A formulation of the fin efficiency based on New- ton＇s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the sur- rounding fluid to the heat conducted through...A formulation of the fin efficiency based on New- ton＇s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the sur- rounding fluid to the heat conducted through the base. The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known, whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known. This paper shows the first for- mulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the non- linear fin equations have been determined. The second for- mulation of the fin efficiency is exact when the first integrals can be determined.展开更多
The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance ...The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.展开更多
In this paper,differential transform method(DTM)is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient.Using DTM...In this paper,differential transform method(DTM)is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient.Using DTM,the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally,the coefficients of power series are obtained based on the solution of this set of equations.DTM overcame on nonlinearity without using restrictive assumptions or linearization.Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters.DTM results are compared with special case of the problem that has an exact closed-form solution,and an excellent accuracy is observed.展开更多
文摘A formulation of the fin efficiency based on New- ton＇s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the sur- rounding fluid to the heat conducted through the base. The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known, whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known. This paper shows the first for- mulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the non- linear fin equations have been determined. The second for- mulation of the fin efficiency is exact when the first integrals can be determined.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51106082)the Tsinghua University Initiative Scientific Research Program
文摘The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.
文摘In this paper,differential transform method(DTM)is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient.Using DTM,the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally,the coefficients of power series are obtained based on the solution of this set of equations.DTM overcame on nonlinearity without using restrictive assumptions or linearization.Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters.DTM results are compared with special case of the problem that has an exact closed-form solution,and an excellent accuracy is observed.
