Minimum Entropy Generation Principle Research Articles

Optimization of volume to point conduction problem based on a novel thermal conductivity discretization algorithm

A conduction heat transfer process is enhanced by filling prescribed quantity and optimized-shaped high thermal conductivity materials to the substrate. Numerical simulations and analyses are performed on a volume to point conduction problem based on the principle of minimum entropy generation. In the optimization, the arrangement of high thermal conductivity materials is variable, the quantity of high thermal-conductivity material is constrained, and the objective is to obtain the maximum heat conduction rate as the entropy is the minimum. A novel algorithm of thermal conductivity discretization is proposed based on large quantity of calculations. Compared with other algorithms in literature, the average temperature in the substrate by the new algorithm is lower, while the highest temperature in the substrate is in a reasonable range. Thus the new algorithm is feasible. The optimization of volume to point heat conduction is carried out in a rectangular model with radiation boundary condition and constant surface temperature boundary condition. The results demonstrate that the algorithm of thermal conductivity discretization is applicable for volume to point heat conduction problems.

Entropy generation analysis of laminar forced convection through uniformly heated helical coils considering effects of high length and heat flux and temperature dependence of thermophysical properties

In this study, combined effects of length and heat flux of the coil as well as the effects of temperature dependence of thermophysical properties on entropy generation rates and optimal operation of uniformly heated helical coils with laminar forced convection have been analyzed analytically. For these purposes, comprehensive analytical formulas, which could be used for any duct shape and flow regime, are derived for thermal, frictional, and total entropy generation rates, and the effects of involved parameters on the entropy generation rates are examined for laminar forced flow of water through uniformly heated helical coils. Then, using the minimal entropy generation principle, the inlet Reynolds number is optimized for various values of the involved parameters, and some correlations are proposed for optimal values of this parameter which extend and modify the existing correlations of water. It is found that the entropy generation rates are highly dependent on the combined effects of length and heat flux of the coil, introduced by the parameter ηC, and temperature dependence of thermophysical properties, such that all of them noticeably augment with increase in ηC and the inlet temperature.

Entropy generation minimization in transient heat conduction processes PART II – Transient heat conduction in solids

Abstract Formulation and solution of the initial boundary-value problem of heat conduction in solids have been presented when an entropy generation minimization principle is imposed as the arbitrary constraint. Using an entropy balance equation and the Euler-Lagrange variational approach a new form of the heat conduction equation (non-linear partial difference equation) is derived.

Entropy generation minimization in steady-state and transient diffusional heat conduction processes Part I – Steady-state boundary value problem

Abstract An application of the Entropy Generation Minimization principle allows new formulation of the boundary and initial boundaryvalue problems. Applying Euler-Lagrange variational formalism new mathematical form of heat conduction equation describing steady-state processes have been derived. Mathematical method presented in the paper can also be used for any diffusion heat and mass transfer process. Linear and non-linear problems with internal heat sources have been analyzed.

Entransy and entropy analyses of heat pump systems

In this paper, heat pump systems are analyzed with entransy increase and entropy generation. The extremum entransy increase principle is developed. When the equivalent temperatures of the high and low temperature heat sources are fixed, the theoretical analyses and numerical results both show that the maximum COP leads to the maximum entransy increase rate for fixed input power, while it leads to the minimum entransy increase rate for fixed heat flow absorbed from the low temperature heat source. The minimum entropy generation principle shows that the minimum entropy generation rate always leads to the maximum COP for fixed input power or fixed heat flow absorbed from the low temperature heat source when the equivalent thermodynamic forces of the high and low temperature heat sources are given. Further discussions show that only the entransy increase rate always increases with increasing heat flow rate into the high temperature heat source for the discussed cases.

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the blackbody emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization principles are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles (EEDPs) developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle (EEGP) for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.

Heat-work conversion optimization of one-stream heat exchanger networks

Heat exchanger networks (HENs) are widely used in industry. This paper extends the entransy theory to heat-work conversion optimization in one-stream HENs. The expression for entransy loss is set up for the open system with work output. The entransy loss, as well as entropy generation, is used to analyze the one-stream HENs with the Carnot engines. The fluid friction is ignored in the analyses. For the cases discussed in this paper, the dimensional and non-dimensional parameters analyses show that the applicability of the minimum entropy generation principle is conditional. The minimum entropy generation does not always correspond to the maximum output power, while the minimum entropy generation number and the minimum revised entropy generation number do not always correspond to the maximum heat-work conversion efficiency. On the other hand, greater power output always corresponds to larger entransy loss and larger entransy loss coefficient always corresponds to larger heat-work conversion efficiency for all the cases discussed in this paper.

Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process

Based on theories of thermodynamics, the energy equation in terms of entransy in heat transfer process is introduced, which not only describes the change of entransy, but also defines the entransy consumption rate. According to the regularity of entransy change in heat transfer process and the effect of entransy consumption rate on the irreversibility of heat transfer process, it can be found that entransy is a state variable, from which a new expression for the second law of thermodynamics is presented. Then by setting entransy consumption rate and power consumption rate as optimization objective and constraint condition for each other, the Lagrange conditional extremum principle is used to deduce momentum equation, constraint equation and boundary condition for optimizing flow field of convective heat transfer, which are applied to simulate convective heat transfer coupling with energy equation in an enclosed cavity. Through the numerical simulation, the optimized flow field under different constraint conditions is obtained, which shows that the principle of minimum entransy consumption is more suitable than the principle of minimum entropy generation for optimizing convective heat transfer process.

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.

Analysis of entransy dissipation in heat exchangers

The optimization of heat exchangers is an important topic. Entropy generation is used to describe the irreversibility of heat transfer processes and the principle of minimum entropy generation is sometimes used to optimize heat exchanger designs. This paper defines the heat exchanger thermal resistance based on its entransy dissipation and analyses various heat exchangers. Entropy generation analyses are also presented for comparison. The results indicate that the minimum entransy-dissipation-based thermal resistance always corresponds to the highest heat transfer rate, while the design with the minimum entropy generation is not always related to the design with the highest heat transfer rate.

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.

Optimization principles for convective heat transfer

Optimization for convective heat transfer plays a significant role in energy saving and high-efficiency utilizing. We compared two optimization principles for convective heat transfer, the minimum entropy generation principle and the entransy dissipation extremum principle, and analyzed their physical implications and applicability. We derived the optimization equation for each optimization principle. The theoretical analysis indicates that both principles can be used to optimize convective heat-transfer process, subject to different objectives of optimization. The minimum entropy generation principle, originally derived from the heat engine cycle process, optimizes the convective heat-transfer process with minimum usable energy dissipation focusing on the heat–work conversion. The entransy dissipation extremum principle however, originally for pure heat conduction process, optimizes the heattransfer process with minimum heat-transfer ability dissipation, and therefore is more suitable for optimization of the processes not involving heat–work conversion. To validate the theoretical results, we simulated the convective heat-transfer process in a two-dimensional foursquare cavity with a uniform heat source and different temperature boundaries. Under the same constraints, the results indicate that the minimum entropy production principle leads to the highest heat–work conversion while the entransy dissipation extremum principle yields the maximum convective heat-transfer efficiency. Published by Elsevier Ltd.

Optimal Porosity in an Air Heater Conduit Filled with a Porous Matrix

In the present study, flow and forced convective heat transfer in an air heater conduit filled with a porous matrix with a uniform constant solar heat flux has been investigated analytically, based on minimal entropy generation principle. While trying to decrease entropy generation due to heat transfer, pressure loss entropy generation increases, which indicates that an optimal porosity value exists. The influence of Reynolds number, fluid properties, constant uniform heat flux, flow, and geometry of the system on the optimum matrix porosity has been investigated. It was revealed that optimum matrix porosity values increase as Reynolds number increases. In the range of the present study, a correlation predicting optimal matrix porosity was proposed using least squares analysis.

A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios

The present paper analyzes the entropy generation induced by turbulent forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For a baseline case with Re = 20,000, external heat flux q⁎ = 0.112 and aspect ratio γ = 1, the results show the entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly occurs near the outer wall of the duct where the external heat flux imposed. Except the baseline case, two additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy generation is minimal in the γ = 1 case. Accordingly, the case with γ = 1 is concluded to be the optimal aspect ratio under the current flow condition based on the minimal entropy generation principle.

Optimal Reynolds number of laminar forced convection in a helical tube subjected to uniform wall temperature

In this study, fully developed laminar flow and heat transfer in a helically coiled tube with uniform wall temperature have been investigated analytically based on minimal entropy generation principle. The influence of coil curvature ratio and fluid properties, β 1 and β 2 on the optimum Reynolds number have been investigated for two well-known fluids viz. air and water. It was revealed that optimum Reynolds numbers decrease as curvature ratio increases except in the low ranges of curvature ratio where transition to turbulent flow occurs. In the range of the present study, a correlation predicting optimal Reynolds number was proposed for each fluid using least square analysis.

