Nonsimilar second order viscoelastic boundary layer flow at a stagnation point over a moving wall

An analysis is presented to investigate the fluid dynamic characteristics of a steady, laminar second order viscoelastic boundary layer flow at a two-dimensional stagnation point over a moving wall. The governing boundary layer equations have been solved by means of a series solution approach. Numerical solutions for the series functions have been given in tabular form. The development of the velocity distribution has been illustrated for several positive and negative values of the wall velocity. The values of the Weissenberg numbers ranged from 0 to 0.3.     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.     

Heat transfer in a second order viscoelastic boundary layer flow at a stagnation point

The steady and transient heat transfer characteristics of a second order viscoelastic boundary layer flow at a stagnation point have been studied in this paper. The implicit cubic spline numerical procedure is used to solve the governing boundary layer equations. The details of the temperature profiles and wall heat flux rates have been graphically illustrated. The range of values of the Prandtl number was from 5 to 1000 while the Weissenberg number was varied from 0.1 to 0.3.     

Heat transfer in micropolar boundary layer flow near a stagnation point

Using the micropolar theory, a set of boundary layer equations are obtained for the two dimensional flow of an incompressible micropolar fluid near a stagnation point. The boundary conditions of isothermal and insulated wall are taken with VISCOUS DISSIPATION effects. Numerical results for the temperature distribution has been shown graphically for different values of the material parameters and Prandtl number.     

Effect of large blowing rates on the compressible boundary layer flow at the stagnation point of a rotating sphere

Summary The effect of a large surface blowing (injection) rate on the steady laminar compressible boundary-layer flow at the forward stagnation point of a rotating sphere has been studied. The resulting coupled nonlinear ordinary differential equations have been solved using two methods, namely, the method of matched asymptotic expansion and the implicit finite difference scheme in combination with the quasilinearization technique. It is found that the boundary layer thickness increases considerably with the blowing rate. The location of the dividing streamline moves away from the surface with increasing blowing rates, but moves towards the surface when the total enthalpy at the wall or the rotation parameter increases. For large blowing rates and small rotation parameter the surface heat transfer and the surface shear stress in the tangential direction tend to zero, but the longitudinal shear stress remains finite but small. Also, for this case, the longitudinal shear stress at the wall is approximately found to be directly proportional to the sum of the total enthaply at the wall and to the square of the rotation parameter and inversely proportional to the blowing rates. The rotation parameter induces overshoot in the longitudinal velocity, and the magnitude of the velocity overshoot increases significantly with rotation and blowing parameters. However, there is no overshoot in the longitudinal velocity in the absence of rotation whatever may be the values of the blowing parameter.     

Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface

The growth of the boundary-layer flow of a micropolar fluid started impulsively from rest near the forward stagnation point of a two-dimensional plane surface is studied theoretically. The transformed non-similar boundary-layer equations are solved numerically using a very efficient finite-difference method known as Keller-box method. This method may present well-behaved solutions for the transient (small time) solution and those of the steady-state flow (large time) solution. Numerical results are given for the reduced velocity and microrotation profiles, as well as for the skin friction coefficient when the material parameter K takes the value K=0 (Newtonian fluid), 0.5, 1, 1.5, 2, 2.5 and 3. Important features of these flow characteristics are shown on graphs and in tables.     

Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the $\text{y-}\text{wise}$ velocity profile, and overshoot in the $\text{x-}\text{wise}$ velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.     

Three-dimensional stagnation point flow of a second grade fluid towards a moving plate

The problem dealing with the steady three-dimensional flow of a second grade fluid near the stagnation point of an infinite plate moving parallel to itself with constant velocity has been investigated. By using the appropriate transformations for the velocity components and temperature, the basic equations governing flow and heat transfer have been reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions by employing a numerical technique. The effect of a nondimensional elastic parameter on the velocity components, wall shear stress, temperature and heat transfer has been examined carefully.     

Nonsimilar axisymmetric stagnation flow on a moving cylinder

An analysis is presented to investigate the fluid dynamic characteristics of an axisymmetric stagnation flow on a moving circular cylinder. The governing boundary layer equations have been solved numerically. The range of Reynolds numbers considered was from 0.01 to 100. The development of the velocity distribution has been illustrated for various positive and negative values of the wall velocity.     

Annular axisymmetric stagnation flow on a moving cylinder

Fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. Using similarity transform, the Navier-Stokes equations reduce to a set of nonlinear ordinary differential equations, which are integrated numerically. Asymptotic solutions for large and small cross-flow Reynolds numbers and small gap widths are also found. Drag, torque and heat transfer on the moving rod are determined. The problem is particularly important in pressure-lubricated bearings.     

Series solutions of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface

Summary In this paper, the unsteady boundary-layer flow of a micropolar fluid started impulsively from rest near the forward stagnation point of a two-dimensional plane surface is studied by means of an analytic approach, namely homotopy analysis method. This approach gives accurate approximations uniformly valid for all dimensionless time. Besides, analytic results are given for the reduced velocity and microrotation profiles, as well as for the skin friction coefficient when the material parameter K takes the value K=0 (Newtonian fluid), 1, 3, 5 and 10. To the best of our knowledge, such a kind of series solutions has been never reported.     

Unsteady mixed convection flow at the stagnation point

The unsteady mixed convection flow of an electrically conducting fluid at the stagnation point of a two-dimensional body and an axisymmetric body in the presence of an applied magnetic field has been studied. The effect of induced magnetic field has been included in the analysis. Both prescribed wall temperature and prescribed heat flux conditions have been considered. It is found that if the free stream velocity, applied magnetic field and square root of the wall temperature vary inversely as a linear function of time, i.e. as (1 − λt′)⁻¹, the governing boundary layer equations admit a locally self-similar solution. If surface heat flux is prescribed, it should vary as (1 − λt^*)^−5/2 for the existence of a local self-similar solution. The resulting ordinary differential equations have been solved using a finite element method as well as a shooting method with Newton's corrections for missing initial conditions. The skin friction and heat transfer coefficients and x-component of the induced magnetic field on the surface increase with the applied magnetic field or buoyancy force. Also they are found to change more for decelerating free stream velocity than for accelerating free stream velocity. Furthermore, they change little with the reciprocal of the magnetic Prandtl number. The buoyancy parameter causes overshoot in the velocity profile. For a given Prandtl number, beyond a certain critical value of the dissipation parameter, the hot wall ceases to be cooled due to the “heat cushion” provided by frictional heat.     

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

Summary The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.With 14 Figures     

On extra boundary condition in the stagnation point flow of a second grade fluid

The two dimensional stagnation point flow of a second grade fluid is considered. The flow is governed by a boundary value problem in which the order of differential equations is one more than the number of available boundary conditions. It is shown that without augmenting the boundary conditions at infinity it is possible to obtain a numerical solution of the problem for all values of K, where K is the dimensionless viscoelastic fluid parameter. The numerical results using the algorithm foreshadow an asymptotic behavior for large K. The asymptotic solution is derived up to terms of O(K⁻¹). Perturbation solutions are also obtained up to the terms of O(K²). Finally an approximate solution is developed, based on stretching of the independent variable and minimizing the residual of the differential equation in the least square sense. All these solutions are compared with the exact numerical solution and the appropriate conclusions are drawn.     

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Summary Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.