There are many problems in science and engineering where the solution shows a boundary layer character. Near the boundary the gradient is large in contrast with the smooth behaviour in the central core. A uniform grid...There are many problems in science and engineering where the solution shows a boundary layer character. Near the boundary the gradient is large in contrast with the smooth behaviour in the central core. A uniform grid is, therefore, not suitable for a numerical solution. MHD flow problems belong to this category where a velocity and induced magnetic field profiles get flattened in a transverse flow. In the present paper an optimized grid has been generated using interpo-lating wavelets. The results are compared with those obtained using uniform grid, the finite element method and also from the analytical solution.展开更多
Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrica...Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrically-conducting nanofluid from a vertical cylinder.The mathematical model includes the effects of viscous dissipation,second order velocity slip and thermal slip,has been considered.The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations.The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest.Furthermore,the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method(HAM).The present analytical results achieve good correlation with numerical results(shooting method).Entropy is found to be an increasing function of second order velocity slip,magnetic field and curvature parameter.Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter.The flow is accelerated with curvature parameter but decelerated with magnetic parameter.Heat transfer rate(Nusselt number)is enhanced with greater mixed convection parameter,curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter.Entropy generation is also increased with magnetic parameter,second order slip velocity parameter,curvature parameter,thermophoresis parameter,buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter,Brownian motion parameter and thermal slip parameter.展开更多
文摘There are many problems in science and engineering where the solution shows a boundary layer character. Near the boundary the gradient is large in contrast with the smooth behaviour in the central core. A uniform grid is, therefore, not suitable for a numerical solution. MHD flow problems belong to this category where a velocity and induced magnetic field profiles get flattened in a transverse flow. In the present paper an optimized grid has been generated using interpo-lating wavelets. The results are compared with those obtained using uniform grid, the finite element method and also from the analytical solution.
文摘Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrically-conducting nanofluid from a vertical cylinder.The mathematical model includes the effects of viscous dissipation,second order velocity slip and thermal slip,has been considered.The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations.The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest.Furthermore,the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method(HAM).The present analytical results achieve good correlation with numerical results(shooting method).Entropy is found to be an increasing function of second order velocity slip,magnetic field and curvature parameter.Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter.The flow is accelerated with curvature parameter but decelerated with magnetic parameter.Heat transfer rate(Nusselt number)is enhanced with greater mixed convection parameter,curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter.Entropy generation is also increased with magnetic parameter,second order slip velocity parameter,curvature parameter,thermophoresis parameter,buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter,Brownian motion parameter and thermal slip parameter.
