This research explores the characteristics of boiling in inclined pipes,a domain of great importance in engineering.Employing an experimental visualization technique,the boiling dynamics of deionizedwater are examined...This research explores the characteristics of boiling in inclined pipes,a domain of great importance in engineering.Employing an experimental visualization technique,the boiling dynamics of deionizedwater are examined at varying inclination angles,paying special attention to the emerging flow patterns.The findings demonstrate that the inclination angle significantly impacts flow pattern transitions within the 0°to 90°range.As the heat flux rises,bubbles form in the liquid.The liquid’s inertia extends the bubble-wall contact time,thereby delaying the onset of bulk bubble flow.Beyond a 90°inclination,however,the patterning behavior is more influenced by the fluid velocity.At low speeds,incomplete pipe filling results in a large liquid plug hindering flow,while high speeds lead to full pipe filling.In general,gravity,inertia,buoyancy forces,and capillary forces are themain influential factors in the considered problem.However,an analysis of the heat transfer coefficient and boiling curve for different inclination angles reveals that the observed variations are essentially due to corresponding changes in the flow pattern.Finally,an optimal mass flux and inclination angle,able to minimize total entropy generation and improve heat transfer efficiency,are determined by means of an entropy generation analysis.展开更多
The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage dev...The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.展开更多
The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to anal...The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to analyze the influence of the blade wrap angle on flow characteristics and energy distribution of a centrifugal pump evaluated as a low specific speed with a value of 69.This study investigates six impellermodels that possess varying blade wrap angles(95°,105°,115°,125°,135°,and 145°)that were created while maintaining the same volute and other geometrical characteristics.The investigation of energy loss was conducted to evaluate the values of total and entropy generation rates(TEG,EGR).The fluid-structure interaction was considered numerically using the software tools ANSYS Fluent and ANSYSWorkbench.The elastic structural dynamic equation was used to estimate the structural response,while the shear stress transport k–ωturbulence model was utilized for the fluid domain modeling.The findings suggest that the blade wrap angle has a significant influence on the efficiency of the pump.The impeller featuring a blade wrap angle of 145°exhibits higher efficiency,with a notable increase of 3.76%relative to the original model.Variations in the blade wrap angle impact the energy loss,shaft power,and pump head.The model with a 145°angle exhibited a maximum equivalent stress of 14.8MPa and a total deformation of 0.084 mm.The results provide valuable insights into the intricate flow mechanism of the centrifugal pump,particularly when considering various blade wrap angles.展开更多
With the entropy generation minimization （EGM） method, the thermodynamical performance optimization in a thermoelectric refrigeration system is studied. The optimization is affected by the irreversibility of heat tr...With the entropy generation minimization （EGM） method, the thermodynamical performance optimization in a thermoelectric refrigeration system is studied. The optimization is affected by the irreversibility of heat transfer caused by finite temperature differences, the heat leak between external heat reservoirs and the internal dissipation of working fluids. EGM is taken as an objective function for the optimization. The objective function and design parameters are obtained. Optimal performance curves are presented by thermal and electronic parameters. Effects of these parameters on general and optimal performances are investigated. Results are helpful in determining optimal design conditions in real thermoelectric refrigeration systems.展开更多
Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is cond...Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed.展开更多
In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body emissive power U will lead to two different definitions of radiation entransy flow and the ...In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body 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 prin ciples 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.展开更多
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） ...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.展开更多
Thermal optimization is very important for improving the performances of thermal systems. In engineering, the entropy generation minimization （EGM） has been widely used to optimize and evaluate the performances of t...Thermal optimization is very important for improving the performances of thermal systems. In engineering, the entropy generation minimization （EGM） has been widely used to optimize and evaluate the performances of thermal systems. However, the consistency between the EGM and the optimization objective should be specified when the EGM is used. In this paper, we discuss the view angle of irreversibility of entropy generation, and show that entropy generation directly reflects the exergy destruction or the ability loss of doing work. As the design objective in a thermal system is not often consistent with the view angle of irreversibility of entropy generation, the EGM may not lead to the optimal value of the design objective. In heat transfer and heat-work conversion, the inconsistence between the design objectives and the EGM is shown with some examples, and the applicability of the EGM is found to be conditional. The “entropy generation paradox” in heat exchanger analyses is also discussed, and it is shown that there is no direct monotonic relation between the minimum entropy generation rate and the best heat transfer performance of heat exchangers.展开更多
Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determ...Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determine entropy generation of fully developed flow, two approaches are employed and it is shown that only one of these methods can provide appropriate results for flow inside annuli. The effects of concentration of nanoparticles, Reynolds number and thermal boundaries on heat transfer enhancement and entropy generation of developing laminar flow inside annuli with different radius ratios and same cross sectional areas are studied. The results show that radius ratio is a very important decision parameter of an annular heat exchanger such that in each Re, there is an optimum radius ratio to maximize Nu and minimize entropy generation. Moreover, the effect of nanoparticles concentration on heat transfer enhancement and minimizing entropy generation is stronger at higher Reynolds.展开更多
In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can b...In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can be maximized with the increase of mass transfer rate,based on which the velocity field can be optimized.The oxygen gas–liquid mass transfer is the major rate–limiting step of the toluene emissions biodegradation process in bubble column reactor,so the entropy generation due to oxygen mass transfer is used as the objective function,and the conservation equations of the gas–liquid flow and species concentration are taken as constraints.This optimization problem is solved by the calculus of variations,the optimal liquid flow pattern is obtained and the relationship of the maximum mass transfer enhancement on viscous dissipation is revealed,which can be used to improve the design of internal structure of the bubble column reactor.展开更多
Entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates is investigated analytically on the basis of the Darcy flow model where the viscous dissipatio...Entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates is investigated analytically on the basis of the Darcy flow model where the viscous dissipation effects had also been taken into account. A parametric study showed that decreasing the group parameter and the Peclet number increases the entropy generation while for the Brinkman number the converse is true. Heatline visualization technique is applied with an emphasis on the Br 〈 0 case where there is somewhere that heat transfer changes direction at some streamwise location to the wall instead of its original direction, i.e., from the wall.展开更多
In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformati...In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(n<1),the temperature dominates and the velocity rises.Local entropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.展开更多
The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The ana...The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.展开更多
Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is a...Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio （width to height ratio）. These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Rant [14].展开更多
The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe_(3)O_(4) based Brinkmann type nanofluid flow over a vertical rotating frame.The Tiwari ...The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe_(3)O_(4) based Brinkmann type nanofluid flow over a vertical rotating frame.The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers,including Grashof,Eckert,and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles,Hall current,magnetic field,viscous dissipation,and the chemical reaction on the physical quantities.The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg(RKF-45)method.The variation of dimensionless velocity,temperature,concentration,skin friction,heat,and mass transfer rate,as well as for entropy generation and Bejan number with governing parameters,are presented graphically and are provided in tabular form.The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles.Furthermore,the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.展开更多
Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation d...Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation due to magnetic field,nonlinear thermal radiation,viscous dissipation,thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk.The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow,heat and mass transfer,while the second law of thermodynamics is used to analyze the entropy and irreversibility.The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method.The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks.The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks.Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks.The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion.The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant.It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip.The current results present many applications in the lubrication phenomenon,heating processes,cooling of devices,thermal engineering,energy production,extrusion processes etc.展开更多
The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjec...The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjected to different locations of(CO_(2))contaminants to allow for the variation of the buoyancy strength(N).However,the horizontal walls are assumed adiabatic.The simulations are conducted using the finite volume method to solve the conservation equations of continuity,momentum,energy,and species transport.Good agreement with other numerical results in the literature is obtained.The effect of multiple parameters,namely,buoyancy ratio(N),thermal Rayleigh number(Ra),and inclination angle(α)on entropy generation rate is analyzed and discussed in the postprocessing stage,while considering both laminar and turbulent flow regimes.The computations reveal that these parameters considerably affect both the heat and mass transfer performances of the system.展开更多
