Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation ...Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.展开更多
Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat e...Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using opti-mal-control theory,and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches,four maximum-efficiency branches,and two adiabatic branches. The interval of each branch is obtained,as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective,those with linear phe-nomenological heat transfer law for the maximum efficiency objective,and those with radiative heat transfer law for the maximum power output objective.展开更多
The optimal configuration of a heat engine operating between a finite high-temperature source and an infinite low-temperature reservoir is derived by using finite time thermodynamics based on a complex heat transfer l...The optimal configuration of a heat engine operating between a finite high-temperature source and an infinite low-temperature reservoir is derived by using finite time thermodynamics based on a complex heat transfer law,including Newtonian heat transfer law,linear phenomenological heat transfer law,radiative heat transfer law,Dulong-Petit heat transfer law,generalized convective heat transfer law and generalized radiative heat transfer law,q ∝(△T n). In the engine model the only irreversibility of finite rate heat transfer is considered. The optimal relation between the power output and efficiency of the heat engine is also derived by using an equivalent temperature of the hot reservoir. The obtained results include those obtained in recent literature and can provide some theoretical guidance for the designs of practical engines.展开更多
The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law(q∝△(T-1)) is analyzed by taking the processes as heat engines which work between high-and low-tempera...The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law(q∝△(T-1)) is analyzed by taking the processes as heat engines which work between high-and low-temperature reservoirs and produce enthalpy and energy flows out of the system,and the temperatures of the heat reservoirs are assumed to be time-and space-variables.A numerical method is employed to solve convex optimization problem and Lagrangian function is employed to solve the average optimal control problem.The dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient are adopted to indicate the major influence factors on the performance of the separation process,such as the properties of different materials and various separation requirements for the separation process.The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained.The obtained results are compared with those obtained with the Newtonian heat transfer law(q∝△(T)).展开更多
An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law ...An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝△(T -1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton’s heat transfer law [q ∝△(T )]. The results also show that optimizing the piston motion can improve power and efficiency of the engine by more than 9%. This is primarily due to the decrease in heat leakage loss on the initial portion of the power stroke.展开更多
Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid,in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological h...Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid,in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝Δ(T-1)],are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model,respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model,which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs,a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir's temperature on the maximum power of the heat engine are analyzed. The obtained results are,in addition,compared with those obtained with Newtonian heat transfer law [q ∝Δ(T)].展开更多
An irreversible light-driven engine is described in this paper, in which the heat transfer between the working fluid and the environment obeys a linear phenomenological heat transfer law [ q ∝Δ(T -1)], with a workin...An irreversible light-driven engine is described in this paper, in which the heat transfer between the working fluid and the environment obeys a linear phenomenological heat transfer law [ q ∝Δ(T -1)], with a working fluid composed of the bimolecular reacting system 2SO 3 F■S 2 O 6 F2. Piston trajectories maximizing work output and minimizing entropy generation are determined for such an engine with rate-dependent loss mechanisms of friction and heat leakage. The optimal control theory is applied to determine the optimal configurations of the piston motion trajectory and the fluid temperature. Numerical examples for the optimal configuration are provided, and the obtained results are compared with those derived with Newtonian heat transfer law [ q ∝Δ(T )].展开更多
A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convecti...A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝(ΔT) m ] is investigated in this paper.Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations,which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid.Based on the universal optimization results,the analytical solution for the Newtonian heat transfer law (m=1) is also obtained.Since there are no analytical solutions for the other heat transfer laws (m≠1),the continuous HJB equations are discretized and dynamic programming algorithm is performed to obtain the complete numerical solutions of the optimization problem.The relationships among the maximum power output of the system,the process period and the fluid temperature are discussed in detail.The results obtained provide some theoretical guidelines for the optimal design and operation of practical energy conversion systems.展开更多
The results stemming from the calculation of heat transfer in torch furnaces by the laws, relating to radiation from solid surfaces and gas volumes are analyzed. The article presents the laws for radiation from gas vo...The results stemming from the calculation of heat transfer in torch furnaces by the laws, relating to radiation from solid surfaces and gas volumes are analyzed. The article presents the laws for radiation from gas volumes and the procedure for calculating heat transfer in torch furnaces, fire boxes, and combustion chambers, elaborated on their basis. The example of heat transfer calculation in a torch furnace is given, and it is significantly non-uniform in nature. Non-uniformity of heat flux distribution on heating surfaces is given. According to the results of calculations, a new furnace is designed to decrease the non-uniformity of ingot heating, fuel rate, and increase the furnace capacity. The calculation results of the distribution of heat fluxes on the heating surfaces are given in changing torch geometric dimensions. These results are confirmed by experimental studies.展开更多
The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governi...The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.展开更多
The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of simila...The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.展开更多
Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mat...Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.展开更多
基金supported by the Natural Science Foundation of China(Grant No. 51136001)the Tsinghua University Initiative ScientificResearch Program
文摘Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.
