Wave propagation in a mixed convection boundary‐layer over a horizontal surface

The propagation of disturbances in a mixed convection boundary‐layer flow over a horizontal plate is described by a triple deck problem in the case of the buoyancy parameter being small. The pressure correction in the lower deck consists of two parts: One due to the buoyancy effects in the main deck and one due to the displacement of the outer flow field. The response of the boundary layer flow to an oscillator of frequency ω will be computed and upstream travelling waves will be identified.     

Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.     

Mixed convection on a vertical circular cylinder

The problem of the mixed convection boundary-layer flow past an isothermal vertical circular cylinder is considered in both the cases when the buoyancy forces aid and oppose the development of the boundary layer. A series solution is obtained, valid near the leading edge, and this is extended by a numerical solution of the full equations, which in the aiding case, becomes inaccurate downstream. An approximate solution is also derived which gives a good estimate for the heat transfer near the leading edge and has the correct asymptotic form well downstream. In the opposing case, the boundary layer is seen to separate at a finite distance downstream, with, for moderate values of the buoyancy parameter, the numerical solution indicating a regular behaviour near separation.     

Non-Darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in a porous medium with thermal radiation and variable viscosity

The unsteady mixed convection boundary layer flow near the stagnation point on a heated vertical plate embedded in a fluid saturated porous medium is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature. Both the buoyancy assisting and the buoyancy opposing flow situations are considered with combined effects of the first and second order resistance of solid matrix of non-Darcy porous medium, variable viscosity and radiation. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. The features of the flow and the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The surface shear stress and the heat transfer of the present study are compared with the available results and a good agreement is found.     

The Trailing Edge Problem For Mixed Convection Flow Past a Horizontal Plate

The influence of buoyancy onto the boundary‐layer flow past a horizontal plate aligned parallel to a uniform free stream is characterized by the buoyancy parameter K = Gr/Re^5/2 where Gr and Re are the Grashof and Reynolds number, respectively. An asymptotiy analysis of the complete flow field including potential flow, boundary layer, wake and interaction region is given for small buoyancy parameters and large Reynolds numbers in the distinguished limit KRe^1/4 = O(1). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates

Non-similar solution of a steady mixed convection flow over a horizontal flat plate in the presence of surface mass transfer (suction or injection) is obtained when there is power-law variation in surface temperature. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A non-similar mixed convection parameter is considered which covers the whole convection regime, namely from pure free convection to pure forced convection. Numerical results are reported here to account the effects of Prandtl number, surface temperature, surface mass transfer parameter (suction or injection) on velocity and temperature profiles, and skin friction and heat transfer coefficients.     

Similarity solutions for mixed convection boundary layer flow over a permeable horizontal flat plate

The effects of suction and injection on steady laminar mixed convection boundary layer flow over a permeable horizontal flat plate in a viscous and incompressible fluid is investigated in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction and injection parameter f₀, the constant exponent n of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using a finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the reduced local Nusselt number, and the velocity and temperature profiles are obtained for various values of the parameters considered. Dual solutions are found to exist for the opposing flow.     

Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes

This work presents nonsimilar boundary layer solutions for double-diffusion natural convection near a sphere with constant wall heat and mass fluxes in a micropolar fluid. A coordinate transformation is employed to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. Higher vortex viscosity tends to retard the flow, and thus decreases the local convection heat and mass transfer coefficients, raising the wall temperature and concentration. Moreover, the local convection heat and mass transfer coefficients near a sphere in Newtonian fluids are higher than those in micropolar fluids.     

MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, f_w. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, Ri (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of Ri determines the effect of the magnetic parameter on the momentum and heat transfer.     

MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect

The effects of temperature dependent viscosity and non-uniform heat source/sink on non-Darcy MHD mixed convection boundary layer flow over a vertical stretching sheet embedded in a fluid-saturated porous media is studied in this paper. Boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge-Kutta-Fehlberg method with shooting technique for various values of the governing parameters. The effects of variable viscosity, porosity, electric field parameter, non-uniform heat source/sink parameters, Soret number and Schmidt number on concentration profiles are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for variation of the local Sherwood number with buoyancy parameter, Schmidt number, and Soret number are reported graphically to show some interesting aspects of the physical parameters.     

