For MHD flows in a rectangular duct with unsymmetrical walls, two analytical solutions have been obtained by solving the gov- erning equations in the liquid and in the walls coupled with the boundary conditions at flu...For MHD flows in a rectangular duct with unsymmetrical walls, two analytical solutions have been obtained by solving the gov- erning equations in the liquid and in the walls coupled with the boundary conditions at fluid-wall interface. One solution of ＇Case I＇ is for MHD flows in a duct with side walls insulated and unsymmetrical Hartmann walls of arbitrary conductivity, and another one of ＇Case II＇ is for the flows with unsymmetrical side walls of arbitrary conductivity and Hartmann walls perfectly conductive. The walls are unsymmetrical with either the conductivity or the thickness different from each other. The solutions, which include three parts, well reveal the wall effects on MHD. The first part represents the contribution from insulated walls, the second part represents the contribution from the conductivity of the walls and the third part represents the contribution from the unsymmetri- cal walls. The solution is reduced to the Hunt＇s analytical solutions when the walls are symmetrical and thin enough. With wall thickness runs from 0 to co, there exist many solutions for a fixed conductance ratio. The unsymmetrical walls have great effects on velocity distribution. Unsymmetrical jets may form with a stronger one near the low conductive wall, which may introduce stronger MHD instability. The pressure gradient distributions as a function of Hartmann number are given, in which the wall effects on the distributions are well illustrated.展开更多
In this paper,the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends,where the tube is composed of two different incompressible neo-Hoo...In this paper,the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends,where the tube is composed of two different incompressible neo-Hookean materials.Significantly,the implicit analytical solutions describing the deformation of the tube are proposed.Numerical simulations are given to further illustrate the qualitative properties of the solutions and some meaningful conclusions are obtained.In the tension case,with the increasing axial loads or with the decreasing ratio of shear moduli of the outer and the inner materials,it is proved that the tube will shrink more along the radial direction and will extend more along the axial direction.Under either tension or compression,the deformation along the axial direction is obvious near the two ends of the tube,while in the rest,the change is relatively small.Similarly,for a large domain of the middle part,the axial elongation is almost constant;however,the variation is very fast near the two ends.In addition,the absolute value of the axial displacement increases gradually from the central cross-section of the tube and achieves the maximum at the two endpoints.展开更多
Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and ...Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11125212 and 50936066)the International Thermonuclear Experimental Reactor Project in China(Grant No.2013GB11400)
文摘For MHD flows in a rectangular duct with unsymmetrical walls, two analytical solutions have been obtained by solving the gov- erning equations in the liquid and in the walls coupled with the boundary conditions at fluid-wall interface. One solution of ＇Case I＇ is for MHD flows in a duct with side walls insulated and unsymmetrical Hartmann walls of arbitrary conductivity, and another one of ＇Case II＇ is for the flows with unsymmetrical side walls of arbitrary conductivity and Hartmann walls perfectly conductive. The walls are unsymmetrical with either the conductivity or the thickness different from each other. The solutions, which include three parts, well reveal the wall effects on MHD. The first part represents the contribution from insulated walls, the second part represents the contribution from the conductivity of the walls and the third part represents the contribution from the unsymmetri- cal walls. The solution is reduced to the Hunt＇s analytical solutions when the walls are symmetrical and thin enough. With wall thickness runs from 0 to co, there exist many solutions for a fixed conductance ratio. The unsymmetrical walls have great effects on velocity distribution. Unsymmetrical jets may form with a stronger one near the low conductive wall, which may introduce stronger MHD instability. The pressure gradient distributions as a function of Hartmann number are given, in which the wall effects on the distributions are well illustrated.
基金supported by the National Natural Science Foundation of China(Grant Nos.10872045 and 11232003)the Program for New Century Excellent Talents in University(Grant No.NCET-09-0096)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.DC120101121)the Program for Liaoning Excellent Talents in University(Grant No.LR2012044)
文摘In this paper,the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends,where the tube is composed of two different incompressible neo-Hookean materials.Significantly,the implicit analytical solutions describing the deformation of the tube are proposed.Numerical simulations are given to further illustrate the qualitative properties of the solutions and some meaningful conclusions are obtained.In the tension case,with the increasing axial loads or with the decreasing ratio of shear moduli of the outer and the inner materials,it is proved that the tube will shrink more along the radial direction and will extend more along the axial direction.Under either tension or compression,the deformation along the axial direction is obvious near the two ends of the tube,while in the rest,the change is relatively small.Similarly,for a large domain of the middle part,the axial elongation is almost constant;however,the variation is very fast near the two ends.In addition,the absolute value of the axial displacement increases gradually from the central cross-section of the tube and achieves the maximum at the two endpoints.
文摘Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.
