In this paper,the field synergy principle is firstly performed on the viscoelastic fluid-based nanofluid and other relevant fluid in channel at turbulent flow state to scrutinize their heat transfer performance based ...In this paper,the field synergy principle is firstly performed on the viscoelastic fluid-based nanofluid and other relevant fluid in channel at turbulent flow state to scrutinize their heat transfer performance based on our direct numerical simulation database.The cosine values of intersection angle between velocity vector and temperature gradient vector are calculated for different simulated cases with varying nanoparticle volume fraction,nanoparticle diameter,Reynolds number and Weissenberg number.It is found that the filed synergy effect is enhanced when the nanoparticle volume fraction is increased,nanoparticle diameter is decreased and Weissenberg number is decreased,i.e.the heat transfer is also enhanced.However,the filed synergy effect is weakened with the increase of Reynolds number which may be the possible reason for the power function relationship in empirical correlation of heat transfer between heat transfer performance and Reynolds number with the constant power exponent lower than 1.Finally,it is also observed that the field synergy principle can be used to analyze the heat transfer process of viscoelastic fluid-based nanofluid at the turbulent flow state even if some negative cosine values of intersection angle exist in the flow field.展开更多
For MHD flows in a rectangular duct with unsymmetrical walls, two analytical solutions have been obtained by solving the governing equations in the liquid and in the walls coupled with the boundary conditions at fluid...For MHD flows in a rectangular duct with unsymmetrical walls, two analytical solutions have been obtained by solving the governing 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 unsymmetrical 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∞, 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
A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insu...A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insulated walls or with thin conductive walls,in which wall effects on MHD are represented by the wall conductance ratio.With wall thickness resolved,it is stressed that the solution of Sloan and Smith's and the solution of Butler's can be used to check the error of the thin wall approximation condition used for Hunt's solutions.It is noted that Tao and Ni's solutions can be used as a benchmark for MHD flows in a duct with wall symmetrical or unsymmetrical,thick or thin.When the walls are symmetrical,Tao and Ni's solutions are reduced to Sloan and Smith's solution and Butler's solution,respectively.展开更多
基金supported by China Postdoctoral Science Foundation(Grant No.2014M561037)President Fund of University of Chinese Academy of Sciences(Grant No.Y3510213N00)+2 种基金National Natural Science Foundation of China(Grant No.51276046)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20112302110020)National Natural Science Foundation of China(Grant No.51325603)
文摘In this paper,the field synergy principle is firstly performed on the viscoelastic fluid-based nanofluid and other relevant fluid in channel at turbulent flow state to scrutinize their heat transfer performance based on our direct numerical simulation database.The cosine values of intersection angle between velocity vector and temperature gradient vector are calculated for different simulated cases with varying nanoparticle volume fraction,nanoparticle diameter,Reynolds number and Weissenberg number.It is found that the filed synergy effect is enhanced when the nanoparticle volume fraction is increased,nanoparticle diameter is decreased and Weissenberg number is decreased,i.e.the heat transfer is also enhanced.However,the filed synergy effect is weakened with the increase of Reynolds number which may be the possible reason for the power function relationship in empirical correlation of heat transfer between heat transfer performance and Reynolds number with the constant power exponent lower than 1.Finally,it is also observed that the field synergy principle can be used to analyze the heat transfer process of viscoelastic fluid-based nanofluid at the turbulent flow state even if some negative cosine values of intersection angle exist in the flow field.
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 governing 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 unsymmetrical 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∞, 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. 11125212 and 50936066)the National Magnetic Confinement Fusion Science Program of China (Grant No. 2009GB10401)
文摘A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insulated walls or with thin conductive walls,in which wall effects on MHD are represented by the wall conductance ratio.With wall thickness resolved,it is stressed that the solution of Sloan and Smith's and the solution of Butler's can be used to check the error of the thin wall approximation condition used for Hunt's solutions.It is noted that Tao and Ni's solutions can be used as a benchmark for MHD flows in a duct with wall symmetrical or unsymmetrical,thick or thin.When the walls are symmetrical,Tao and Ni's solutions are reduced to Sloan and Smith's solution and Butler's solution,respectively.