Effects of corrugation angle on developing laminar forced convection and entropy generation in a wavy channel

This paper investigates the effects of corrugation angle (β) on the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The studied cases cover β = 10-, 15-, 20-, 25-, 30- and 35°, whilst Reynolds number (Re) is varied as 100, 200 and 400. The analyzed flow characteristics include recirculating flows, secondary vortices, temperature distributions, and friction factor as well as Nusselt number. In particular, the effects of corrugation angle on the distributions and magnitudes of local entropy generation resulted from frictional irreversibility (S ′′′ ) and heat transfer irreversibility (S ′′′ ) are separately discussed in detail in the present paper. Based on the minimal entropy generation principle, the optimal corrugation angle and favorable Re are reported.

A numerical study on developing laminar forced convection and entropy generation in half- and double-sine ducts

In the present paper, the developing laminar forced convection and entropy generation in both double- and half-sine ducts are investigated with numerical methods. The studied cases cover Re ranging from 86 to 2000. The duct aspect ratio ( Λ / a ) and the external heat flux ( q ∗ ) are varied as Λ / a = 2 , 4 and 8, and the values of q ∗ are varied as 0.0405, 0.0811 and 0.1622, respectively. The comparisons of the flow features, including the distributions of axial velocity, temperature, Nusselt number and the local entropy generation, in the double- and half-sine ducts are provided in detail in the paper. Particularly, the optimal analysis of the two-type ducts based on the minimal entropy generation principle is the major concern. Through the evaluations of the overall entropy generation in the whole flow domain, the optimal option between the double- and half-sine duct is found to be dependent on the duct aspect-ratio, external heat flux and Re. Among all the cases studied, the half-sine duct with Λ / a = 2 is found to have the minimal entropy generation, and therefore is concluded as the optimal option for achieving the least irreversibility and best exergy utilization in the thermal system.

06/02443 Analysis of optimal Reynolds number for developing laminar forced convection in double sine ducts based on entropy generation minimization principle: Ko, T. H. Energy Conversion and Management, 2006, 47, (6), 655–670.

06/02443 Analysis of optimal Reynolds number for developing laminar forced convection in double sine ducts based on entropy generation minimization principle: Ko, T. H. Energy Conversion and Management, 2006, 47, (6), 655–670.

06/01351 Augmentation of heat transfer coefficient by using 90† broken transverse ribs on absorber plate of solar air heater: Sahu, M. M. and Bhagoria, J. L. Renewable Energy, 2005, 30, (13), 2057–2073

Three-dimensional laminar forced convective flow and entropy generation in a 180-deg curved rectangular duct with longitudinal ribs equipped on the heated wall are investigated by numerical methods. The development of secondary vortices, temperature and local entropy generation distributions as well as the overall entropy generation in whole flow fields, including the entrance and fully developed region, are analyzed. The effects of rib size are particularly highlighted in the present paper. Calculations of cases with various rib sizes under different Dean numbers and external heat fluxes are carried out to examine the influence of rib on the flow field and entropy generation. The entropy generated from frictional irreversibility and heat transfer irreversibility is investigated separately in detail. The results reveal that the addition of rib can effectively reduce the entropy generation from heat transfer irreversibility since the secondary vortices are augmented by the rib, through which the heat transfer performance is enhanced, in turn making the temperature gradient become smoother. Nevertheless, the entropy generation due to frictional irreversibility is raised at the same time because larger fluid friction is resulted from the wider solid walls and the complex flows disturbed by ribs. Due to the opposite influences of rib on the entropy generations from irreversibilities, the analysis of the optimal trade-off is carried out based on the minimal entropy generation principle. The optimal rib size which induces the minimal entropy generation in the flow fields is found to be dependent on the external heat flux and Dean number. Even under some flow conditions, the resultant entropy generation could not be reduced but becomes worse when ribs are added. These results provide worthwhile information for considerations of adding ribs on a curved duct and the determinations of rib sizes from view point of thermodynamic second law.

A numerical study on entropy generation and optimization for laminar forced convection in a rectangular curved duct with longitudinal ribs

The effects of longitudinal ribs on laminar forced convection and entropy generation in a curved rectangular duct are investigated in the present paper by numerical methods. The major concern is to explore the optimal rib number and arrangement of the mounted rib based on the minimal entropy generation principle. The detailed information of local distributions of entropy generation due to frictional and heat transfer irreversibility as well as the overall entropy generation in the whole flow field are analyzed separately. The results show that the flow features in the curved duct, including the secondary flow motion, and the distributions of velocity and temperature, are considerably influenced by the number and arrangement of mounted ribs. Through the comparison of the cases with none to four ribs mounted on duct walls with various arrangements, it is found that a single rib on the heated duct wall is the most effective way to reduce entropy generation, whereas additional ribs can not give further reduction in entropy generation. The rib arrangement is suggested to be used in practical applications so that the irreversibility due to the laminar forced convection in the curved duct would be minimal and the best exergy utilization could be achieved.