基金the Program for New Century Excellent Talents in University of China (Grant No 20041006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No 200136)
文摘Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using opti-mal-control theory,and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches,four maximum-efficiency branches,and two adiabatic branches. The interval of each branch is obtained,as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective,those with linear phe-nomenological heat transfer law for the maximum efficiency objective,and those with radiative heat transfer law for the maximum power output objective.
基金Supported by the Program for New Century Excellent Talents in University of China (Grant No. 20041006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘The optimal configuration of a heat engine operating between a finite high-temperature source and an infinite low-temperature reservoir is derived by using finite time thermodynamics based on a complex heat transfer law,including Newtonian heat transfer law,linear phenomenological heat transfer law,radiative heat transfer law,Dulong-Petit heat transfer law,generalized convective heat transfer law and generalized radiative heat transfer law,q ∝(△T n). In the engine model the only irreversibility of finite rate heat transfer is considered. The optimal relation between the power output and efficiency of the heat engine is also derived by using an equivalent temperature of the hot reservoir. The obtained results include those obtained in recent literature and can provide some theoretical guidance for the designs of practical engines.
基金Supported by the Program for New Century Excellent Talents of China (Grant No. NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law(q∝△(T-1)) is analyzed by taking the processes as heat engines which work between high-and low-temperature reservoirs and produce enthalpy and energy flows out of the system,and the temperatures of the heat reservoirs are assumed to be time-and space-variables.A numerical method is employed to solve convex optimization problem and Lagrangian function is employed to solve the average optimal control problem.The dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient are adopted to indicate the major influence factors on the performance of the separation process,such as the properties of different materials and various separation requirements for the separation process.The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained.The obtained results are compared with those obtained with the Newtonian heat transfer law(q∝△(T)).
基金Supported by the Program for New Century Excellent Talents in University of China (Grant No. 20041006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝△(T -1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton’s heat transfer law [q ∝△(T )]. The results also show that optimizing the piston motion can improve power and efficiency of the engine by more than 9%. This is primarily due to the decrease in heat leakage loss on the initial portion of the power stroke.
基金Supported by the Program for New Century Excellent Talents in University of China (Grant No. 20041006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid,in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝Δ(T-1)],are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model,respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model,which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs,a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir's temperature on the maximum power of the heat engine are analyzed. The obtained results are,in addition,compared with those obtained with Newtonian heat transfer law [q ∝Δ(T)].
基金supported by the Program for New Century Excellent Tal-ents in University of China (Grant No. 20041006)the Foundation for the Authors of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘An irreversible light-driven engine is described in this paper, in which the heat transfer between the working fluid and the environment obeys a linear phenomenological heat transfer law [ q ∝Δ(T -1)], with a working fluid composed of the bimolecular reacting system 2SO 3 F■S 2 O 6 F2. Piston trajectories maximizing work output and minimizing entropy generation are determined for such an engine with rate-dependent loss mechanisms of friction and heat leakage. The optimal control theory is applied to determine the optimal configurations of the piston motion trajectory and the fluid temperature. Numerical examples for the optimal configuration are provided, and the obtained results are compared with those derived with Newtonian heat transfer law [ q ∝Δ(T )].
基金supported by the National Natural Science Foundation of China(10905093)the Program for New Century Excellent Talents in University of China(NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China(200136)
文摘A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝(ΔT) m ] is investigated in this paper.Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations,which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid.Based on the universal optimization results,the analytical solution for the Newtonian heat transfer law (m=1) is also obtained.Since there are no analytical solutions for the other heat transfer laws (m≠1),the continuous HJB equations are discretized and dynamic programming algorithm is performed to obtain the complete numerical solutions of the optimization problem.The relationships among the maximum power output of the system,the process period and the fluid temperature are discussed in detail.The results obtained provide some theoretical guidelines for the optimal design and operation of practical energy conversion systems.
文摘The results stemming from the calculation of heat transfer in torch furnaces by the laws, relating to radiation from solid surfaces and gas volumes are analyzed. The article presents the laws for radiation from gas volumes and the procedure for calculating heat transfer in torch furnaces, fire boxes, and combustion chambers, elaborated on their basis. The example of heat transfer calculation in a torch furnace is given, and it is significantly non-uniform in nature. Non-uniformity of heat flux distribution on heating surfaces is given. According to the results of calculations, a new furnace is designed to decrease the non-uniformity of ingot heating, fuel rate, and increase the furnace capacity. The calculation results of the distribution of heat fluxes on the heating surfaces are given in changing torch geometric dimensions. These results are confirmed by experimental studies.
文摘The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.
基金Project(50476083) supported by the National Natural Science Foundation of China
文摘The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.
文摘Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.
