Abstract: The unsteady, laminar, incompressible and two dimensional flow of a micropolar fluid between two orthogonally moving porous coaxial disks was considered. An extension of von Karman’s similarity transformations was applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. The analytical solutions were obtained by employing the homotopy analysis method. The effects of various physical parameters like the expansion ratio, the permeability Reynolds number on the velocity fields were discussed in detail.
Abstract: The magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface was investigated. Similarity transformations were used to reduce the governing partial differential equations into a nonlinear ordinary differential equation. The nonlinear problem was solved by employing successive Taylor series linearization method (STLM). Computations for velocity components were carried out for the emerging parameters. Numerical values of skin friction coefficient were presented and analyzed for various parameters of interest entering into the problem.
Abstract: The calculation of cell face velocity in the discretization of continuity equation, momentum equation and scalar equation of a non-staggered grid system were discussed. Both momentum interpolation and linear interpolation were adopted to evaluate the coefficients in the discretized momentum and scalar equation, and their performances were compared. When linear interpolation was used to calculate coefficients, the mass residual term in the coefficients must be dropped to maintain the solution accuracy and its convergence rate.
Abstract: The problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface was investigated.The study considered the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. The basic equations governing the flow and heat transfer were reduced to a set of nonlinear ordinary differential equations by applying suitable similarity transformations. The transformed equations were solved numerically by Runge-Kutta-Fehlberg-45 order method. An analysis was carried out for two different cases of heating processes, namely Variable Wall Temperature (VWT) and Variable Heat Flux (VHF). The effects of various physical parameters such as magnetic parameter, fluid-particle interaction parameter, unsteady parameter, Prandtl number, Eckert number, number density of dust particles and heat source/sink parameter on velocity and temperature profiles were shown in several plots and the effect of wall temperature gradient function and wall temperature function were tabulated and discussed.
Abstract: The effects of viscous dissipation and heat source/sink on fully-developed mixed convection for the laminar flow in a parallelplate vertical channel were investigated. The plate exchanged heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid were considered. First, the simple cases of negligible Brinkman number or negligible Grashof number were solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink were analyzed by a perturbation series method valid for small values of perturbation parameter. To relax the conditions on perturbation parameter, the velocity and temperature fields were solved using Runge-Kutta fourth-order method with shooting technique. The velocity, temperature, skin friction and Nusselt numbers at the plates were discussed numerically and presented through graphs.
Abstract: Peristaltic flow of a Johnson-Segalman fluid in a planar channel was investigated in the presence of an induced magnetic field and slip condition. Symmetric nature of flow in a channel was adopted. The velocity slip condition in terms of shear stress was taken into account. Mathematical formulation was first presented and then the subjected equations were solved under the long wavelength and low Reynolds number approximations. Perturbations solutions were established for the pressure rise, axial velocity, microrotation component, stream function, magnetic-force function, axial induced magnetic field, and current distribution across the channel. Solution expressions for small Weissenberg number were derived. The flow quantities of interest were sketched and analyzed.
Abstract: In most cases, the research on the buckling of helical spring is based on column, the spring is equivalent to column and the torsion around the axial line is ignored. The 3D helical spring model was considered,and its equilibrium equations were established by introducing two coordinate systems, named Frenet and principal axis coordinate systems, to describe the spatial deformation of center line and the torsion of cross section of spring respectively. By using small deformation assumption, the variables on deflection could be expanded by Taylor’s series and the terms of high orders were ignored. So the equations could be simplified to the functions of twist angle and arc length, which was possible to be solved in numerical method. The reaction loads of spring caused by axial load subjected at the center point were also discussed, which provided boundary conditions to gain the solution of equilibrium equations. This present work can be helpful to the continued research on the behavior of postbuckling of compressed helical spring.
Abstract: The present investigation was concerned with a study effect of rotation on an infinite circular cylinder subjected to certain boundary conditions. An analytical procedure for evaluation of thermal stresses, displacements and temperature in rotating cylinder subjected to thermal load along the radius was presented. The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface was maintained at zero temperature was discussed. Such situation could arise due to melting of insulating material deposited on the surface cylinder. A solution and numerical results were obtained for the stress components, displacement components, and temperature. It was shown that the results obtained from the present semianalytical method were in a good agreement with those obtained using the previously developed methods.
Abstract: The authors considered a family of systems parameterized by H,which described Langmuir’s turbulence, and studied the asymptotic behavior of the solutions (EH , nH ) when H went to zero. They state convergence results of (EH , nH ) to the couple (E,n) which is the solution of the Zakharov equations.