In the present paper, effects of entropy generation and nonlinear thermal radiation on Jeffery nanofluid over permeable stretching sheet with partial slip effect were analyzed. The suitable similarity transformation i...In the present paper, effects of entropy generation and nonlinear thermal radiation on Jeffery nanofluid over permeable stretching sheet with partial slip effect were analyzed. The suitable similarity transformation is utilized for the reduction of a set of governing equations,which are solved by using Differential Transformation Method(DTM) with the help of symbolic software MATHEMATICA. The accuracy of impact of slip parameter on coefficient of skin friction by using DTM and numerical method(Shooting technique with fourth-order RungeKutta) is illustrated and good agreement is found. Further, velocity, temperature, nanoparticle volume fraction and entropy generation profiles are shown graphically and studied in detail for various physical parameters. We notice that, as slip parameter rises the velocity and entropy generation profile rises. Enhancement in the effect of nonlinear thermal radiation reduces the entropy generation.展开更多
Based on the entropy generation concept of thermodynamics, this paper estabfished a general theoretical model for the analysis of entropy generation to optimize fins, in which the minimum entropy generation was select...Based on the entropy generation concept of thermodynamics, this paper estabfished a general theoretical model for the analysis of entropy generation to optimize fins, in which the minimum entropy generation was selected as the object to be studied. The irreversibility due to heat transfer and friction was taken into account so that the minimum entropy generation number has been analyzed with respect to second law of thermodynamics in the forced cross-flow. The optimum dimensions of cylinder pins were discussed. It＇s found that the minimum entropy generation number depends on parameters related to the fluid and fin physical parameters. Varlatioms of the minimum entropy generation number with different parameters were analyzed.展开更多
The flow over a backward facing step （BFS） has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Rich...The flow over a backward facing step （BFS） has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many prac- tical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy gen- eration number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.展开更多
基金supported by the National Natural Science Foundation of China(Project No.52166004)the National Key Research and Development Program of China(Project No.2022YFC3902000)the Major Science and Technology Special Project of Yunnan Province(Project Nos.202202AG050007,202202AG050002).
文摘This research explores the characteristics of boiling in inclined pipes,a domain of great importance in engineering.Employing an experimental visualization technique,the boiling dynamics of deionizedwater are examined at varying inclination angles,paying special attention to the emerging flow patterns.The findings demonstrate that the inclination angle significantly impacts flow pattern transitions within the 0°to 90°range.As the heat flux rises,bubbles form in the liquid.The liquid’s inertia extends the bubble-wall contact time,thereby delaying the onset of bulk bubble flow.Beyond a 90°inclination,however,the patterning behavior is more influenced by the fluid velocity.At low speeds,incomplete pipe filling results in a large liquid plug hindering flow,while high speeds lead to full pipe filling.In general,gravity,inertia,buoyancy forces,and capillary forces are themain influential factors in the considered problem.However,an analysis of the heat transfer coefficient and boiling curve for different inclination angles reveals that the observed variations are essentially due to corresponding changes in the flow pattern.Finally,an optimal mass flux and inclination angle,able to minimize total entropy generation and improve heat transfer efficiency,are determined by means of an entropy generation analysis.
文摘The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.
文摘The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to analyze the influence of the blade wrap angle on flow characteristics and energy distribution of a centrifugal pump evaluated as a low specific speed with a value of 69.This study investigates six impellermodels that possess varying blade wrap angles(95°,105°,115°,125°,135°,and 145°)that were created while maintaining the same volute and other geometrical characteristics.The investigation of energy loss was conducted to evaluate the values of total and entropy generation rates(TEG,EGR).The fluid-structure interaction was considered numerically using the software tools ANSYS Fluent and ANSYSWorkbench.The elastic structural dynamic equation was used to estimate the structural response,while the shear stress transport k–ωturbulence model was utilized for the fluid domain modeling.The findings suggest that the blade wrap angle has a significant influence on the efficiency of the pump.The impeller featuring a blade wrap angle of 145°exhibits higher efficiency,with a notable increase of 3.76%relative to the original model.Variations in the blade wrap angle impact the energy loss,shaft power,and pump head.The model with a 145°angle exhibited a maximum equivalent stress of 14.8MPa and a total deformation of 0.084 mm.The results provide valuable insights into the intricate flow mechanism of the centrifugal pump,particularly when considering various blade wrap angles.
