Entransy Dissipation Extremum Research Articles

Optimization of the Urea SCR injector based on entropy generation minimization and entransy dissipation extremum

A urea injection model with a mixer was established, and the of the urea-water-solution (UWS) heat transfer behavior in the pipeline was studied using the ML-CFD method, The influence of the urea injector parameters on NH3 concentration and uniformity was analyzed through parameter analysis. To improve the quality of NH3 produced by the UWS, according to the heat transfer efficiency of UWS in the pipeline, the parameters of the urea injector were optimized with the mutil-objectives of entropy generation minimization (EGM) and entransy dissipation extremum (EDE) respectively. The corresponding Pareto front was obtained, and the CFD model was established to compare the application of the two heat transfer indicators in engineering practice. The results show that both the EGM and the EDE methods can effectively optimize the heat transfer of UWS in the flow field, but the EDE method is better than EDG. The uniformity is 0.724% higher, and the NH3 concentration is 6.411% higher. This provides technical support for enhancing the UWS heat transfer.

Optimization of the content distribution of expanded natural graphite in a multilayer metal hydride bed for thermochemical heat storage

• Effect of expanded natural graphite (ENG) content gradient on reactor was studied. • An optimization method for ENG distribution based on entransy theory was proposed. • A larger ENG content gradient led to a more uniform temperature distribution. • The number of optimization iterations had little effect on optimal results. • A simplified configuration based on the optimized results was discussed. The poor thermal conductivity of MH beds limits hydrogen absorption in metal hydride (MH) reactors for thermochemical heat storage. The compaction of MH powder with expanded natural graphite (ENG) is an efficient and cost-effective approach for the heat transfer enhancement of MH beds. However, the addition of ENG reduces the hydrogen storage density of the compacted composites. How to optimize the allocation of a limited amount of ENG in the MH bed has not been studied. In this study, a multilayer MH bed configuration with an ENG grade content was adopted to improve the heat transfer performance of an MH reactor for thermochemical heat storage. The effect of the ENG content gradient on the performance of the MH reactor was investigated using a mathematical model of the MH reactor. Furthermore, an optimization method based on the entransy dissipation extremum principle (EDEP) was proposed to optimize the ENG distribution in magnesium hydride (MgH 2 )-ENG compacts. The results showed that a larger ENG content gradient resulted in faster hydrogen absorption and better heat-discharge performance. Compared with a configuration with a uniform ENG content, the optimized configuration based on the EDEP exhibited a shorter reaction time, more uniform bed temperature distribution, and 15.33% higher gravimetric exergy-output rate. In addition, the number of optimization iterations had little effect on the optimal results, which could be obtained by implementing only one optimization iteration. The optimization results showed that more ENG should be allocated to the internal layer of the MgH 2 -ENG compact. The compacts were divided into three layers, and the ENG content of each layer was calculated according to the optimized configuration based on the EDEP. The optimization method proposed in this study can be applied to optimize the high-conductivity material allocation in the volume-to-point problem for transient heat conduction.

Optimization of the Urea Scr Injector Based on Entropy Generation Minimization and Entransy Dissipation Extremum

Optimization of the Urea Scr Injector Based on Entropy Generation Minimization and Entransy Dissipation Extremum

Entransy functions for steady heat transfer

In this paper, the entransy functions for steady heat transfer are summarized and discussed based on the variational theory and the entransy theory. The entransy functions for steady convective heat transfer are derived for the first time. In steady heat transfer processes, it is shown that the steady distributions of heat flux and temperature (radiative thermal potential) should make the corresponding entransy functions reach their minimum values when the temperature (radiative thermal potential) or the heat flux of the boundary is given. The extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles are compared with the entransy functions It is shown that the entransy functions can describe a steady state, but cannot directly give a way to optimize heat transfer processes, while the extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles act in an opposite way.

