In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing ...In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.展开更多
An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a cl...An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.展开更多
The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous me...The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous medium are investigated numeri cally. The governing nonlinear dimensionless equations are solved by an implicit finite difference scheme of the CrankNicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimension less velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, tem perature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.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 nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal condu...A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.展开更多
基金the financial support of National Board forHigher Mathematics (NBHM),DAE,Mumbai,India for pursuing this workThe research of A. Alsaedi is partially supported by the Deanship of Scientific Research (DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.
文摘An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.
文摘The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous medium are investigated numeri cally. The governing nonlinear dimensionless equations are solved by an implicit finite difference scheme of the CrankNicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimension less velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, tem perature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.
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.
文摘A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.
