In this study, the laminar heat transfer and nanofluid flow between two porous horizontal concentric cylinders was investigated. The problem is investigated in two different geometries and the Re=10, 25, 50, 75, 100 a...In this study, the laminar heat transfer and nanofluid flow between two porous horizontal concentric cylinders was investigated. The problem is investigated in two different geometries and the Re=10, 25, 50, 75, 100 and volume fraction 0, 0.2%, 0.5%, 2% and 5% that related to copper nanoparticles, and porous medium porosity of 0.5 and 0.9. Compared to the first geometry, the convective coefficient in the second geometry increases by 8.3%, 7% and 5.5% at Reynolds numbers of 100, 75 and 50, respectively. Comparison of the outlet temperatures for two heat fluxes of 300 and 1200 W/m^2 indicates a 2.5% temperature growth by a fourfold increase in the heat fluxes. Also, the higher Nusselt number is associated with the second geometry occurring at porosities of 0.9 and 0.5, respectively. In both geometries, the Nusselt number values at the porosity of 0.9 are higher, which is due to the increased nanofluid convection at higher porosities. The velocity of the nanofluid experiences a two-fold increase at the outlet compared to its inlet velocity in the first geometry and for both porosities. Similarly, a three-fold increase was achieved in the second geometry and for both porosities.展开更多
An analytical solution to annular pipe flow of the second fluid and Maxwell fluid is given using Weber integral transform. The formulas can be used to analyse the behavior of unsteady flow of viscoelastic fluid in ann...An analytical solution to annular pipe flow of the second fluid and Maxwell fluid is given using Weber integral transform. The formulas can be used to analyse the behavior of unsteady flow of viscoelastic fluid in annular pipe, especially to analyse the flow character of double-gap concentric cylinder rheometer. It is found by computation that when the outer cylinder is in simple periodic motion, there are step junctions along the history curve of Maxwell fluid’s velocity and shear stress, and at step junctions both amplitude and phase of oscillatory wave vary sharply; when the outer cylinder makes uniform rotation, the velocity and shear stress of Maxwell fluid exhibit rhombic wave oscillation, and its period is in close parabolic relation with material constant H.展开更多
The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the a...The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the analytical solution of which the derivative order is 1/2 is derived with the analytical solution and the reliability of Laplace numerical inversion based on Crump algorithm for the problem is verified, then the characteristics of second-order fluid flow in the rheometer by using Crump method is analyzed. The results indicate that the more obvious the viscoelastic properties of fluid are, the more sensitive the dependence of velocity and stress on fractional derivative order is.展开更多
Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domai...Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation,the boundary conditions on the free surface and on the sea bed.The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls.In the paper,the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy's law.Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant.Wave loading on the outer and inner cylinder is presented in the numerical results.展开更多
In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem ...In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.展开更多
A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect.The system equations for coupled plasma,heat conduction with phase-lags(PLs),and ...A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect.The system equations for coupled plasma,heat conduction with phase-lags(PLs),and motion equations are introduced and solved by using the Laplace transform technique.The photothermal,thermal,and elastic waves in a rotating solid cylinder of semiconductor material are analyzed with the proposed model.The cylinder surface is constrained and subjected to a time-dependent pulse heat flux.The sensitivity of the physical fields for the angular velocity,PLs,and thermal vibration parameters is investigated.In addition,the effects of the effective parameters on the physical quantities are graphically illustrated and discussed in detail.展开更多
A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the li...A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.展开更多
This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Cr...This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.展开更多
A cylinder-cylinder dielectric-barrier discharge (DBD) ozone generator has been developed. The ozone concentration was measured at an oxygen pressure of 1.02 atm and an oxygen flow rate of 12 L/min. The heat generated...A cylinder-cylinder dielectric-barrier discharge (DBD) ozone generator has been developed. The ozone concentration was measured at an oxygen pressure of 1.02 atm and an oxygen flow rate of 12 L/min. The heat generated in the ozone tube during the operation of the ozone generator was investigated using a thermal camera. The infrared (IR) images and corresponding temperatures of the ozone tube surfaces at different operating times were observed. The IR images showed the generating of the inhomogeneous heat-up along the ozone tube surface which results in the decrease of the ozone production efficiency.展开更多
Soil samples with clay content ranging from 15% to 31%, were taken from three debris flow gullies in Southwest China. Three debris flow slurry samples were prepared and tested with four measuring systems of an Anton P...Soil samples with clay content ranging from 15% to 31%, were taken from three debris flow gullies in Southwest China. Three debris flow slurry samples were prepared and tested with four measuring systems of an Anton Paar Physica MCR301 rheometer, including the concentric cylinder system,the parallel-plate system, the vane geometry, and the ball measuring system. All systems were smoothwalled. Flow curves were plotted and yield stress was determined using the Herschel-Bulkley model,showing differences among the different systems.Flow curves from the concentric cylinder and parallelplate systems involved two distinct regions, the low shear and the high shear regions. Yield stresses determined by data fitting in the low shear region were significantly lower than the values from the inclined channel test which is a practical method for determining yield stress. Flow curves in the high shear region are close to those from the vane geometry and the ball measuring system. The fitted values of yield stress are comparable to the values from the inclined channel test. The differences are caused by wall-slip effects in the low shear region.Vane geometry can capture the stress overshoot phenomenon caused by the destruction of slurry structure, whereas end effects should be considered in the determination of yield stress. The ball measuring system can give reasonable results, and it is applicable for rheological testing of debris flow slurries.展开更多
文摘In this study, the laminar heat transfer and nanofluid flow between two porous horizontal concentric cylinders was investigated. The problem is investigated in two different geometries and the Re=10, 25, 50, 75, 100 and volume fraction 0, 0.2%, 0.5%, 2% and 5% that related to copper nanoparticles, and porous medium porosity of 0.5 and 0.9. Compared to the first geometry, the convective coefficient in the second geometry increases by 8.3%, 7% and 5.5% at Reynolds numbers of 100, 75 and 50, respectively. Comparison of the outlet temperatures for two heat fluxes of 300 and 1200 W/m^2 indicates a 2.5% temperature growth by a fourfold increase in the heat fluxes. Also, the higher Nusselt number is associated with the second geometry occurring at porosities of 0.9 and 0.5, respectively. In both geometries, the Nusselt number values at the porosity of 0.9 are higher, which is due to the increased nanofluid convection at higher porosities. The velocity of the nanofluid experiences a two-fold increase at the outlet compared to its inlet velocity in the first geometry and for both porosities. Similarly, a three-fold increase was achieved in the second geometry and for both porosities.