A collaborative optimization method for heat transfer systems based on the heat current method and entransy dissipation extremum principle

Optimization of the heat transfer system (HTS) plays an important role in energy utilization fields. However, two aspects of HTS optimization: local optimization for components and system global optimization, are generally performed independently, thus a combination of them is required. This contribution proposes a collaborative optimization strategy for HTS and minimizes the total pumping power consumption for a typical HTS. The global optimization employs the heat current method to derive global optimum results without redundant intermediate variables, and the local optimization applies the CFD-based simulation and the entransy dissipation extremum principle which obtains the optimum flow field directly. Besides, these two parts are integrated by the iteration and updating strategy with an optimization platform. Results present local optimization of components and global optimization of the HTS influence each other. As the heat transfer duty of the HTS increases, the minimum pumping power consumption, optimal frequencies of pumps and mass flow rates increase simultaneously. However, due to the performance improvement of the convective heat transfer process in the evaporator, it requires less increment of mass flow rate. That is, the global optimization of the HTS not only requires system and component optimization but also requires an efficient collaborative optimization strategy.

Research on the dissipative characteristics of unsteady heat conduction for the one-dimensional sphere

In this paper, the dissipative characteristics of unsteady heat conduction process for the one-dimensional sphere is studied. The dissipation function can be regarded as a Lyapunov function for the heat conduction system, which determines the evolution direction of the system and the stability of the steady state. By use of the vector formula, the relationship between the thermal potential and dissipation function is derived, and its similarity with the dissipation system of mechanical energy is shown. The expression of dissipation function is obtained when the boundary temperature is fixed. In addition, an example for optimization of heat conduction process is discussed based on the entransy dissipation extremum principle.

Constructal Optimizations for Heat and Mass Transfers Based on the Entransy Dissipation Extremum Principle, Performed at the Naval University of Engineering: A Review.

Combining entransy theory with constructal theory, this mini-review paper summarizes the constructal optimization work of heat conduction, convective heat transfer, and mass transfer problems during the authors’ working time in the Naval University of Engineering. The entransy dissipation extremum principle (EDEP) is applied in constructal optimizations, and this paper is divided into three parts. The first part is constructal entransy dissipation rate minimizations of heat conduction and finned cooling problems. It includes constructal optimization for a “volume-to-point” heat-conduction assembly with a tapered element, constructal optimizations for “disc-to-point” heat-conduction assemblies with the premise of an optimized last-order construct and without this premise, and constructal optimizations for four kinds of fin assemblies: T-, Y-, umbrella-, and tree-shaped fins. The second part is constructal entransy dissipation rate minimizations of cooling channel and steam generator problems. It includes constructal optimizations for heat generating volumes with tree-shaped and parallel channels, constructal optimization for heat generating volume cooled by forced convection, and constructal optimization for a steam generator. The third part is constructal entransy dissipation rate minimizations of mass transfer problems. It includes constructal optimizations for “volume-to-point” rectangular assemblies with constant and tapered channels, and constructal optimizations for “disc-to-point” assemblies with the premise of an optimized last-order construct and without this premise. The results of the three parts show that the mean heat transfer temperature differences of the heat conduction assemblies are not always decreased when their internal complexity increases. The average heat transfer rate of the steam generator obtained by entransy dissipation rate maximization is increased by 58.7% compared with that obtained by heat transfer rate maximization. Compared with the rectangular mass transfer assembly with a constant high permeability pathway (HPP), the maximum pressure drops of the element and first-order assembly with tapered HPPs are decreased by 6% and 11%, respectively. The global transfer performances of the transfer bodies are improved after optimizations, and new design guidelines derived by EDEP, which are different from the conventional optimization objectives, are provided.

Comment on “Study on the consistency between field synergy principle and entransy dissipation extremum principle”

Comment on “Study on the consistency between field synergy principle and entransy dissipation extremum principle”

