Oscillatory motion of a viscoelastic fluid past a stretching sheet

Summary The boundary layer flow of a viscoelastic fluid (Walters' B model) past a stretching sheet is considered for investigation. The solution of the equation of motion is obtained using the power series method. The effects of the viscoelastic parameterk ₁ on the flow have been investigated. It is also found that the effects of unsteadiness in the wall velocity and skin-friction are appreciable.     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.     

Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge

The candid intension of this article is to inspect the heat and mass transfer of a magnetohydrodynamic tangent hyperbolic nanofluid. The nanofluid flow has been assumed to be directed by a wedge on its way. In addition, the collective stimulus of the convective heating mode with thermal radiation is inspected. The governing set of PDEs is rendered into that of the coupled nonlinear ODEs. The resulting ordinary differential equations are then solved by the well known shooting technique for two different cases; the flow over a static wedge and flow over a stretching wedge. The impact of intricate physical parameters on the velocity, temperature and concentration profiles is analyzed graphically. It is noticed that the intensifying values of the generalized Biot number, Brownian motion parameter, thermophoresis parameter and Weissenberg number enhances the dimensionless temperature profile.     

Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet

The steady two-dimensional mixed convection flow of a micropolar fluid over a non-linear stretching sheet is investigated. The governing non-linear equations and their associated boundary conditions are transformed into coupled non-linear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy analysis method (HAM). The convergence of the obtained series solutions is carefully checked. The physical significance of interesting parameters on the flow and the thermal fields are shown through graphs and discussed in detail. The values of wall shear stress, couple wall stress and the local Nusselt number are tabulated. Comparison is also made with the corresponding results of viscous fluid with no mixed convection and an excellent agreement is noted.     

Magnetohydrodynamic flow of a viscoelastic fluid

The non-linear differential equation for the magnetohydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT) conducting fluid is derived. Using the homotopy analysis method (HAM), the series solution is developed and its convergence is discussed. Also, the results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes: Stability analysis

This work aims at evaluating the effects of magnetohydrodynamics (MHD) on the stagnation point flow along a nonlinear stretching/shrinking sheet in carbon nanotubes. Numerical methods for ordinary differential equations are obtained using the BVP4C solver in MATLAB software. Two kinds of base fluids, particularly water and kerosene, with single-walled and multi-walled carbon nanotubes are adopted in this analysis. The effect of various limitations on the Nusselt number and skin friction coefficient, as well as the temperature and velocity profiles are examined. From the numerical results, it is observed that non-unique solutions are visible for some limits of shrinking parameter. It is also found that nonlinear parameter and magnetohydrodynamic parameter act in widening the range of solution to exist. Therefore, the stability of flow was executed to identify the most stable solution between these two solutions. The stable and unstable flow of the first and second solutions, respectively, are confirmed.     

MHD stagnation point flow towards a stretching sheet

The steady two-dimensional MHD stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The governing system of partial differential equations are transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. ε>1, and the opposite is observed when ε<1.     

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

Induced magnetic field stagnation point flow of nanofluid past convectively heated stretching sheet with Buoyancy effects

This paper presents the buoyancy effects on the magneto-hydrodynamics stagnation point flow of an incompressible,viscous,and electrically conducting nanofluid over a vertically stretching sheet.The impacts of an induced magnetic field and viscous dissipation are taken into account.Both assisting and opposing flows are considered.The overseeing nonlinear partial differential equations with the associated boundary conditions are reduced to an arrangement of coupled nonlinear ordinary differential equations utilizing similarity transformations and are then illuminated analytically by using the optimal homotopy investigation strategy(OHAM).Graphs are introduced and examined for different parameters of the velocity,temperature,and concentration profile.Additionally,numerical estimations of the skin friction,local Nusselt number,and local Sherwood number are explored using numerical values.     

Magnetohydrodynamic plane Couette flow of an elasto-viscous fluid

Summary Using the Laplace transform, an analytical solution of the Navier-Stokes equation is obtained for a two-dimensional incompressible elasto-viscous fluid past between two infinite parallel walls. It is assumed that the lower wall is moving with velocity which is a function of any given free stream velocity. As an application of the solution, two cases for the stream velocity are studied.     

Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet

The approximate solution of the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.     

Soliton formations for magnetohydrodynamic viscous flow over a nonlinear stretching sheet

In the present paper, the main focus is to study soliton formations of a two-dimensional magnetohydrodynamic flow over a nonlinear stretching sheet with the help of transformed rational function method. The fluid is electrically conductive, normal to the stretching sheet and there is no induced magnetic field. The flow problem is described by the continuity and momentum equation with suitable boundary conditions. For solving the model, the nonlinearity poses a great challenge. Nonlinear partial differential equation has been converted into a nonlinear ordinary differential equation by using similarity transformations, and then a trial solution is assumed. The results indicate complete consistency and effectiveness of the suggested scheme compared with the existing literature.     

Approximate solution of the flow over a nonlinear magneto-hydrodynamic stretching sheet

The approximate solution of the magneto-hydrodynamic(MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method.The approximate solution is tabulated,plotted for the values of various parameters and compared with the known solutions.It is found that the approximate solution agrees very well with the known numerical solutions,showing the reliability and validity of the present work.     

Stability of fluid flow past a membrane

The stability of the flow of a fluid past a solid membrane of infinitesimal thickness is investigated using a linear stability analysis. The system consists of two fluids of thicknesses R and H R and bounded by rigid walls moving with velocities and , and separated by a membrane of infinitesimal thickness which is flat in the unperturbed state. The fluids are described by the Navier-Stokes equations, while the constitutive equation for the membrane incorporates the surface tension, and the effect of curvature elasticity is also examined for a membrane with no surface tension. The stability of the system depends on the dimensionless strain rates and in the two fluids, which are defined as and for a membrane with surface tension , and and for a membrane with zero surface tension and curvature elasticity K. In the absence of fluid inertia, the perturbations are always stable. In the limit , the decay rate of the perturbations is O(k ³ ) smaller than the frequency of the fluctuations. The effect of fluid inertia in this limit is incorporated using a small wave number asymptotic analysis, and it is found that there is a correction of smaller than the leading order frequency due to inertial effects. This correction causes long wave fluctuations to be unstable for certain values of the ratio of strain rates and ratio of thicknesses H. The stability of the system at finite Reynolds number was calculated using numerical techniques for the case where the strain rate in one of the fluids is zero. The stability depends on the Reynolds number for the fluid with the non-zero strain rate, and the parameter , where is the surface tension of the membrane. It is found that the Reynolds number for the transition from stable to unstable modes, , first increases with , undergoes a turning point and a further increase in the results in a decrease in . This indicates that there are unstable perturbations only in a finite domain in the plane, and perturbations are always stable outside this domain. Received: 29 May 1997 / Revised: 9 October 1997 / Accepted: 26 November 1997     

Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet

We examine the problem of flow and heat transfer in a second grade fluid over a stretching sheet [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)]. The equations considered by Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)], are found to be incorrect in the literature. In this paper, we not only corrected the equation but found a useful analytic solution to this important problem. We also extended the problem for hydromagnetic flow and heat transfer with Hall effect. The explicit analytic homotopy solution for the velocity field and heat transfer are presented. Graphs for the velocity field, skin friction coefficient, and rate of heat transfer are presented. Tables for the skin friction coefficient and rate of heat transfer are also presented. The convergence of the solution is also properly checked and discussed.     

Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet

The problem of flow and heat transfer of an electrically conducting viscoelastic fluid over a continuously stretching sheet in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the sheet temperature. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature. The basic equations comprising the balance laws of mass, linear momentum, and energy modified to include the electromagnetic force effect, the viscous dissipation, internal heat generation or absorption and work due to deformation are solved numerically.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species

This article looks at the mass transfer of the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid past a porous shrinking sheet in the presence of chemical reaction. The resulting nonlinear partial differential equations are reduced to the system of nonlinear ordinary differential equations by means of similarity transformations. Expressions of velocity and the concentration fields are obtained using the homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly discussed. The influences of sundry parameters on the velocity and the concentration fields are made and discussed in detail. The values of the skin friction coefficient and the surface mass transfer for various interesting parameters are also tabulated.