通过Jeffreys无信息先验分布描述了Gamma退化过程中参数的相关性,由贝叶斯模型得到各参数满条件分布,使用马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法得到参数后验期望估计,最后给出可靠度评价模型。工程实例表明,所得可靠...通过Jeffreys无信息先验分布描述了Gamma退化过程中参数的相关性,由贝叶斯模型得到各参数满条件分布,使用马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法得到参数后验期望估计,最后给出可靠度评价模型。工程实例表明,所得可靠性评估较独立情形更为保守,能够更早地给出产品修理建议。同时,仿真表明,可靠度要求越高,相关与独立情形寿命估计结果偏差越大,0.9999可靠度下偏差率最大可达9.26%。展开更多
The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic com...The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.展开更多
The thermal nanofluids have garnered widespread attention for their use in multiple thermal systems,including heating processes,sustainable energy,and nuclear reactions.Research on nanofluids has revealed that the the...The thermal nanofluids have garnered widespread attention for their use in multiple thermal systems,including heating processes,sustainable energy,and nuclear reactions.Research on nanofluids has revealed that the thermal efficiencies of such materials are adversely affected by various thermal features.The purpose of the current work is to demonstrate the thermal analysis of Jeffrey nanofluids with the suspension of microorganisms in the presence of variable thermal sources.The variable effects of thermal conductivity,Brownian diffusivity,and motile density are utilized.The investigated model also reveals the contributions of radiation phenomena and chemical reactions.A porous,saturated,moving surface with a suction phenomenon promotes flow.The modeling of the problem is based on the implementation of the Cattaneo-Christov approach.The convective thermal constraints are used to promote the heat transfer features.A simplified form of the governing model is treated with the assistance of a shooting technique.The physical effects of different parameters for the problem are presented.The current problem justifies its applications in heat transfer,coating processes,heat exchangers,cooling systems in microelectronics,solar systems,chemical processes,etc.展开更多
In this study,an analytical investigation is carried out to assess the impact of magnetic field-dependent(MFD)viscosity on the momentum and heat transfers inside the boundary layer of a Jeffrey fluid flowing over a ho...In this study,an analytical investigation is carried out to assess the impact of magnetic field-dependent(MFD)viscosity on the momentum and heat transfers inside the boundary layer of a Jeffrey fluid flowing over a horizontally elongating sheet,while taking into account the effects of ohmic dissipation.By applying similarity transformations,the original nonlinear governing equations with partial derivatives are transformed into ordinary differential equations.Analytical expressions for the momentum and energy equations are derived,incorporating the influence of MFD viscosity on the Jeffrey fluid.Then the impact of different parameters is assessed,including magnetic viscosity,magnetic interaction,retardation time,Deborah number,and Eckert number,on the velocity and temperature profiles in the boundary layer.The findings reveal that an increase in magnetic viscosity leads to a decrease in the local Nusselt number,thereby impairing heat transfer.Moreover,a higher retardation time enhances the local Nusselt number by thinning the momentum and thermal boundary layers,while a higher Deborah number decreases the local Nusselt number due to the reduction in fluid viscosity.展开更多
In this paper,the authors examine various slip effects on themagnetic field and thermal radiative impacts on the flow,mass and heat transfer of a Jeffrey nanofluid over a 2-dimensional inclined stretching sheet by a p...In this paper,the authors examine various slip effects on themagnetic field and thermal radiative impacts on the flow,mass and heat transfer of a Jeffrey nanofluid over a 2-dimensional inclined stretching sheet by a porous media.The offered work is modelled to be in the form of a combination of coupled highly nonlinear partial differential equations in dimensional contexts.Governing equations were obtained,dimensionless parameters were defined in terms of similarity parameters,and the solutionswere obtained by the Homotopy Analysis Method(HAM).The analysis is significant as the effects of viscosity are identified and the important parameters are to be determined that could eventually control a type of flowbehaviour,especially in promoting the flowand inhibiting flowof velocity,temperature,and concentrations.The findings show that such an increase in themagnetic parameter decreases the velocity profile by approximately 15%due to more Lorentz forces,and thermal radiation increases the temperature profile by up to 25%,therefore,enhancing the rate of heat transfer.The process of Brownian motion and thermophoresis increases the depth of the thermal boundary layer by 10–20 percent and reduces in concentration profiles by 12 percent when the Brownian motion parameter increases.A velocity slip parameter lowers the velocity field by about 18 percent,and a parameter of permeability lowers the momentum of flow by another 10 percent.The HAM solutions show very high accuracy levels,having an order of convergence at level 15 and errormargins are well below 0.01 percent compared to the earlier studies.All these findings can provide profound knowledge in improving heat transmission in non-Newtonian fluid systems and can be used in biomedical engineering,thermal insulation,and industrial processes such as polymer extrusion and cooling technology.Principles of heat and mass transfer give us the crucial foundation on which to study the behavior of heat andmaterial flows in other engineering and scientific disciplines.Such principles apply to various fields of study,including the following engineering fields:mechanical,chemical,aerospace,civil,and environmental.展开更多
文摘通过Jeffreys无信息先验分布描述了Gamma退化过程中参数的相关性,由贝叶斯模型得到各参数满条件分布,使用马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法得到参数后验期望估计,最后给出可靠度评价模型。工程实例表明,所得可靠性评估较独立情形更为保守,能够更早地给出产品修理建议。同时,仿真表明,可靠度要求越高,相关与独立情形寿命估计结果偏差越大,0.9999可靠度下偏差率最大可达9.26%。
基金supported by the National Natural Science Foundation of China(Grant No. 10972117)
文摘The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.