Laminar thermal and fluid flow characteristics in tubes with sinusoidal ribs

The article presents the effect of novel sinusoidal ribs transversely mounted in a tubular heat exchanger on convective heat transfer and flow pressure loss characteristics. The numerical study was performed under a constant heat flux condition for laminar water flow with Reynolds number (Re) ranged from 400 to 1800. The employment of sinusoidal ribs in the tube was aim to induce longitudinal vortex streams to give more intense flow mixing and to interrupt thermal boundary layer at the tube wall. The sinusoidal rib tubes (SRTs) were investigated at four rib height to diameter ratios (H/D = 0.026, 0.042, 0.058 and 0.074), three rib amplitude to diameter ratios (A/D = 0.211, 0.316 and 0.421), four rib width to diameter ratios (W/D = 0.158, 0.263, 0.368 and 0.474), three rib pitch to diameter ratios (P/D = 1.053, 1.316 and 1.579) and six circumferential rib numbers (N = 1, 2, 3, 4, 5 and 6). The obtained results reveal that increasing rib height, decreasing rib amplitude, decreasing rib width and decreasing rib pitch at most of Re lead to increase of both Nusselt number (Nu) and overall thermal performance evaluation criterion (PEC) while Nu and PEC increase from N = 1 to 3 and then decrease from N = 3 to 6. The enhanced heat transfer rate up to 4.89 times above that of the plain tube is found in the SRTs and the augmented friction loss is up to 5.62 times. The PEC is gained in the range of about 1.03–2.75 in the case studies and can be further improved by combined employing of the optimized individual geometric parameters in the preliminary trend analysis with the maximum value being about 3.64. The well organized flow patterns in the SRTs imply the probability in active controlling heat transfer characteristics by geometries. In addition, the obtained results indicate that the dimensionless absolute vorticity analysis, the entransy dissipation extremum principle and the field synergy theories could well depict and evaluate the heat transfer behaviors. At last, by comparing the present work with previous studies, the SRTs possess a potential promise in laminar heat transfer enhancement.

Study on the consistency between field synergy principle and entransy dissipation extremum principle

This paper is aiming at numerically demonstrating the interrelationship and consistency between field synergy principle (FSP) via the field synergy number (Fc) and the entransy dissipation extremum principle (EDEP). Numerical simulation is conducted by using the FLUENT software and the user defined function programs (UDF) for fin-and-tube surfaces (plain plate and slotted fins) and composite porous materials. The thermal boundary conditions include given heat flux and given surface temperature. The flow includes laminar and turbulent. The air properties may be constant or vary with temperature. Based on the numerical data the analyzed results from the FSP via Fc are totally consistent with the results analyzed by the EDEP for all the cases studied. Such consistency between the FSP and the entransy theory can be regarded as a kind of demonstration of the reliability and correctness of both the FSP and the entransy theory.

Heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks

One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object, while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional.

Heat transfer and flow behaviors of a wavy corrugated tube

A new design of wavy corrugated tube (WCT) aiming to improve heat transfer by employing multi-longitudinal vortices was put forward. Effects of corrugation number N (N=1, 2, 3 and 4), arrangement (parallel arrangement, counter arrangement, two-parallel and counter arrangement and five-parallel and counter arrangement), corrugation amplitude A (A=1mm, 3mm, 5mm and 7mm), corrugation width W (W=3mm, 5mm, 7mm and 9mm) and corrugation height H (H=0.5mm, 0.8mm, 1.1mm and 1.4mm) on turbulent fluid flow and heat transfer behaviors were investigated numerically as well as overall thermal performance evaluation criterion (PEC) also being discussed. The operating Reynolds number (Re) ranged from 7500 to 20000 and the constant temperature condition was imposed on the tube wall. Local streamlines, velocity contours, turbulent kinetic energy contours, turbulent intensity contours, temperature contours, heat flux contours and variations of absolute vorticity versus axis distance were plotted to illustrate the heat transfer enhancement mechanisms. Equivalent temperature difference (ETD) stemming from the entransy dissipation extremum principle theory was used to evaluate heat transfer enhancement. It is found that the varying geometric parameters of the WCT play an important role in thermal-hydraulic characteristics. The main findings are that the WCTs exhibits superior heat transfer rate and PEC compared with the plain tube, due to improved flow mixing and enhanced heat flux by multi-longitudinal vortices induced by corrugations. The Nusselt number, friction factor and PEC in the WCTs with both parallel arrangement and counter arrangement increase generally with the rise in corrugation number until N=3 and then decrease with the further increase of corrugation number from N=3 to N=4. The obtained results in ETD are matched with the heat transfer performance for WCTs with parallel arrangement which indicates that the heat transfer ability in the WCTs can be well described. Among the investigated different arrangements, it is found that the WCT with parallel arrangement has the maximum PEC. Furthermore, in results of corrugation amplitude variations versus thermal performance, the PEC in the WCT with A=5mm has the largest value. The PEC can be further enhanced by increasing corrugation width with the largest PEC obtained by the WCT with W=9mm. For varying corrugation height, the WCT with H=1.1mm has the best PEC at most of Re. Under operating conditions and geometric parameters considered, the WCT with A=5mm, N=3, W=9mm, H=1.4mm and parallel arrangement at Re=7500 offers the highest PEC value of about 1.56.