文摘With the entropy generation minimization （EGM） method, the thermodynamical performance optimization in a thermoelectric refrigeration system is studied. The optimization is affected by the irreversibility of heat transfer caused by finite temperature differences, the heat leak between external heat reservoirs and the internal dissipation of working fluids. EGM is taken as an objective function for the optimization. The objective function and design parameters are obtained. Optimal performance curves are presented by thermal and electronic parameters. Effects of these parameters on general and optimal performances are investigated. Results are helpful in determining optimal design conditions in real thermoelectric refrigeration systems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51106082)the Tsinghua University Initiative Scientific Research Program, China
文摘Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed.
基金supported by the Tsinghua University Initiative Scientific Research Programthe National Natural Science Foundation of China(GrantNo.51136001)
文摘In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body 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 prin ciples 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.
基金Project supported by the Youth Programs of Chongqing Three Gorges University,China(Grant No.13QN18)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.51376101)the National Natural Science Fund for Creative Research Groups,China(Grant No.51621062)
文摘Thermal optimization is very important for improving the performances of thermal systems. In engineering, the entropy generation minimization （EGM） has been widely used to optimize and evaluate the performances of thermal systems. However, the consistency between the EGM and the optimization objective should be specified when the EGM is used. In this paper, we discuss the view angle of irreversibility of entropy generation, and show that entropy generation directly reflects the exergy destruction or the ability loss of doing work. As the design objective in a thermal system is not often consistent with the view angle of irreversibility of entropy generation, the EGM may not lead to the optimal value of the design objective. In heat transfer and heat-work conversion, the inconsistence between the design objectives and the EGM is shown with some examples, and the applicability of the EGM is found to be conditional. The “entropy generation paradox” in heat exchanger analyses is also discussed, and it is shown that there is no direct monotonic relation between the minimum entropy generation rate and the best heat transfer performance of heat exchangers.
文摘Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determine entropy generation of fully developed flow, two approaches are employed and it is shown that only one of these methods can provide appropriate results for flow inside annuli. The effects of concentration of nanoparticles, Reynolds number and thermal boundaries on heat transfer enhancement and entropy generation of developing laminar flow inside annuli with different radius ratios and same cross sectional areas are studied. The results show that radius ratio is a very important decision parameter of an annular heat exchanger such that in each Re, there is an optimum radius ratio to maximize Nu and minimize entropy generation. Moreover, the effect of nanoparticles concentration on heat transfer enhancement and minimizing entropy generation is stronger at higher Reynolds.
基金supported by the National Natural Science Foundation of China(91834303 and 22108261)the Open Foundation of State Key Laboratory of Chemical Engineering(SKL-ChE-19B02)+1 种基金Fundamental Research Program of Shanxi Province(20210302124618)Scientific Technological Innovation Programs of Higher Education Institution in Shanxi(2020L0284).
文摘In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can be maximized with the increase of mass transfer rate,based on which the velocity field can be optimized.The oxygen gas–liquid mass transfer is the major rate–limiting step of the toluene emissions biodegradation process in bubble column reactor,so the entropy generation due to oxygen mass transfer is used as the objective function,and the conservation equations of the gas–liquid flow and species concentration are taken as constraints.This optimization problem is solved by the calculus of variations,the optimal liquid flow pattern is obtained and the relationship of the maximum mass transfer enhancement on viscous dissipation is revealed,which can be used to improve the design of internal structure of the bubble column reactor.
