Slip Magnetohydrodynamic Viscous Flow over a Permeable Shrinking Sheet

The magnetohydrodynamic （MHD） flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations. Interesting solution behavior ＆ observed with multiple solution branches for certain parameter domain. The effects of the mass transfer, slip, and magnetic parameters are discussed.     

Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer

The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier-Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet.     

MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity

A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.     

Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition

This paper presents a numerical solution for the steady mixed convection magnetohydrodynamic (MHD) flow of an electrically conducting micropolar fluid over a porous shrinking sheet. The velocity of shrinking sheet and magnetic field are assumed to vary as power functions of the distance from the origin. A convective boundary condition is used rather than the customary conditions for temperature, i.e., constant surface temperature or constant heat flux. With the aid of similarity transformations, the governing partial differential equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically, using the variational finite element method (FEM). The influence of various emerging thermophysical parameters, namely suction parameter, convective heat transfer parameter, magnetic parameter and power index on velocity, microrotation and temperature functions is studied extensively and is shown graphically. Additionally the skin friction and rate of heat transfer, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, have also been computed for these parameters. Under the limiting case an analytical solution of the flow velocity is compared with the present numerical results. An excellent agreement between the two sets of solutions is observed. Also, in order to check the convergence of numerical solution, the calculations are carried out by reducing the mesh size. The present study finds applications in materials processing and demonstrates excellent stability and convergence characteristics for the variational FEM code.     

Simulation of Viscous Flows Around a Moving Airfoil by Field Velocity Method with Viscous Flux Correction

Based on the field velocity method, a novel approach for simulating unsteady pitching and plunging motion of an airfoil is presented in this paper. Responses to pitching and plunging motions of the airfoil are simulated under different conditions. The obtained results are compared with those of moving grid method and good agreement is achieved. In the conventional field velocity method, the Euler solver is usually used to simulate the movement of the airfoil. However, when viscous effect is considered, unsteady Navier-Stokes equations have to be solved and the viscous flux correction must be taken into account. In this work, the viscous flux correction is introduced into the conventional field velocity method when non-uniform grid speed distribution is occurred. Numerical experiments for the flow around NACA0012 airfoil showed that the proposed approach can well simulate viscous moving boundary flow problems.     

MHD Flow and Heat Transfer of a Generalized Burgers' Fluid Due to an Exponential Accelerating Plate with Effects of the Second Order Slip and Viscous Dissipation

In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.     

Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation:A Comparative Study

This article examines a mathematical model to analyze the rotating flow of three-dimensional water based nanofluid over a convectively heated exponentially stretching sheet in the presence of transverse magnetic field with additional effects of thermal radiation,Joule heating and viscous dissipation.Silver(Ag),copper(Cu),copper oxide(Cu O),aluminum oxide(Al_2O_3)and titanium dioxide(Ti O_2)have been taken under consideration as the nanoparticles and water(H_2O)as the base fluid.Using suitable similarity transformations,the governing partial differential equations(PDEs)of the modeled problem are transformed to the ordinary differential equations(ODEs).These ODEs are then solved numerically by applying the shooting method.For the particular situation,the results are compared with the available literature.The effects of different nanoparticles on the temperature distribution are also discussed graphically and numerically.It is witnessed that the skin friction coefficient is maximum for silver based nanofluid.Also,the velocity profile is found to diminish for the increasing values of the magnetic parameter.     

Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition

The present work deals with the three-dimensional hybrid Cu-Al₂O₃/water nanofluid flow towards a stretching/shrinking sheet with the presence of velocity slip and convective conditions. A permeable sheet is considered to maintain the shrinking flow through an adequate wall mass suction. The nonlinear governing boundary layer coupled with energy equations are transformed into the ordinary differential equations using similarity transformation. Numerical computations are performed with the aid of boundary value problem solver (bvp4c) in the Matlab software and the results are presented in the tables and graphs. The boundary layer separation occurs in the shrinking flow region. An upsurge of slip and copper nanoparticle volume fraction parameters can increase the range of first and second solutions whereas Biot parameter give zero impact on delaying the boundary layer separation. However, an increase of Biot and slip parameters can boost the heat transfer rate while opposite result is obtained with the augmentation of the copper solid volume fraction. The stability of both solutions are examined, and it is validated that the first (upper branch) solution is more stable than second solution.     

