The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of...The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium is examined.Moreover,the thermal radiation and viscous dissipation effects are considered.The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method.The computed results can reveal many vital findings of practical importance.Firstly,dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows,the solution is unique.The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium.But different shapes of nanoparticles are not disturbing the dual solution existence range,though it has a considerable impact on thermal conductivity of the mixture.Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid,i.e.,the water here.On the other hand,the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium.Regarding the cooling rate of the heated surface,it rises with the permeability parameter,shape factor(related to various shapes of Cu-nanoparticles),and radiation parameter.The surface drag force becomes stronger with the permeability parameter.Also,with growing values of nanoparticle volume fraction,the boundary layer thickness(BLT)increases and the thermal BLT becomes thicker with larger values of shape factor.For decelerating unsteady flow,the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed.The thermal BLT is thicker with radiation parameter.Due to the existence of dual solutions,a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.展开更多
In vitro experimental set-up is an important tool for investigating abdominal aortic aneurysm (AAA). Accurate reproduction of the physiological pulsatile flow waveform in the abdominal aorta at various anatomic locati...In vitro experimental set-up is an important tool for investigating abdominal aortic aneurysm (AAA). Accurate reproduction of the physiological pulsatile flow waveform in the abdominal aorta at various anatomic locations is an important component of these experimental methods. The objective of this study is to establish an experimental set-up to generate a physiological pulsatile flow for in vitro simulations of the abdominal aorta. The physiological flow was established by a computer-controlled peristaltic pump and the flow field in a circular straight pipe is measured under pulsatile flow conditions by a 2-dimensional particle image velocimetry system (2D-PIV). Experimental results show that the in vitro experimental set-up provides a flow with a period of 2 s, a reasonable cross-sectional velocity distribution and an approximate inlet velocity profile that is close to the human abdominal aorta.展开更多
A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean...A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.展开更多
The lower Yellow River still faces the threat of flood due to the unusual precipitation caused by global environmental change, river channel sedimentation, hidden danger in the dike and unfavorable river regime of ＂h...The lower Yellow River still faces the threat of flood due to the unusual precipitation caused by global environmental change, river channel sedimentation, hidden danger in the dike and unfavorable river regime of ＂hanging river＂. According to the characteristics of the dike-break flood of the Yellow River, this paper has simulated, in six different scenarios, the dike-break flood routing by inputting the terrain data, typical historical flood data and land use data of study area to two-dimensional unsteady flow model. The results show that： firstly, the routing process of flood will occupy other rivers on the way and return to the rivers after reaching the lower reaches; secondly, in the same river reach, flood inundating area of north band is bigger than that at corresponding location of south bank under the same historical flood; thirdly, it is different in the degree of flood inundation in different regions due to different geographical locations in flood plain; fourthly, the area of mainstream where flood is deep and flow velocity is quick is relatively smaller, but the area of non-mainstream, where flood is shallow and flow velocity is slow, is relatively big; and finally, the possible influenced area of the dike-break flood is 141,948 km^2.展开更多
In order to explore the unforced unsteadiness of centrifugal pumps,a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions.The r...In order to explore the unforced unsteadiness of centrifugal pumps,a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions.The results showed that,the unsteady flow field was not only affected by rotor and stator interaction,but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area.Moreover,as the flow rates decreased,this unsteady flow structure gradually weakened and disappeared.When the flow rate was reduced to 0.6 times of design flow rate,another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area.Therefore,with the operating condition smaller than design flow rate,the internal flow became more and more complex.In addition to the forced unsteadiness,the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.展开更多
This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overc...This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overcome the difficulties and inaccurancies associated with the determination of characteristics near the flow boundaries. The MacCormack two step explicit scheme with second order accurancy is used for the solution of the transformed system of equations. Comparison between computed and experimental data shows a satisfactory agreement.展开更多
文摘The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium is examined.Moreover,the thermal radiation and viscous dissipation effects are considered.The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method.The computed results can reveal many vital findings of practical importance.Firstly,dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows,the solution is unique.The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium.But different shapes of nanoparticles are not disturbing the dual solution existence range,though it has a considerable impact on thermal conductivity of the mixture.Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid,i.e.,the water here.On the other hand,the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium.Regarding the cooling rate of the heated surface,it rises with the permeability parameter,shape factor(related to various shapes of Cu-nanoparticles),and radiation parameter.The surface drag force becomes stronger with the permeability parameter.Also,with growing values of nanoparticle volume fraction,the boundary layer thickness(BLT)increases and the thermal BLT becomes thicker with larger values of shape factor.For decelerating unsteady flow,the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed.The thermal BLT is thicker with radiation parameter.Due to the existence of dual solutions,a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.
文摘In vitro experimental set-up is an important tool for investigating abdominal aortic aneurysm (AAA). Accurate reproduction of the physiological pulsatile flow waveform in the abdominal aorta at various anatomic locations is an important component of these experimental methods. The objective of this study is to establish an experimental set-up to generate a physiological pulsatile flow for in vitro simulations of the abdominal aorta. The physiological flow was established by a computer-controlled peristaltic pump and the flow field in a circular straight pipe is measured under pulsatile flow conditions by a 2-dimensional particle image velocimetry system (2D-PIV). Experimental results show that the in vitro experimental set-up provides a flow with a period of 2 s, a reasonable cross-sectional velocity distribution and an approximate inlet velocity profile that is close to the human abdominal aorta.
基金supported in part by a Sloan fellowship and an NSERC grant for Chenby a grant from NSF of China for Li.by a grant from NSF of USA for Tian
文摘A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.
基金The State Scientific Research Plan, No.96-920-09-01
文摘The lower Yellow River still faces the threat of flood due to the unusual precipitation caused by global environmental change, river channel sedimentation, hidden danger in the dike and unfavorable river regime of ＂hanging river＂. According to the characteristics of the dike-break flood of the Yellow River, this paper has simulated, in six different scenarios, the dike-break flood routing by inputting the terrain data, typical historical flood data and land use data of study area to two-dimensional unsteady flow model. The results show that： firstly, the routing process of flood will occupy other rivers on the way and return to the rivers after reaching the lower reaches; secondly, in the same river reach, flood inundating area of north band is bigger than that at corresponding location of south bank under the same historical flood; thirdly, it is different in the degree of flood inundation in different regions due to different geographical locations in flood plain; fourthly, the area of mainstream where flood is deep and flow velocity is quick is relatively smaller, but the area of non-mainstream, where flood is shallow and flow velocity is slow, is relatively big; and finally, the possible influenced area of the dike-break flood is 141,948 km^2.
基金supported by the National Natural Science Foundation of China(Grant No.51976125)Open Research Subject of Key Laboratory of Fluid and Power Machinery(Xihua University),Ministry of Education(Grant number zj2015-024)Natural Science Fund of Shanghai(Grant No.19ZR1425900)。
文摘In order to explore the unforced unsteadiness of centrifugal pumps,a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions.The results showed that,the unsteady flow field was not only affected by rotor and stator interaction,but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area.Moreover,as the flow rates decreased,this unsteady flow structure gradually weakened and disappeared.When the flow rate was reduced to 0.6 times of design flow rate,another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area.Therefore,with the operating condition smaller than design flow rate,the internal flow became more and more complex.In addition to the forced unsteadiness,the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.
文摘This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overcome the difficulties and inaccurancies associated with the determination of characteristics near the flow boundaries. The MacCormack two step explicit scheme with second order accurancy is used for the solution of the transformed system of equations. Comparison between computed and experimental data shows a satisfactory agreement.