文摘Entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates is investigated analytically on the basis of the Darcy flow model where the viscous dissipation effects had also been taken into account. A parametric study showed that decreasing the group parameter and the Peclet number increases the entropy generation while for the Brinkman number the converse is true. Heatline visualization technique is applied with an emphasis on the Br 〈 0 case where there is somewhere that heat transfer changes direction at some streamwise location to the wall instead of its original direction, i.e., from the wall.
文摘In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(n<1),the temperature dominates and the velocity rises.Local entropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.
基金partly supported by a grant from the Center of Excellence on Modeling and Control Systems (CEMCS) of Ferdowsi University of Mashhad,Iran
文摘The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.
文摘Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio （width to height ratio）. These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Rant [14].
文摘The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe_(3)O_(4) based Brinkmann type nanofluid flow over a vertical rotating frame.The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers,including Grashof,Eckert,and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles,Hall current,magnetic field,viscous dissipation,and the chemical reaction on the physical quantities.The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg(RKF-45)method.The variation of dimensionless velocity,temperature,concentration,skin friction,heat,and mass transfer rate,as well as for entropy generation and Bejan number with governing parameters,are presented graphically and are provided in tabular form.The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles.Furthermore,the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.
基金funding this work through the Research Groups Program under grant number R.G.P-1/75/42。
文摘Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation due to magnetic field,nonlinear thermal radiation,viscous dissipation,thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk.The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow,heat and mass transfer,while the second law of thermodynamics is used to analyze the entropy and irreversibility.The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method.The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks.The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks.Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks.The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion.The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant.It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip.The current results present many applications in the lubrication phenomenon,heating processes,cooling of devices,thermal engineering,energy production,extrusion processes etc.
文摘The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjected to different locations of(CO_(2))contaminants to allow for the variation of the buoyancy strength(N).However,the horizontal walls are assumed adiabatic.The simulations are conducted using the finite volume method to solve the conservation equations of continuity,momentum,energy,and species transport.Good agreement with other numerical results in the literature is obtained.The effect of multiple parameters,namely,buoyancy ratio(N),thermal Rayleigh number(Ra),and inclination angle(α)on entropy generation rate is analyzed and discussed in the postprocessing stage,while considering both laminar and turbulent flow regimes.The computations reveal that these parameters considerably affect both the heat and mass transfer performances of the system.
文摘In the present paper, effects of entropy generation and nonlinear thermal radiation on Jeffery nanofluid over permeable stretching sheet with partial slip effect were analyzed. The suitable similarity transformation is utilized for the reduction of a set of governing equations,which are solved by using Differential Transformation Method(DTM) with the help of symbolic software MATHEMATICA. The accuracy of impact of slip parameter on coefficient of skin friction by using DTM and numerical method(Shooting technique with fourth-order RungeKutta) is illustrated and good agreement is found. Further, velocity, temperature, nanoparticle volume fraction and entropy generation profiles are shown graphically and studied in detail for various physical parameters. We notice that, as slip parameter rises the velocity and entropy generation profile rises. Enhancement in the effect of nonlinear thermal radiation reduces the entropy generation.
文摘Based on the entropy generation concept of thermodynamics, this paper estabfished a general theoretical model for the analysis of entropy generation to optimize fins, in which the minimum entropy generation was selected as the object to be studied. The irreversibility due to heat transfer and friction was taken into account so that the minimum entropy generation number has been analyzed with respect to second law of thermodynamics in the forced cross-flow. The optimum dimensions of cylinder pins were discussed. It＇s found that the minimum entropy generation number depends on parameters related to the fluid and fin physical parameters. Varlatioms of the minimum entropy generation number with different parameters were analyzed.
基金Project supported by the National Natural Science Foundation of China (Nos. 51176061 and51006043)the Research Foundation for Out standing Young Teachers of Huazhong University of Science and Technology (No. 2012QN168)the Research Fund for the Doctoral Program of Higher Education of China (No. 20100142120048)
文摘The flow over a backward facing step （BFS） has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many prac- tical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy gen- eration number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.