Thermally Radiative Viscous Fluid Flow Over Curved Moving Surface in Darcy-Forchheimer Porous Space

A numerical analysis is developed for incompressible hydromagnetic viscous fluid passed through a curved stretching surface. Fluid saturated by porous space is bounded by curved surface. Term of porous medium is characterized by implementation of Darcy-Forchheimer theory. Adequate similarity variables are implemented to develop a system of non-linear ordinary differential system of equations, which govern the flow behavior. The impact of radiation constraint and Eckert number is incorporated in the energy equation. Numerical scheme based on RKF45 technique is implemented to solve the derived flow model. Prescribed heat flux(PHF) and prescribed surface temperature(PST) boundary conditions are utilized on temperature with Prescribed Surface Concentration(PSC) and Prescribed Mass Flux(PMF)on concentration. Flow behavior is discussed for both the slip and no-slip conditions. Dimensionless physical quantities are presented through graphs and tables.     

Dual Solutions of MHD Boundary Layer Flow of a Micropolar Fluid with Weak Concentration over a Stretching/Shrinking Sheet

We investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differential equations.Closed forms solutions are also obtained in terms of confluent hypergeometric function. This is the first attempt to determine the exact solutions for the non-linear equations of MHD micropolar fluid model. It is demonstrated that the microrotation parameter helps in increasing Nusselt number and the dual solutions exist for all fluid flow parameters under consideration. The dual behavior of dimensionless velocity, temperature, microrotation, skin-friction coefficient,local Nusselt number is displayed on graphs and examined.     

Large Slip Length over a Nanopatterned Surface

A thermodynamic method is employed to analyse the slip length of hydrophobic nanopatterned surface. The maximal slip lengths with respect to the hydrophobicity of the nanopatterned surface are computed. It is found that the slip length reaches more than 50 μm if the nanopatterned surfaces have a contact angle larger than 160°. Such results are expected to find extensive applications in micro-channels and helpful to understand recent experimental observations of the slippage of nanopatterned surfaces.     

Slip Flow of Powell-Eyring Liquid Film Due to an Unsteady Stretching Sheet with Heat Generation

This paper is focused on the study of the viscous Powell-Eyring liquid thin film flow and heat transfer driven by an unsteady stretching sheet in the presence of slip velocity and non-uniform heat generation. A system of equations for momentum and thermal energy are reduced to a set of coupled non-linear ordinary differential equations with the aid of dimensionless transformation. The resulting seven-parameter problem has been solved numerically by using an efficient shooting technique coupled with the fourth-order Runge-Kutta algorithm over the entire range of physical parameters. To interpret various physical parameters governing the flow and heat transfer which appear in the momentum and energy equations, the results are presented graphically. The present results are compared with some of the earlier published work in some limiting cases and are found to be in an excellent agreement. This favorable comparison lends confidence in the numerical results to be reported in the present work. Furthermore, the effects of the parameters governing the thin film flow and heat transfer are examined and discussed through graphs and tables. Also, the values of the local skin-friction coefficient and the local Nusselt number for different values of physical parameters are presented through tables. Additionally, the obtained results for some particular cases of the present problem appear in good agreement with the literature review.     

MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux

The steady magnetohydrodynamic （MHD） mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.     

Shear Flow of a Viscous Fluid over a Cavity with a Pulsating Gas Bubble

Doklady Physics - For the first time, the effect of pressure fluctuations on the averaged shear stress in a shear viscous flow over a two-dimensional rectangular microcavity containing a pulsating...