This paper deals with the study of the MHD flow of non-Newtonian fluid on a porous plate. Two exact solutions for non-torsionally generated unsteady hydromagnetic flow of an electrically conducting second order incompressible fluid bounded by an infinite non-conducting porous plate subjected to a uniform suction or blowing have been analyzed. The governing partial differential equation for the flow has been established. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. The effect of presence of the material constants of the second order fluid on the velocity field is discussed.
The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit.The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactantfree bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure.The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The largetime evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.
PurposeThe purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. The principal question the authors address in this paper is in regard to the applicability of the no‐slip condition at a solid‐liquid boundary. The authors present the effects of slip, magnetohydrodynamics (MHD) and heat transfer for the plane Couette, plane Poiseuille and plane Couette‐Poiseuille flows in a homogeneous and thermodynamically compatible third grade fluid. The problem of a non‐Newtonian plane Couette flow, fully developed plane Poiseuille flow and Couette‐Poiseuille flow are investigated.Design/methodology/approachThe present investigation is an attempt to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. A very effective and higher order numerical scheme is used to solve the resulting system of nonlinear differential equations with nonlinear boundary conditions. Numerical solutions are obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method.FindingsDue to the nonlinear and highly complicated nature of the governing equations and boundary conditions, finding an analytical or numerical solution is not easy. The authors obtained numerical solutions of the coupled nonlinear ordinary differential equations with nonlinear boundary conditions using higher order Chebyshev spectral collocation method. Spectral methods are proven to offer a superior intrinsic accuracy for derivative calculations.Originality/valueTo the best of the authors' knowledge, no such analysis is available in the literature which can describe the heat transfer, MHD and slip effects simultaneously on the flows of the non‐Newtonian fluids.
SUMMARYThin film flow of an Oldroyd 6-constant fluid on a vertical moving belt is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one-dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equations are solved analytically and the exact solution is obtained in an elegant way. Numerical solutions are also obtained using higher-order Chebyshev spectral methods. The influence of various non-Newtonian parameters, gravitational force and applied magnetic field is investigated. The results showing the effect of gravity, magnetic field and material constants 1 and 2 are presented.
The phenomenon of liquid jet breakup is studied for the case of a very viscous jet containing one or more solid particles on its axis of symmetry. A mathematical model is derived which represents the complex dynamics as a combination of two relatively simpler problems. Governing equations for the dynamics are derived for Stokes flow using long wavelength assumptions for the capillarity-driven flow, and the influence of the force-free particle is represented by a symmetric hydrodynamic force dipole, also termed a stresslet. The total flow field is the combination of the "outer" long wavelength approximated flow, combined with the "inner" flow induced by the force dipole representation of a particle. Imposing the standard stress balance and kinematic condition at the jet surface to the combined flow leads to a well-posed problem for the evolution of the jet shape. The model equations are solved numerically by an implicit finite-difference scheme. The theoretical calculations based on this hybrid long wavelength and singularity approach yield qualitatively accurate and encouraging agreement with experimental observations. Results of calculations for one particle centered or off-center (with respect to the period of the jet) and for two particles are presented. Results showing the influence of varying particle size are also presented.
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