MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

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.     

Transient response behavior of an axisymmetric stagnation flow on a circular cylinder due to time dependent free stream velocity

An analysis is presented to investigate the unsteady response behavior of an axisymmetric stagnation flow on a circular cylinder due to transient free stream velocity. The governing boundary layer equations are integrated by the steepest descent method. Numerical results have been presented for the unsteady wall stress by assuming explicit time dependent forms for the free stream velocity.     

Unsteady compressible boundary layer swirling flow in a nozzle and a diffuser

This paper presents the results of the study of unsteady swirling boundary-layer flow of compressible fluid in a nozzle and a diffuser when the free stream velocity, mass transfer and wall temperature vary arbitrarily with time. The set of coupled nonlinear partial differential equations governing the flow which involves three independent variables has been solved numerically using an implicit finite-difference scheme. Both the heat transfer and skin friction are strongly affected by the free stream velocity, variation of the density-viscosity product across the boundary layer, mass transfer and swirl parameter. However, the variation of the wall temperature with time strongly affects only the heat transfer. Also, separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction.     

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.     

An asymptotic analysis of free convection boundary layer on a horizontal flat plate due to small fluctuations in surface temperature

Unsteady free convective boundary layer flow, over a semi-infinite horizontal plate is analysed when the plate temperature oscillates with a non-zero mean, the free stream being at rest. The method of matched asymptotic expansions is employed to solve the singular perturbation problem revealing the existence of four distinct oscillating layers at large distances from the leading edge of the plane surface. It is found that the asymptotic values far downstream are approached through damped oscillations.     

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.     

Self similar unsteady boundary layers

Summary This paper deals with unsteady laminar boundary layers contiguous to self-similar flows. The following general result is obtained: when the self-similar structure of the external flow is apparent in the boundary layer system of coordinates, and when there is no heat transfer through the wall, then the boundary layer is self-similar too. This property can be applied to a lot of known self-similar motions. Some examples are considered for which the final form of the boundary layer equations is formulated.     

Unsteady compressible flow in the stagnation region of two-dimensional and axi-symmetric bodies

Summary This paper deals with a new similarity solution of unsteady laminar compressible two-dimensional and axi-symmetric boundary layers. It has been shown that a self-similar solution is possible when the free stream velocity varies inversely with time. The two-point boundary value problems governed by self-similar equations have been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. It is observed that the effect of the acceleration parameter (A) in the free stream velocity on the skin friction is more pronounced compared to the heat transfer. For certain values of the acceleration parameter and the total enthalpy at the wall, the surface shear stress (skin friction) vanishes. The skin friction and heat transfer increase due to suction, and the effect of injection is found to be just opposite. Velocity profiles are presented with reverse flow and without reverse flow depending on the values of toal enthalpy at the wall and the acceleration parameter.     

Unsteady nonsimilar compressible boundary layer flow over a rotating sphere

Summary The problem of determining the development of the nonsimilar viscous compressible boundary layer flow with time over a rotating sphere is considered when both free stream velocity and rotation vary arbitrarily with time. Variations of skin friction, heat transfer and displacement thickness with mass injection, rotation, wall enthalpy and time are discussed.     

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.     

Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.     

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.     

Micropolar boundary layer flow at a stagnation point on a moving wall

The theory of micropolar fluids due to Eringen is used to formulate a set of boundary layer equations for 2-dimensional flow of an incompressible, constant density micropolar fluid at a stagnation point on a moving wall. The governing boundary layer equations are solved numerically. The development of the velocity of distribution has been illustrated for several positive and negative values of the wall velocity. A discussion is provided for the dependence of the important flow characteristics on the material parameters.     

The effect of transpiration on self-similar boundary layer flow over moving surfaces

The simultaneous effects of normal transpiration through and tangential movement of a semi-infinite plate on self-similar boundary layer flow beneath a uniform free stream is considered. The flow is therefore governed by a plate velocity parameter λ and a transpiration parameter μ and the computed wall shear stress parameter is f″(0). Dual solutions are found for each value of μ in λ–f″(0) parameter space. It is shown that the range of known dual solutions for zero transpiration increases with suction and decreases with blowing. A stability analysis for this self-similar flow reveals that, for each value of μ, lower solution branches are unstable while upper solution branches are stable.     

Unsteady compressible 3-dimensional boundary-layer flow near an asymmetric stagnation point with mass transfer

The heat and mass transfer for unsteady laminar compressible boundary-layer flow, which is asymmetric with respect to a 3-dimensional stagnation point (i.e. for a jet incident at an angle on the body), have been studied. It is assumed that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time and also that the gas has variable properties. The solution in the neighbourhood of the stagnation point has been obtained by series expansion in the longitudinal distance. The resulting partial differential equations have been solved numerically using an implicit finite-difference scheme. The results show that, in contrast with the symmetric flow, the maximum heat transfer does not occur at the stagnation point. The skin-friction and heat-transfer components due to asymmetric flow are only weakly affected by the mass transfer as compared to those components associated with symmetric flow. The variation of the wall temperature with time has a strong effect on the heat transfer component associated with the symmetric part of the flow. The skin friction and heat transfer are strongly affected by the variation of the density-viscosity product across the boundary layer. The skin friction responds more to the fluctuations of the free stream oscillating velocities than the heat transfer. The results have been compared with the available results and they are found to be in excellent agreement.     

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

A perturbation solution for the Laminar boundary layer on a continuous moving surface

Summary A perturbation solution is presented for the nonsimilar boundary layer flow past a moving surface with constant wall velocity. A zero pressure gradiant is assumed and the tangential velocity and stagnation enthalpy profiles are prescribed at the initial station. The eigen values obtained for the first order perturbation solution are integers and the eigen functions are the derivatives of the error function. The same Green's function is obtained for all the higher order perturbation equations, and the higher order perturbation solutions are given in integral form in terms of the Green's function. The analyses include both the momentum equation and the energy equation which is uncoupled with the momentum equation, and which is subjected to a nonsimilar velocity flow field.     

Parametric method of calculating an unsteady laminar boundary layer in an incompressible liquid with suction or injection

The equation for the unsteady boundary layer at a porous wall is reduced with the help of three series of parameters to a universal form not containing explicitly either the velocity at the outer edge of the boundary layer or the velocity of suction or injection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 4, pp. 698–703, October, 1976.     

湍流边界层激励下加筋平板振声响应特性研究

船舶、汽车和飞机等高速运动时,其外壳受湍流边界层壁面脉动压力激励而产生的内场声辐射成为该类交通工具自噪声的重要成分。基于模态叠加法计算结构振动响应。采用湍流壁面脉动压力功率谱Corcos模型,计算了外侧气流或水流湍流边界层激励下简支平板振动及内场辐射声,计算值与解析解和试验值吻合良好,验证了算法的有效性。采用湍流壁面脉动压力功率谱改进型Corcos模型,研究了外侧水流湍流边界层激励下平板及板格的振声响应特性,结果表明:水流马赫数低,壁面脉动压力迁移波数大于平板结构弯曲波数,壁面脉动压力波数-频率谱的迁移脊对平板的激励作用可以忽略;横向或纵向加筋对板格振动速度自功率谱级基本无影响;减小板格宽度与长度之比,适当增大板格流向长度可使平板振动辐射声功率在2 000 Hz以上明显降低。