MHD flow of power-law fluid on moving surface with power-law velocity and special injection/blowing

The problem of magnetohydrodynamic （MHD） flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differen- tial equations. The skin friction coefficients of the MHD boundary layer flow are derived, and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method （HAM）. The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter, and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.     

Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

Boundary layer flow over a moving surface in a nanofluid with suction or injection

An analysis is performed to study the heat transfer characteristics of steady two-dimensional boundary layer flow past a moving permeable flat plate in a nanofluid. The effects of uniform suction and injection on the flow field and heat transfer characteristics are numerically studied by using an implicit finite difference method. It is found that dual solutions exist when the plate and the free stream move in the opposite directions. The results indicate that suction delays the boundary layer separation, while injection accelerates it.     

Flow past a plate with a moving surface

On the basis of a numerical solution of the unsteady Navier-Stokes equations, the flow past a finite plate with an upstream-moving surface is investigated. For the Reynolds numbers Re =10²−10⁴, the flow past the plate is analyzed as a function of the relative plate surface velocity. On the basis of this analysis a limiting mathematical model of the flow as Re → ∞ is proposed.     

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.     

Axisymmetric stagnation point flow and mass transfer for power-law fluids

The boundary-layer equations for axisymmetric stagnation point flow of a power-law fluid are solved by a similarity transformation, and values of the wall shear rate are obtained. Theoretical expressions for local and average Sherwood numbers are derived from the convective diffusion equation for systems with high Schmidt numbers. The results can be used to predict diffusion coefficients of dilute species in fluids with specified power-law characteristics.     

Stability analysis of gravity driven shear flows with free surface for power-law fluids

Summary We study the stability of thin films of fluids subject to gravity along inclined planes, obeying a power-law constitutive relation of the Ostwald-de Waele type. A first analysis, in which the inertia terms are ignored, shows such flow to be stable against small, linear perturbations; a second analysis, in which the inertia terms are included, proves that there are stable and unstable regimes that are separated by a critical Ostwald-de Waele number O. Numerical computations for selected values of O demonstrate the decay and growth rate behavior of some finite amplitude disturbances. Received 12 May 1997; accepted for publication 23 July 1997     

Nonlinear hydromagnetic flow and heat transfer over a surface stretching with a power-law velocity

 Nonlinear hydromagnetic flow and heat transfer over a surface stretching with a power-law velocity is analysed. A special form of the magnetic field is chosen to obtain similarity equations. Resulting equations are numerically solved using Runge–Kutta shooting method. Values of skin-friction and rate of heat transfer are obtained and the effect of magnetic field, stretching parameter and Prandtl number over these are discussed. Received on 2 May 2001 / Published online: 29 November 2001     

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–24, September–October, 1986.     

Heat transfer to a continuous moving flat surface with variable wall temperature

Transient heat transfer from a continuous moving flat surface with varying wall temperature is studied. Numerical results are presented for the transient temperature profiles and heat transfer rates from the wall for Prandtl numbers varying from 0.01 to 1000. Asymptotic solutions for steady state heat transfer rates for large Prandtl number are also presented.     

MHD Flow and heat transfer of non-Newtonian power-law fluid with diffusion and chemical reaction on a moving cylinder

The problem of flow and heat transfer of an electrically conducting non-Newtonian fluid over a continuously moving cylinder in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the temperature and concentration at the cylinder surface. A diffusion equation with a chemical reaction source term is taken into account. The governing non-similar partial differential equation are solved numerically by employing shooting method. The effects of various parameters on the velocity, temperature and concentration profiles as well as the heat and mass transfer rate from the cylinder surface to the surrounding fluid are presented graphically and in tabulated form.     

Moving wedge and flat plate in a power-law fluid

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving wedge in a moving fluid is studied in this paper. The transformed boundary-layer equation is solved numerically for some values of the involved parameters. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that multiple solutions exist when the wedge and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids.     

Asymptotic structure of unsteady flow over a semi-infinite plate with a moving surface

Laminar incompressible flow over a semi-infinite flat plate, whose surface moves counter to the oncoming stream, is considered. The asymptotic flow structure is investigated and a numerical solution of the time-dependent Navier-Stokes equations is obtained.     

Effect of boundary layer on Mach reflection over a wedge surface

Abstract. In this paper, we consider the phenomenon of unsteady Mach reflection generated by a plane shock wave advancing over a straight wedge surface, with particular attention to the deviation of the flow field from the self-similar nature. We examine the observed change in angle between incident and reflected shocks, which is in contrast to the fact that the angle should remain constant with time in a self-similar flow. The effect of the boundary layer behind the advancing shock wave over the surface of the wedge is considered to cause this, and boundary layer theory is utilized to estimate the thickness of the layer. It is found that the thickness increases as to the time t compared with t by the overall expansion in the self-similar flow. Assuming that the thicker boundary layer is effectively equivalent to a change in wedge angle, the effect of the boundary layer on the flow field should be less in later stages with larger t values in accordance with the observation above. Received 6 March 2000 / Accepted 23 April 2001     

Drag reduction of a nonnewtonian fluid by fluid injection on a moving wall

Summary A boundary layer problem of a nonnewtonian fluid flow with fluid injection on a semi-infinite flat plate whose surface moves with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. Concluding similarity equations are solved numerically to show the dependence of the problem to the velocity ratio λ of the plate to uniform flow and to the injection velocity parameter C. The critical values of λ and C for each nonnewtonian power-law index n are obtained, and their significance in drag reduction is discussed. Received 26 August 1997; accepted for publication 21 October 1998     

Non-Newtonian flow over a wedge with suction

A pseudo-similarity solution is obtained for the flow of an incompressible fluid of second grade past a wedge with suction at the surface. The non-linear differential equation is solved using quasi-linearization and orthonormalization. The numerical method developed for this purpose enables computation of the flow characteristics for any values of the parameters K, a and b, where K is the dimensionless normal stress modulus of the fluid, a is related to the wedge angle and b is the suction parameter. A significant effect of suction on the wall shear stress is observed. The present results match exactly those from an earlier perturbation analysis for Kx^2a ? 0·01 but differ significantly as Kx^2a increases.