This paper aims to present the experimental result obtained from dynamic response on flee-flee beam in driving point and transfer mobility analysis using impact test method using hammer tips that are steel, plastic an...This paper aims to present the experimental result obtained from dynamic response on flee-flee beam in driving point and transfer mobility analysis using impact test method using hammer tips that are steel, plastic and rubber. The 8630C accelerometer and analyzer is used for data logging and for the analysis, the plastic hammer tip is chosen. The analytical and the experimental value then are compared for the free-free beam natural frequency, damping ratio, and stiffness value. As a result, the highest percentage error for natural frequency is approximated to 2.7%, the damping ratio is approximated to 3.115 × 10^-3 and the stiffness value gives the major different between the experiment value and theoretical value. Finally, this method can be used to determine the properties of a structure such as natural frequency, mode shapes, damping ration and stiffness, respectively.展开更多
Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the vel...Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.展开更多
This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing syste...This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method（HAM）. It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.展开更多
In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct pow...In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations （PDEs） are transformed into non linear self-similar ordinary differential equations （ODEs） by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.展开更多
The steady two-dimensional, laminar flow of a viscous, incompressible, electrically conducting fluid near a stagnation point with heat transfer over a permeable surface in the presence of a uniform magnetic field is c...The steady two-dimensional, laminar flow of a viscous, incompressible, electrically conducting fluid near a stagnation point with heat transfer over a permeable surface in the presence of a uniform magnetic field is considered. Taking suitable similarity variables, the governing boundary layer equations are transformed to ordinary differential equations and solved numerically by Shooting method. The effects of the suction parameter, the magnetic parameter, the Prandtl number and the Eckert number are studied on the velocity and temperature distributions.展开更多
In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type f...In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.展开更多
This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy ...This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.展开更多
In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a syste...In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.展开更多
The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation ef...The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.展开更多
AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anteri...AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.展开更多
This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the s...This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.展开更多
The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed po...The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.展开更多
The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper. Considering the effect of he...The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper. Considering the effect of heat transfer on temperature of the reactor, a new model is set up. For any initial power, the variations of output power and reactivity with time are obtained by numerical method. The effects of the big inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed. It was found that the effect of heat transfer on the output power and reactivity can be neglected under any initial power, and the output power obtained by the adiabatic model is basically in accordance with that by the model of this paper, and the analytical solution can be adopted. The results provide a theoretical base for safety analysis and operation management of a power reactor.展开更多
文摘This paper aims to present the experimental result obtained from dynamic response on flee-flee beam in driving point and transfer mobility analysis using impact test method using hammer tips that are steel, plastic and rubber. The 8630C accelerometer and analyzer is used for data logging and for the analysis, the plastic hammer tip is chosen. The analytical and the experimental value then are compared for the free-free beam natural frequency, damping ratio, and stiffness value. As a result, the highest percentage error for natural frequency is approximated to 2.7%, the damping ratio is approximated to 3.115 × 10^-3 and the stiffness value gives the major different between the experiment value and theoretical value. Finally, this method can be used to determine the properties of a structure such as natural frequency, mode shapes, damping ration and stiffness, respectively.
基金supported by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.
基金supported by the National Natural Science Foundation of China (No. 50476083)
文摘This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method（HAM）. It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.
基金the National Board for Higher Mathematics(NBHM),DAE,Mumbai,India
文摘In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations （PDEs） are transformed into non linear self-similar ordinary differential equations （ODEs） by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.
文摘The steady two-dimensional, laminar flow of a viscous, incompressible, electrically conducting fluid near a stagnation point with heat transfer over a permeable surface in the presence of a uniform magnetic field is considered. Taking suitable similarity variables, the governing boundary layer equations are transformed to ordinary differential equations and solved numerically by Shooting method. The effects of the suction parameter, the magnetic parameter, the Prandtl number and the Eckert number are studied on the velocity and temperature distributions.
基金This work is supported by the Scientific Research Foundation of Bijie University.
文摘In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.
文摘This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.
文摘In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.
基金Project supported by the National Natural Science Foundation of China(Nos.51709191,51706149,and 51606130)the Key Laboratory of Advanced Reactor Engineering and Safety,Ministry of Education of China(No.ARES-2018-10)the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University of China(No.Skhl1803)
文摘The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.
文摘AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.
基金supported by Universiti Kebangsaan Malaysia(No.UKM-GUP-2011-202)
文摘This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.
基金the National Natural Science Foundation of China
文摘The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.
基金Supported by the National Natural Science Foundation of China (No.10575131)
文摘The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper. Considering the effect of heat transfer on temperature of the reactor, a new model is set up. For any initial power, the variations of output power and reactivity with time are obtained by numerical method. The effects of the big inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed. It was found that the effect of heat transfer on the output power and reactivity can be neglected under any initial power, and the output power obtained by the adiabatic model is basically in accordance with that by the model of this paper, and the analytical solution can be adopted. The results provide a theoretical base for safety analysis and operation management of a power reactor.