文摘An analytical solution to annular pipe flow of the second fluid and Maxwell fluid is given using Weber integral transform. The formulas can be used to analyse the behavior of unsteady flow of viscoelastic fluid in annular pipe, especially to analyse the flow character of double-gap concentric cylinder rheometer. It is found by computation that when the outer cylinder is in simple periodic motion, there are step junctions along the history curve of Maxwell fluid’s velocity and shear stress, and at step junctions both amplitude and phase of oscillatory wave vary sharply; when the outer cylinder makes uniform rotation, the velocity and shear stress of Maxwell fluid exhibit rhombic wave oscillation, and its period is in close parabolic relation with material constant H.
文摘The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the analytical solution of which the derivative order is 1/2 is derived with the analytical solution and the reliability of Laplace numerical inversion based on Crump algorithm for the problem is verified, then the characteristics of second-order fluid flow in the rheometer by using Crump method is analyzed. The results indicate that the more obvious the viscoelastic properties of fluid are, the more sensitive the dependence of velocity and stress on fractional derivative order is.
基金Supported by the National Natural Science Foundation of China under Grant No.51079032
文摘Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation,the boundary conditions on the free surface and on the sea bed.The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls.In the paper,the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy's law.Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant.Wave loading on the outer and inner cylinder is presented in the numerical results.
基金the National Natural Science Foundation of China(Nos.10571142,10771167)
文摘In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.
文摘A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect.The system equations for coupled plasma,heat conduction with phase-lags(PLs),and motion equations are introduced and solved by using the Laplace transform technique.The photothermal,thermal,and elastic waves in a rotating solid cylinder of semiconductor material are analyzed with the proposed model.The cylinder surface is constrained and subjected to a time-dependent pulse heat flux.The sensitivity of the physical fields for the angular velocity,PLs,and thermal vibration parameters is investigated.In addition,the effects of the effective parameters on the physical quantities are graphically illustrated and discussed in detail.
基金supported by the National Natural Science Foundation of China (Grants 11502108 and 11232007)the Program for New Century Excellent Talents in Universities (Grant NCET-12-0625)+2 种基金the Natural Science Foundation of Jiangsu Province (Grant BK20140037)the Fundamental Research Funds for Central Universities (Grant NE2013101)Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
文摘A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.
文摘This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.
文摘A cylinder-cylinder dielectric-barrier discharge (DBD) ozone generator has been developed. The ozone concentration was measured at an oxygen pressure of 1.02 atm and an oxygen flow rate of 12 L/min. The heat generated in the ozone tube during the operation of the ozone generator was investigated using a thermal camera. The infrared (IR) images and corresponding temperatures of the ozone tube surfaces at different operating times were observed. The IR images showed the generating of the inhomogeneous heat-up along the ozone tube surface which results in the decrease of the ozone production efficiency.
基金financially supported by the Key Research Program of the Chinese Academy of Sciences (CAS) (Grant No. KZZD-EW-05-01)the Youth Talent Team Program of Institute of Mountain Hazards and Environment, CAS (Grant No. SDSQB-2013-01)the National Natural Science Foundation of China (Grant No. 41201011)
文摘Soil samples with clay content ranging from 15% to 31%, were taken from three debris flow gullies in Southwest China. Three debris flow slurry samples were prepared and tested with four measuring systems of an Anton Paar Physica MCR301 rheometer, including the concentric cylinder system,the parallel-plate system, the vane geometry, and the ball measuring system. All systems were smoothwalled. Flow curves were plotted and yield stress was determined using the Herschel-Bulkley model,showing differences among the different systems.Flow curves from the concentric cylinder and parallelplate systems involved two distinct regions, the low shear and the high shear regions. Yield stresses determined by data fitting in the low shear region were significantly lower than the values from the inclined channel test which is a practical method for determining yield stress. Flow curves in the high shear region are close to those from the vane geometry and the ball measuring system. The fitted values of yield stress are comparable to the values from the inclined channel test. The differences are caused by wall-slip effects in the low shear region.Vane geometry can capture the stress overshoot phenomenon caused by the destruction of slurry structure, whereas end effects should be considered in the determination of yield stress. The ball measuring system can give reasonable results, and it is applicable for rheological testing of debris flow slurries.