Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle

Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.

Constructal design for a steam generator based on entransy dissipation extremum principle

Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube,the dimensionless pressure difference number and the dimensionless length of flow channel of gas.Besides the three dimensionless groups,the optimal numbers of riser tubes and downcomer tubes and their summation all depend on the dimensionless height of one tube.The maximum entransy dissipation rate increases as the pressure difference that drives the gas flowing increases,and as the diameter of one tube and the length of flow channel both decrease.The mean heat flux in the heat transfer process of hot gas grows greatly,and the performance of the system is improved.Compared with the optimal construct with heat transfer rate maximization,the optimal construct with entransy dissipation rate maximization can improved the heat transfer effect of the steam generator more.

Comparative study on constructal optimizations of T-shaped fin based on entransy dissipation rate minimization and maximum thermal resistance minimization

The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipation and the minimization of maximum thermal resistance as optimization objectives, respectively. The effects of the global parameter a (integrating the coefficient of convective heat transfer, the overall area occupied by fin and its thermal conductivity) and the volume fraction ? of fin on the minimums of equivalent thermal resistance and maximum thermal resistance as well as their corresponding optimal configurations are analyzed. The comparison of the results based on the above two optimization objectives is conducted. The results show that the optimal structures based on the two optimization objectives are obviously different from each other. Compared with the optimization result by taking the minimization of maximum thermal resistance as the objective, the optimization result by taking the equivalent thermal resistance minimization as the objective can reduce the average temperature difference in the fin obviously. The increases of a and ? can all improve the working status of local hot spot and the global heat transfer performance of the system. But the improvement effects of the increases of a and ? on the minimization of equivalent thermal resistance are different from those on the minimization of maximum thermal resistance. For either objective, the effect of a is different from that of ?. The T-shaped fin with minimum equivalent thermal resistance is much taller than that with minimum maximum thermal resistance; for either optimization objective, the stem of fin is thicker than the branches of fin, and the stem thickness is relatively close to branch thickness when the minimization of equivalent thermal resistance is taken as the optimization objective. The T-shaped fin with flat stem and slender branches can benefit the reduction of the maximum thermal resistance.

Constructal entransy dissipation rate minimization for umbrella-shaped assembly of cylindrical fins

Umbrella-shaped assembly of cylindrical fins is optimized by adopting analytical method and taking dimensionless mean thermal resistance (MTR) as performance index. The optimal construct of umbrella-shaped assembly is obtained. The results show that the heat conductance performance of the assembly becomes ever worse with ever greater number of elemental cylindrical fins,the umbrella-shaped assembly reduces to cylindrical fin in some values of design parameters,and the diameters’ dependence on design parameters is weak for the optimized assembly. An equivalent thermal resistance defined based on entransy dissipation rate (EDR) reflects an average heat transfer effect of the assembly. The constructal design corresponding to the minimum EDR (or MTR) should be adopted for designing an assembly of fins in engineering at the limit safe condition.

“Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale

Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.

Constructal entransy dissipation rate minimization for leaf-like fins

Based on constructal theory,the constructs of the leaf-like fins are optimized by taking minimum entransy dissipation rate(for the fixed total thermal current,i.e.,the equivalent thermal resistance) as optimization objective.The optimal constructs of the leaf-like fins with minimum dimensionless equivalent thermal resistance are obtained.The results show that there exists an optimal elemental leaf-like fin number,which leads to an optimal global heat conduction performance of the first order leaf-like fin.The Biot number has little effects on the optimal elemental fin number,optimal ratios of length and width of the elemental and first order leaf-like fins;with the increase of the thermal conductivity ratio of the vein and blade,the optimal elemental fin number and optimal ratio of the length and width of the elemental leaf-like fin increase,and the optimal shape of the first order leaf-like fin becomes tubbier.The optimal construct based on entransy dissipation rate minimization is obviously different from that based on maximum temperature difference minimization.The dimensionless equivalent thermal resistance based on entransy dissipation rate minimization is reduced by 11.54% compared to that based on maximum temperature difference minimization,and the global heat conduction performance of the leaf-like fin is effectively improved.For the same volumes of the elemental and first order leaf-like fins,the minimum dimensionless equivalent thermal resistance of the first order of the leaf-like fin is reduced by 30.10% compared to that of the elemental leaf-like fin,and the global heat conduction performance of the first order leaf-like fin is obviously better than that of the elemental leaf-like fin.Essentially,this is because the temperature gradient field of the first order leaf-like fin based on entransy dissipation rate minimization is more homogenous than that of the elemental leaf-like fin.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the leaf-like fin,and can provide some guidelines for the thermal design of the fins from the viewpoint of heat transfer optimization.