Theoretically and numerically investigation about the novel evaluating standard for convective heat transfer enhancement based on the entransy theory

This paper theoretically and numerically investigated a novel evaluating standard δe for the enhancement of convective heat transfer based on the entransy theory. In the theoretical derivation, the differential equations about entransy are established using the method of micro-control volume which can give the obvious physical changing processes. And then, an efficiency factor δe is recommended according to physical mechanisms of entransy dissipation which is considered the impact of energy dissipation. The principle is verified by numerical simulation. The results indicated that δe is more appropriate for evaluating the ability of convective heat transfer enhancement comparing with the traditional method of FSP (field synergy principle) and EDEP (entransy dissipation extremum principle). The results also showed that the higher the factor of δe, the more efficient heat transfer process.

Constructal design for blast furnace wall based on the entransy theory

Based on the entransy dissipation extremum principle for thermal insulation process, constructal design of blast furnace wall is performed in this paper. Optimal construct of the cooling stave in the furnace wall is obtained by using finite element method. The results show that there exists twice optimal axial diameter ratio and optimal cooling water velocity which makes the entransy dissipation rate of the blast furnace wall reach its critical minimum. Moreover, the optimal cross-section shape of the cooling pipe is approximately round. Within the discussed variation range of the axial diameter ratios, the minimum entransy dissipation rate is 2.73% less than the maximum entransy dissipation rate when the cooling water velocity is preset. Within the discussed variation range of the cooling water velocities, the minimum entransy dissipation rate is 2.09% less than the maximum entransy dissipation rate. Besides, increasing inlet temperature of cooling water appropriately is propitious to improve the global thermal insulation performance of the blast furnace wall while it cannot reduce the cooling water. The global thermal insulation performance of the furnace wall with approximately round cooling pipe is higher than that with composite-oblate cooling pipe.

Effects of rib arrangements on the flow pattern and heat transfer in an internally ribbed heat exchanger tube

A numerical simulation was carried out to investigate the effects of rib arrangements on the flow pattern and heat transfer in an internally ribbed heat exchanger tube. Details of the flow structures in the tube with parallel type ribs (P-type ribs) and V shape type ribs (V-type ribs) were presented and analyzed, respectively. The results reveal that rib arrangements have perceptible effects upon the flow pattern and heat transfer in the ribbed tube. The average Nusselt number and friction factor in the V-type ribbed tubes were about 57–76% and 86–94% higher than those in the P-type ribbed tube, respectively. The performance evaluation criterion (PEC) based on the same pumping power in the V-type ribbed tube varied from 1.32 to 1.74, which were about 27–41% higher than that in the P-type ribbed tube. To further understand the effects of rib arrangements on the heat transfer in the ribbed tube and reveal the essence of heat transfer enhancement, an analysis was also carried out from the point view of entransy dissipation extremum principle. The results demonstrate that the longitudinal swirl flow with multiple vortices induced in the V-type ribbed tube was a more effective flow pattern for heat transfer, compared to the longitudinal swirl flow with single vortex generated in the P-type ribbed tube.

Assessment of two different optimization principles applied in heat conduction

Optimization principles play a crucial role in the intensification of the heat-transfer process. In this study, we assess and compare two principles, i.e., the entransy dissipation extremum (EDE) principle and the minimum entropy generation (MEG) principle, used in a typical “area to point” heat conduction problem solved via a cellular automaton algorithm. The simulated results indicate that both rules can ameliorate the tree-network conductive path, leading to a more uniform thermal field and lower average and maximum temperatures. In contrast to the MEG principle, the EDE principle is more appropriate to be linked to the algorithm when dealing with the “area to point” heat conduction optimization, especially with a higher conductivity ratio, kp/k0, between the high conductivity material and the low conductivity material and the fraction of high conductivity, ϕ0. With the analysis of total entransy dissipation rate and entropy generation of the domain optimized by two principles, the results indicate that the EDE principle is more suitable for the heat-transfer processes without heat–work conversion. Moreover, optimization via reducing the total entransy dissipation rate exhibits better performance in decreasing the equivalent resistance theoretically.

