Steady Boundary Layer Equations Research Articles

Numerical Simulation of Slip Flow and Heat Transfer of Biomagnetic Fluid over a Stretching Sheet in the Presence of a Magnetic Dipole with Temperature Dependent Viscosity

The study of flow and heat transfer of biomagnetic fluid past a stretching sheet has a significant importance in a number of bio-medical and engineering applications including cancer treatment, drug delivery, magnetic resonance imaging, reducing blood flow during surgeries etc. Owing to these applications, the aim of the present paper is to study an electrically non-conducting Newtonian biomagnetic fluid in the presence of a magnetic dipole over an extendable sheet subject to velocity slip. The governing steady boundary layer equations with the help of similarity transformations were converted into a set of highly non-linear ordinary differential equations which are then computationally solved by applying the bvp4c function technique in MATLAB software. The results show that blood velocity and temperature can remarkably be influenced by the variation of ferromagnetic parameter. As the ferromagnetic parameter increases, the rate of heat transfer of blood is increased while coefficient of skin friction is reduced. We hope that this study could be useful in cancer treatment as well as in drug administration.

Convection from a semi-finite plate in a fluid saturated porous medium with cross-diffusion and radiative heat transfer

The heat and mass transfer characteristics in mixed convection along a semi-infinite plate in a fluid saturated porous medium with radiative heat transfer has been investigated. Diffusion-thermo and thermo-diffusion effects are assumed to be significant. Using a similarity transformation, the governing steady boundary layer equations for the momentum, heat and mass transfer were reduced to a set of ordinary differential equations and then solved using a recent novel linearization method and the Keller-box method. The results were further confirmed by using the Matlab bvp4c numerical routine. The effects of the Dufour and Soret parameters on the local skin friction and the local heat and mass transfer rates are investigated. Numerical results for the velocity and the temperature profiles are also presented. Key words: Vertical flat plate, porous medium, cross diffusion, radiation, successive linearization method.

Thin Film Flow of a Second Grade Fluid over a Stretching/Shrinking Sheet with Variable Temperature-Dependent Viscosity

Effects of variable viscosity on the flow and heat transfer in a thin film on a horizontal porous stretching sheet are analyzed. The steady boundary layer equations for momentum and thermal energy are simplified by using similarity transformations. The resulted and coupled nonlinear differential equations are solved by Homotopy analysis method. The results are presented graphically to interpret various physical parameters appearing in the problem.

Series solutions of unsteady MHD flow of a non-newtonian fluid near the forward stagnation point

Unsteady flow of a viscous incompressible electrically conducting non-Newtonian power- law fluid near the forward stagnation point of a two-dimensional body in the presence of a magnetic field is studied by means of an analytic technique, namely, the homotopy analysis method. Accurate analytic approximations are obtained, which are uniformly valid for all dimensionless time in the whole region 0 ≤ η< ∞. Effects of integral power- law index of the non-Newtonian fluids for κ =1 , 2, 3 and magnetic number M ≤ 10 on the flow are considered. To the best of authors' knowledge, such kinds of analytic solutions have been never reported. Introduction. Non-Newtonian fluids are very important fluids, which are widely used in industry. Most particulate slurries (china clay and coal in water, sewage sludge, etc.), multiphase mixtures (oil-water emulsions, gas-liquid disper- sions, such as froths and foams, butter) are non-Newtonian fluids. Further exam- ples, including a variety of non-Newtonian characteristics, include pharmaceutical formulations, cosmetics and toiletries, paints, synthetic lubricants, biological fluids (blood, synovial fluid, saliva), and foodstuffs (jams, jellies, soups, marmalades). Indeed, behaviours of the non-Newtonian fluids are so widespread that it would be no exaggeration to say that the Newtonian fluid behaviours are an exception rather than the rule. Since the non-Newtonian fluids have more complicated equa- tions that relate the shear stresses to the velocity field than the Newtonian fluids have, additional factors must be considered in examining various fluid mechanics (see, Irvine and Karni (1)). Several models have been proposed to describe the non-Newtonian behaviour of fluids. Among these models, which are known to follow the empirical Ostwaald- de Waele model, the so-called power-law model, in which the shear stress varies according to a power function of the strain rate, has received wide acceptance. Boundary layer assumptions were successfully applied to this model and much work has been done on it. Schowalter (2) and Acrivos et al. (3) initially theoretically analyzed the steady boundary layer flow of incompressible non-Newtonian power- law fluids and found the existence of the similarity solutions. Kim et al. (4) made a detailed analysis to obtain possible similarity solutions of the steady boundary layer equations of a non-Newtonian fluid. Yukselen and Erim (5) considered the curvature effects on the boundary layer of a non-Newtonian fluid. Thompson and Snyder (6), and Kim and Eraslan (7) investigated the effect of wall mass injection on the flow of a non-Newtonian power-law fluid over a flat plate, near a stagnation point and past a wedge. Akcay and Yukselen (8) analyzed the boundary layer of a non-Newtonian fluid flow with fluid injection on a semi-infinite flat plate, which moves with a constant velocity in the direction opposite to that of the