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.

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

A class of one-way isothermal mass transfer processes with Fick’s diffusive mass transfer law[g ∝Δ(c)]is investigated in this paper.Based on the definition of the mass entransy,the entransy dissipation function which reflects the irreversibility of mass transfer ability loss is derived.The optimal concentration allocations of the key components corresponding to the highand low-concentration sides for the minimum entransy dissipation of the mass transfer process are obtained by applying opti- mal control theory and compared with the strategies of the minimum entropy generation,constant mass transfer flux(constant concentration difference),and constant concentration ratio(constant chemical potential difference).The results are as follows. For the optimal mass transfer strategy of the minimum entransy dissipation,the product of the square of the key component concentration difference between the high-and the low-concentration sides and the inert component concentration at the low-concentration side is a constant,while for that of the minimum entropy generation,the ratio of the square of the key com-ponent concentration difference between the high-and the low-concentration sides to the key component concentration at the low-concentration side is a constant;when the mass transfer process is not involved in energy conversion process,the optimi-zation principle should be the minimum entransy dissipation;the mass transfer strategy of constant concentration difference is superior to that of constant concentration ratio.The results obtained in this paper can provide some theoretical guidelines for optimal designs and operations of practical mass transfer processes.

Entransy dissipation,entransy-dissipation-based thermal resistance and optimization of one-stream hybrid thermal network

The one-stream hybrid thermal network is analyzed and discussed based on the entransy theory,and the results are compared with those from the entropy generation optimization.The theoretical analysis indicates that the minimum heat-flow-weighted temperature of the thermal networks corresponds to the minimum entransy dissipation rate and the minimum thermal resistance.For a simple hybrid thermal network consisting of three thermal components,the expression of entransy dissipation is conducted,and the heat transfer area and the mass flow rate are calculated and optimized.The optimal results are obtained in order to minimize the entransy dissipation and the thermal resistance.The optimal results are calculated for various combinations,such as series connection,parallel connection and other hybrid connections.The numerical results are in accordance with the theoretical analysis.Both the theoretical analysis and the numerical results show that the minimum entransy dissipation and the minimum thermal resistance correspond to the minimum heat-flow-weighted temperature of the thermal networks while the minimum entropy generation does not.

An entransy dissipation-based optimization principle for solar power tower plants

The entransy theory, which can be used to optimize the heat transfer network of a solar power tower system （SPTS） and im- prove its energy efficiency, was introduced in this paper. Firstly, the irreversibility of the heat transfer processes in a SPTS was analyzed and the total entransy dissipation equation of a SPTS was derived. Then, two types of optimization problems （reduc- ing the total circulating flow rate or the total heat-exchanging area） of a SPTS were solved with conditional extremum model based on the formulas of total entransy dissipation. Finally, the entransy dissipation-based optimization principle was applied to a simple SPTS without re-heater and a complex SPTS with a re-heater. The results showed that under the chosen calculation conditions the minimum total thermal conductance was 19306.03 W K-~ for a SPTS without re-heater when the total heat ca- pacity rate of heat transfer fluid （HTF） was 3200 W K-1. The minimum total thermal conductance was about 7.9% lower than the value predicted based on the typical outlet temperature of a receiver. This meant that the total heat exchange area or initial investment could be effectively reduced under the prescribed total HTF circulating flow rate. We also studied the variation trends of the two optimized results including minimum total HTF heat capacity rate and minimum total thermal conductance. The minimum total HTF heat capacity rate decreased with the given total thermal conductance, the minimum total thermal conductance decreased first and then increased with the given total HTF heat capacity rate. We also found that for a SPTS with a re-heater, the mixing temperature and the mixing position of HTF had significant effects on the two types of optimization problems.