Heat Transfer and Thermal Resistance Characteristics of Fin with Built-In Interrupted Delta Winglet Type

The heat transfer and fluid flow characteristics of a new type of fin with built-in interrupted delta winglets is studied in this paper by three-dimensional numerical simulation. In order to ensure reliability of numerical model, plate fin with common-flow-up delta winglets is firstly simulated. The comparison of numerical and experimental results shows a maximum deviation of 11.4% within the entire range of Reynolds number. The computational results show that heat transfer capacity and overall performance increase by 35–60% and 19–64%, respectively. The flow field visualization shows that the interrupted delta winglets can produce longitudinal vortices at the rear of delta winglets and reduce the wake zone behind the tube, so the proposed fin can enhance heat transfer accompanied by low pressure loss. The field synergy theory and entransy dissipation extremum principle are employed on analyzing the mechanism of heat transfer enhancement. The results indicate that enhancement heat transfer mechanism of interrupted delta winglets can be explained as the result of the decrease of synergy angle and reduction of the entransy dissipation.

Numerical study on heat transfer and flow characteristics of a tube fitted with double spiral spring

Heat transfer and friction loss characteristics of a plain tube fitted with double spiral spring (DSS) are investigated by a three dimensional numerical simulation. The outer diameters of the DSS are 9 mm, 12 mm, 15 mm, and 18 mm, respectively. The simulation results indicate that the fluid in the tube inserted with DSS shows three-dimensional helical flow, and that the circumferential and the radial velocity of fluid near the tube wall are improved. At the same Reynolds number, the average radial and tangential velocities of the DSS tube are significantly higher than those of the plain tube. The Nusselt number increases and the friction factor decreases in tube with DSS insert as the Reynolds number increases. With the increase of the ds/D of DSS, the friction factor becomes higher. The field synergy principle (FSP) and entransy dissipation extremum principle (EDEP) analysis provide a reliable criterion for exploring the mechanism of heat transfer enhancement. The field synergy number of the tube inserted with DSS is much higher than that of plain tube, which indicates effective improvement of flow and heat transfer by inserted DSS. Meanwhile, the value of performance evaluation criterion (PEC) could be up to 1.5.

Constructal optimization of variable cross-section insulation layer of steel rolling reheating furnace wall based on entransy theory

Based on the entransy dissipation extremum principle for thermal insulation process, the constructal optimizations of a variable cross-sectional insulation layer of the steel rolling reheating furnace wall with convective and compound heat transfer (mixed convective and radiative heat transfer) boundary conditions are carried out. An optimal construct of the insulation layer with minimum entransy dissipation rate can be obtained. Results show that the global thermal insulation performance of the variable cross-sectional insulation layer at minimum entransy dissipation rate is better than that of the constant cross-sectional one. The optimal constructs of the insulation layer obtained based respectively on the minimizations of the entransy dissipation rate and heat loss rate are different. The optimal construct of the insulation layer at minimum heat loss rate leads to a reduction of the energy loss, and that at minimum entransy dissipation rate leads to an improvement of the global thermal insulation performance. The difference between the optimal constructs of the variable cross-sectional insulation layer based on the minimizations of the entransy dissipation rate and the maximum temperature gradient is small. This makes the global thermal insulation performance and thermal safety of the insulation layer improved simultaneously. The constructal optimization of the insulation layer based on entransy theory can provide some new guidelines for the optimal designs of the insulation systems.

Turbulent Mass Transfer Optimization Control Technology in Coalmine

Gas control in coalmine was the critical issue since gas accidents give rise to a lot of harm. This paper put forward the optimization control strategy based on the turbulent mass transfer mechanism on the basis of previous research. First of all, gas turbulent mass transfer mathematical model was established in heading laneway. Three aspects were describing in detail, gas diffusion law and quality entransy conservation when no wind, gas fluid flow process and momentum entransy conservation when no wind, ventilation airflow turbulent mass transfer process and mathematics when ventilation exits. Turbulent mass transfer optimization control strategy on the basis of the method of Lagrange multipliers was adopted. Moreover, turbulent mass transfer Euler equation which satisfy mass entransy dissipation extremum in turbulent mass transfer process. Finally, simulation experiments were carried out in the experimental platform; the data shows that turbulent mass transfer optimization control strategy was effective.