... 2012 20 06 2012 27 07 2012 27 07 2012 partial differential equations channel flows non-Newtonian fluids heat transfer homotopy analysis method Studies of channel flows have been attractive for many authors. Non-Newtonian fluid flows and heat transfer has considerable...

..., and the induced magnetic field is neglected. The similarity transformations reduce the nonlinear partial differential equations into ordinary differential equations. The convergence of the obtained solutions is checked. Graphs are plotted and discussed for various parameters of interest. We construct...

... layers convection external flows iterative methods laminar flow nonlinear differential equations partial differential equations Runge-Kutta methods vertical plate boundary layer flow heat transfer local Grashof number convective parameter Convective heat transfer studies are very...

... as projection functions to convert original partial differential equations (PDEs) to a small set of nonlinear ordinary differential equations (ODEs) ( 6 ). Galerkin-projection POD/ROM method has been used in the field of fluid mechanics to simulate incompressible and compressible flows for different purposes...

... on the principles of power expended and mass conservation, is exploited with the Papanastasiou approximation for Casson equation employed to model viscoplasticity. The approximation for the nonlinear set of partial differential equations is performed, using a stabilized finite element methodology. A Galerkin least...

... for calculating ice shapes on simple or complex 3D geometries. The resulting ice simulation system, FENSAP-ICE, is built in a modular fashion to successively solve each flow, impingement and accretion via field models based on partial differential equations (PDEs). The FENSAP-ICE system results are compared...

.... In the present work, the method of multiple scales is applied to take the nonparallel flow effects into consideration. The results demonstrate the stabilizing character of the nonparallel flow effects. The vortex instability mode is also considered within the scope of partial differential equations. The results...

... transforms partial differential equations boundary-value problems Fractional calculus is a mathematical concept of differentiation and integration to arbitrary (noninteger) order, such as ∂ − 2 / 3 f / ∂ x − 2 / 3 . Some useful definitions and properties of fractional...

...C. Prud’homme; D. V. Rovas; K. Veroy; L. Machiels; Y. Maday; A. T. Patera; G. Turinici We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components...