Distribution optimization of circulating water in air-cooled heat exchangers for a typical indirect dry cooling system on the basis of entransy dissipation

The flow and heat transfer of air-cooled heat exchangers play important roles in the performance of indirect dry cooling systems in power plants,so it is of benefit to the design and operation of a typical indirect dry cooling system to optimize the thermo-flow characteristics of air-cooled heat exchangers.The entransy dissipation method is applied to the performance optimization of air-cooled heat exchangers in this paper.Two irreversible heat transfer processes in air-cooled heat exchangers,the heat transfer between circulating water and cooling air and the mixing of circulating water,are taken into account and analyzed by means of the entransy dissipation method.The total entransy dissipation rate,which connects the geometrical parameters of air-cooled heat exchanger sectors and the heat capacity rates of the fluids to the heat flow rate in every sector,is obtained.Based on the mathematical relation and the conditional extremum method,an optimization equation group is derived,by which the air-cooled heat exchanger with known air-side parameters is optimized,showing that the entransy dissipation based optimization approach can contribute to the distribution optimization of circulating water in air-cooled heat exchangers of a typical indirect dry cooling system.

Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance（denoted as COP） and heat flow rate Qout which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Qout is the optimization objective,larger entransy increase rate always leads to larger Qout,while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.

Optimization of fin geometry in heat convection with entransy theory

The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.

Experiment and numerical simulation on flow and heat transfer in all-glass evacuated tube solar collectors

The experimental study of natural convection in allglass evacuated tube solar collectors is performed through the experimental platform of the solar-assisted fuel cell system.The experimental facility includes solar collectors with different length and diameter tubes, different coating materials, and with / without guide plates, respectively. Threedimensional mathematical models on natural and forced convections in the solar collectors are established and the experimental data is validated by field synergy and entransy principles. The results of natural convection show that the water temperature increases and thermal efficiency decreases gradually with the evacuated tube length. The thermal efficiency increases when absorption rates increase from 0. 95 to 1. 0 and emission rates decrease from 0. 16 to 0. 06. The thermal efficiency of solar collectors is increased after being equipped with the guide plate, which is attributed to the disappearance of the mixed flowand the enhancement of the heat transfer at the bottom of the evacuated tube. The results of forced convertion indicate that the Reynolds, Nusselt and entransy increments of the horizontal double collectors are higher than those of the vertical single collector while the entransy dissipation is lower than that of the vertical single collector. It is concluded that the solar collectors with guide plates are suitable for natural convection while the double horizontal collectors are suitable for forced convection in the thermal field of solar-assisted fuel cell systems with lowand medium temperatures.

Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft

For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and discussed with the entransy theory.It is found that the optimization objective of this problem and the optimization direction of the extremum entransy dissipation principle are consistent in theory.For a two-branch thermal network system,the distributions of the flow rate of the cold fluid and the heat transfer area are optimized by calculating the extremum entransy dissipation with the Newton method.The influential factors of the optimized distributions are also analyzed and discussed.The results show that the main influence factors are the heat transfer rate of the branches and the total heat transfer area.The total flow rate of the cold fluid has a threshold,beyond which further increasing its value brings very little influence on the optimization results.Moreover,the difference between the extremum entransy dissipation principle and the minimum entropy generation principle is also discussed when they are used to analyze the problem in this paper,and the extremum entransy dissipation principle is found to be more suitable.In addition,the Newton method is mathematically efficient to solve the problem,which could accomplish the optimized distribution in a very short time for a ten-branch thermal network system.

Constructal optimization for H-shaped multi-scale heat exchanger based on entransy theory

Analogizing with the definition of thermal efficiency of a heat exchanger,the entransy dissipation efficiency of a heat exchanger is defined as the ratio of dimensionless entransy dissipation rate to dimensionless pumping power of the heat exchanger.For the constraints of the total tube volume and total tube surface area of the heat exchanger,the constructal optimization of an H-shaped multi-scale heat exchanger is carried out by taking entransy dissipation efficiency maximization as optimization objective,and the optimal construct of the H-shaped multi-scale heat exchanger with maximum entransy dissipation efficiency is obtained.The results show that for the specified total tube volume of the heat exchanger,the optimal constructs of the first order T-shaped heat exchanger based on the maximizations of the thermal efficiency and entransy dissipation efficiency are obviously different with the lower mass flow rates of the cold and hot fluids.For the H-shaped multi-scale heat exchanger,the entransy dissipation efficiency decreases with the increase in mass flow rate when the heat exchanger order is fixed;for the specified dimensionless mass flow rate M(M<32.9),the entransy dissipation efficiency decreases with the increase in the heat exchanger order.The performance of the multi-scale heat exchanger is obviously improved compared with that of the single-scale heat exchanger.Moreover,the heat exchanger subjected to the total tube surface area constraint is also discussed in the paper.The optimization results obtained in this paper can provide a great compromise between the heat transfer and flow performances of the heat exchanger,provide some guidelines for the optimal designs of heat exchangers,and also enrich the connotation of entransy theory.

