources are implemented. The entransy-dissipation-rate-based equivalent thermal resistance(ETR) is minimized in the optimizations. It shows that for the helm-shaped body with multiple inner heat sources, there exist an optimal ratio of the heat source distance to the radius of the extended fin and a twice optimal radius ratio of the centre fin to the extended fin which lead to the double minimum dimensionless ETR. Comparing the optimal result of the body with helm-shaped fin with that with annular fin, the radius of the centre fin and the distance between the heat source and the center of the body are decreased, and the ETR is decreased by 9.57%. Essentially, the temperature gradient field of the helm-shaped body is more homogenous, and its global heat transfer performance is improved.

Entransy dissipation minimization for generalized heat exchange processes

This paper investigates the MED （Minimum Entransy Dissipation） optimization of heat transfer processes with the generalized heat transfer law q ∝ （A（T^n））m. For the fixed amount of heat transfer, the optimal temperature paths for the MED are obtained The results show that the strategy of the MED with generalized convective law q ∝ （△T）^m is that the temperature difference keeps constant, which is in accordance with the famous temperature-difference-field uniformity principle, while the strategy of the MED with linear phenomenological law q ∝ A（T^-1） is that the temperature ratio keeps constant. For special cases with Dulong-Petit law q ∝ （△T）^1.25 and an imaginary complex law q ∝ （△（T^4））^1.25, numerical examples are provided and further compared with the strategies of the MEG （Minimum Entropy Generation）, CHF （Constant Heat Flux） and CRT （Constant Reservoir Temperature） operations. Besides, influences of the change of the heat transfer amount on the optimization results with various heat resistance models are discussed in detail.

Constructal optimization of cylindrical heat sources with forced convection based on entransy dissipation rate minimization

Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective.The effects of the cylindrical height,the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed.The results show that when the volume of the heat source is fixed,there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance.With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity,the minimum dimensionless equivalent thermal resistance decreases gradually.For the heat source model with inverted variable-cross-sectional cylinder,there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance.Therefore,the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section.The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different.When the thermal security is ensured,the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source.The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources,and they can provide some guidelines for the designs of practical heat source systems.

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

Constructal entransy dissipation rate minimization of a rectangular body with nonuniform heat generation

Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate(EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel(HCC) are derived. For the rectangular first order assembly(RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.