基金appreciation to King Saud University for funding this work through researchers supporting project(No.RSPD2025R1056).
文摘The thermal nanofluids have garnered widespread attention for their use in multiple thermal systems,including heating processes,sustainable energy,and nuclear reactions.Research on nanofluids has revealed that the thermal efficiencies of such materials are adversely affected by various thermal features.The purpose of the current work is to demonstrate the thermal analysis of Jeffrey nanofluids with the suspension of microorganisms in the presence of variable thermal sources.The variable effects of thermal conductivity,Brownian diffusivity,and motile density are utilized.The investigated model also reveals the contributions of radiation phenomena and chemical reactions.A porous,saturated,moving surface with a suction phenomenon promotes flow.The modeling of the problem is based on the implementation of the Cattaneo-Christov approach.The convective thermal constraints are used to promote the heat transfer features.A simplified form of the governing model is treated with the assistance of a shooting technique.The physical effects of different parameters for the problem are presented.The current problem justifies its applications in heat transfer,coating processes,heat exchangers,cooling systems in microelectronics,solar systems,chemical processes,etc.
基金supported by the United Arab Emirates University,Al Ain,United Arab Emirates,under Grant No.12R283.
文摘In this study,an analytical investigation is carried out to assess the impact of magnetic field-dependent(MFD)viscosity on the momentum and heat transfers inside the boundary layer of a Jeffrey fluid flowing over a horizontally elongating sheet,while taking into account the effects of ohmic dissipation.By applying similarity transformations,the original nonlinear governing equations with partial derivatives are transformed into ordinary differential equations.Analytical expressions for the momentum and energy equations are derived,incorporating the influence of MFD viscosity on the Jeffrey fluid.Then the impact of different parameters is assessed,including magnetic viscosity,magnetic interaction,retardation time,Deborah number,and Eckert number,on the velocity and temperature profiles in the boundary layer.The findings reveal that an increase in magnetic viscosity leads to a decrease in the local Nusselt number,thereby impairing heat transfer.Moreover,a higher retardation time enhances the local Nusselt number by thinning the momentum and thermal boundary layers,while a higher Deborah number decreases the local Nusselt number due to the reduction in fluid viscosity.
文摘In this paper,the authors examine various slip effects on themagnetic field and thermal radiative impacts on the flow,mass and heat transfer of a Jeffrey nanofluid over a 2-dimensional inclined stretching sheet by a porous media.The offered work is modelled to be in the form of a combination of coupled highly nonlinear partial differential equations in dimensional contexts.Governing equations were obtained,dimensionless parameters were defined in terms of similarity parameters,and the solutionswere obtained by the Homotopy Analysis Method(HAM).The analysis is significant as the effects of viscosity are identified and the important parameters are to be determined that could eventually control a type of flowbehaviour,especially in promoting the flowand inhibiting flowof velocity,temperature,and concentrations.The findings show that such an increase in themagnetic parameter decreases the velocity profile by approximately 15%due to more Lorentz forces,and thermal radiation increases the temperature profile by up to 25%,therefore,enhancing the rate of heat transfer.The process of Brownian motion and thermophoresis increases the depth of the thermal boundary layer by 10–20 percent and reduces in concentration profiles by 12 percent when the Brownian motion parameter increases.A velocity slip parameter lowers the velocity field by about 18 percent,and a parameter of permeability lowers the momentum of flow by another 10 percent.The HAM solutions show very high accuracy levels,having an order of convergence at level 15 and errormargins are well below 0.01 percent compared to the earlier studies.All these findings can provide profound knowledge in improving heat transmission in non-Newtonian fluid systems and can be used in biomedical engineering,thermal insulation,and industrial processes such as polymer extrusion and cooling technology.Principles of heat and mass transfer give us the crucial foundation on which to study the behavior of heat andmaterial flows in other engineering and scientific disciplines.Such principles apply to various fields of study,including the following engineering fields:mechanical,chemical,aerospace,civil,and environmental.