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

Generalized constructal optimization for the secondary cooling process of slab continuous casting based on entransy theory

Based on constructal theory and entransy theory,a generalized constructal optimization of a solidification heat transfer process of slab continuous casting for a specified total water flow rate in the secondary cooling zone was carried out.A complex function was taken as the optimization objective to perform the casting.The complex function was composed of the functions of the entransy dissipation and surface temperature gradient of the slab.The optimal water distribution at the sections of the secondary cooling zone were obtained.The effects of the total water flow rate in the secondary cooling zone,casting speed,superheat and water distribution on the generalized constructal optimizations of the secondary cooling process were analyzed.The results show that on comparing the optimization results obtained based on the optimal water distributions of the 8 sections in the secondary cooling zone with those based on the initial ones,the complex function and the functions of the entransy dissipation and surface temperature gradient after optimization decreased by 43.25%,5.90%and 80.60%,respectively.The quality and energy storage of the slab had obviously improved in this case.The complex function,composed of the functions of the entransy dissipation and surface temperature gradient of the slab,was a compromise between the internal and surface temperature gradients of the slab.Essentially,it is also the compromise between energy storage and quality of the slab.The"generalized constructal optimization"based on the minimum complex function can provide an optimal alternative scheme from the point of view of improving energy storage and quality for the parameter design and dynamic operation of the solidification heat transfer process of slab continuous casting.

The influence of viscous heating on the entransy in two-fluid heat exchangers

In the present work, water and olive oil are taken as working fluids to study the influence of viscous heating on the entransy dissipation caused by heat transfer in two-fluid heat exchangers. The results show that the influence of viscous heating on the entransy loss associated with heat transfer can not be neglected for the liquids having large dynamic viscosity. The viscous heating effect maintains the heat transfer ability of the working fluids, relatively reduces the entransy loss in heat exchangers; the viscous heating effect relatively augments the entropy generation due to heat transfer and the available energy destruction in heat exchangers. For the working fluid having large dynamic viscosity, the increasing rates of the entransy and entropy generation contributed by the viscous heating are even larger than those contributed by heat transfer, when the mass flow rate of working fluid reaches a certain value under the fixed heat transfer area condition. Thus, the entransy loss rate decreases and the growth rate of entropy generation increases as the mass flow rate of the working fluid increases. Under the same other conditions, the heat transfer entransy loss rate and entropy generation rate per unit heat transfer rate obtained when the fluid having a smaller heat capacity rate is cold fluid are less than those obtained when the fluid having a smaller heat capacity rate is hot fluid.

Progress of entransy analysis on the air-conditioning system in buildings

It is of great importance to improve the energy performance of the air-conditioning system for building energy conversation. Entransy provides a novel perspective to investigate the losses existing in the air-conditioning system. The progress of entransy analysis in the air-conditioning system is comprehensively investigated in the present study. Firstly missions and characteris- tics of the air-conditioning system are analyzed with emphasis on heat or mass transfer process. It is found that reducing the temperature difference, i.e. reducing the entransy dissipation helps to improve the performance. Entransy dissipations and thermal resistances of typical transfer processes in the air-conditioning system are presented. Characteristics of sensible heat transfer process and coupled heat and mass transfer processes are researched in terms of entransy dissipation analysis. Reasons leading to entransy dissipation are also clarified with the help of unmatched coefficient 4. Principles for reducing the entransy dissipation and constructing a high temperature cooling system are summarized on the basis of case studies in typical handling processes. It＇s recommended that reducing mixing process, improving match properties are main approaches to reduce the entransy dissipation. The present analysis is beneficial to casting light on the essence of the air-conditioning system and proposing novel approaches for performance optimization.