Stability Analysis of Natural Convection Evolving Along a Vertical Heated Plate

Natural convection evolving along a vertical flat plate is considered under (i) isothermal and (ii) uniform-heat-flux plate boundary conditions. Basic flow is assumed to be governed by steady boundary-layer equations. Linear and weakly-nonlinear stability analyses of the basic flow are made with the aid of the Galerkin method in which the field variables are expanded in terms of Chebyshev polynomials. The Stewartson-Stuart equation for the two-dimensional propagating disturbance is derived and its stability is examined for the cases of the Prandtl number P r = 0.733 (air) and P r = 6.7 (water). The main results are such that (i) the motion is supercritical over almost all the linearly unstable region except for a narrow boundary region defined by small wavenumbers; (ii) Huerre's criterion shows that the motion is convectively unstable along the most highly amplified path over the whole computed range of the Reynolds number; (iii) Newell's criterion shows that the motion tends to be modulationally unstable...

Integral transform method for boundary layer equations in simultaneous heat and fluid flow problems

The two‐dimensional steady boundary layer equations, for simultaneous heat and fluid flow within ducts, are handled through the generalized integral transform technique. The momentum and energy equations are integral transformed by eliminating the transversal coordinate and reducing the PDE’s into an infinite system of coupled non‐linear ordinary differential equations for the transformed potentials. An adaptively truncated version of this ODE system is numerically handled through well known initial value problem solvers, with automatic precision control procedures. The explicit inversion formulae are then recalled to provide analytic expressions for velocity and temperature fields and related quantities of practical interest. Typical examples are presented in order to illustrate the hybrid numerical analytical approach and its convergence behaviour.

Behavior of an Approximate Solution for Laminar Boundary Layer Equations and a Separation Flow Field.

The behavior of an approximate solution of the steady boundary layer equations for two-dimensional incompressible flows is clarified. The moment equations are derived from boundary layer equations as an improvement of the Karman-Pohlhausen method. By means of these results, a simple procedure to construct the boundary layer flow field (including separation flow) with an arbitrarily given retarded outer flow is proposed.

Collision phenomena in free-convective flow over a sphere

Two types of singularity that occur at the upper pole of a heated sphere in a fluid at rest when the Grashof number is large are discussed. The first is a property of a limit solution of the unsteady boundary-layer equations and is indicative of the fact that the boundary layer growing from the lower pole does not remain empty for all time but erupts into a plume above the sphere. The second arises from a solution of the steady boundary-layer equations and illustrates the phenomenon of an axisymmetric boundary layer converging at a point, with a velocity component parallel to the sphere that is non-zero over the major part of the boundary layer. An analysis is prcscnted for each situation and comparison made with a numerical integration of the appropriate equations.

Numerical prediction of incompressible separation bubbles

A method is presented for performing detailed computations of thin incompressible separation bubbles on smooth surfaces. The analysis consists of finite-difference solutions to the time-dependent boundary-layer or Navier-Stokes equations for the flow in the immediate vicinity of the bubble. The method employs the McDonald-Fish turbulence model, to predict the development of the time-mean flow field, as influenced by the free-stream turbulence level. It also employs a viscous-inviscid interaction model, which accounts for the elliptic interaction between the shear layer and inviscid free stream. The numerical method is based on an alternating-direction implicit scheme for the vorticity equation. It employs transformations, to allow the free-stream boundary to change in time with the shape of the computed shear layer, and to ensure an adequate resolution of the sublayer region. Numerical solutions are presented for transitional bubbles on an NACA 663-018 airfoil at zero angle of incidence with chordal Reynolds numbers of 2·0 × 106 and 1·7 × 106. These have a qualitative behaviour similar to that observed in numerous experiments; they are also in reasonable quantitative agreement with available experimental data. Little difference is found between steady solutions of the boundary-layer and Navier-Stokes equations for these flow conditions. Numerical studies based on mesh refinement suggest that the well-known singularity at separation, which is present in conventional solutions of the steady boundary-layer equations when the free-stream velocity is specified, is effectively removed when viscous-inviscid interaction is allowed to influence the imposed velocity distribution.

Aspects of ’’multitime initial-value problem’’ originating from boundary layer equations

Three‐dimensional steady boundary layer equations are considered as a model case of a more general class of problems called ’’multitime initial‐value problem’’ for a parabolic system. Ideas developed in recent years for solving three‐dimensional steady boundary layers are generalized for application to other similar problems, such as unsteady two‐dimensional boundary layers. An unsteady counterpart of the wedge‐shaped zones of influence and dependence is defined and then used to rationalize the calculation of reversed flow in two‐dimensional unsteady case. Schemes used previously for the latter flow are re‐examined in light of this dependence rule, and it is found that these schemes could satisfy such a rule.

Ignition of Stagnation Point Flow by a Hot Body

Abstract The ignition of a cold combustible mixture has been investigated at the forward stagnation region of a hot projectile. The occurrence of temperature maxima at the surface of the projectile acts as the ignition criterion. For quasi-stationary analysis, the characteristic (unknown) parameter of the problem is the surface (or ignition) temperature. The steady boundary layer equations describing the reacting flow have been solved numerically and the ignition temperatures for propane-air mixture are calculated for different values of the various non-dimensional physical parameters.