Mixed convection similarity solutions on a horizontal surface

The mixed convection boundary layer on a horizontal plate is considered for the two separate cases when there is a uniform free stream with the plate held fixed and when there is no outer flow but the plate is moving continuously with a uniform velocity along its length. In both cases we assume that power law temperature distribution on the plate which enables the governing equations to be reduced to similarity form. For the first problem we consider the range of buoyancy parameter for which there are dual solutions, showing how these dual solutions arise from a bifurcation and how the lower branch of solutions terminate as the buoyancy parameter tends to zero. For the second problem we show that there is a unique solution for all positive values of the buoyancy parameter and that for negative values the solution terminates at a singular solution with algebraic decay.

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Zusammenfassung Die Grenzschicht an einer horizontalen Platte mit gemischter Konvektion wird für zwei Fälle untersucht: Für eine ruhende Platte bei gleichförmiger Außenströmung und für eine Platte, die sich kontinuierlich mit konstanter Geschwindigkeit in ihrer eigenen Ebene bewegt, ohne Außenströmung. Für beide Fälle wählen wir ein Potenzgesetz für die Temperaturverteilung entlang der Wand, für welche die Grundgleichungen eine Ähnlichkeitslösung zulassen. In der ersten Problemstellung betrachten wir einen Bereich des Auftriebsparameters, für den zweifache Lösungen existieren. Wir zeigen, wie diese doppelten Lösungen aus einer Bifurkation entstehen und wie der untere Lösungszweig endet, wenn der Auftriebsparameter gegen Null strebt. Für die zweite Problemstellung zeigen wir, daß eine eindeutige Lösung existiert für alle positiven Werte des Auftriebsparameters und daß für negative Werte eine singuläre Lösung mit algebraischem Zerfall erreicht wird.

     

The Small Vorticity Nonlinear Critical Layer for Kelvin Modes on a Vortex

We consider in this paper the propagation of neutral modes along a vortex with velocity profile being the radial coordinate. In the linear stability theory governing such flows, the boundary in parameter space separating stable and unstable regions is usually comprised of modes that are singular at some value of r denoted r_c , the critical point. The singularity can be dealt with by adding viscous and/or nonlinear effects within a thin critical layer centered on the critical point. At high Reynolds numbers, the case of most interest in applications, nonlinearity is essential, but it develops that viscosity, treated here as a small perturbation, still plays a subtle role. After first presenting the scaling for the general case, we formulate a nonlinear critical layer theory valid when the critical point occurs far enough from the center of the vortex so that the vorticity there is small. Solutions are found having no phase change across the critical layer thus permitting the existence of modes not possible in a linear theory. It is found that both the axial and azimuthal mean vorticity are different on either side of the critical layer as a result of the wave–mean flow interaction. A long wave analysis with O (1) vorticity leads to similar conclusions.     

超音速平板边界层转捩中层流突变为湍流的机理研究

采用空间模式,对来流Mach数为4.5的平板边界层转捩过程做了直接数值模拟．对结果进行的分析发现,在层流-湍流转捩的突变(breakdown)过程中,层流剖面得以快速转变为湍流剖面的机理在于平均剖面的修正导致了其稳定性特征的显著变化．虽然在层流下第2模态T-S波更不稳定,但在层流突变为湍流的过程中,第1模态不稳定波也起了重要作用．     

Absolute Instability of Incompressible Boundary Layer over a Compliant Plate

An incompressible boundary layer on a compliant plate is considered. The influence exerted by the tensile stress and bending stiffness of the plate on the stability of the boundary layer is investigated in the limit of high Reynolds numbers on the basis of the triple-deck theory. It is shown that upstream-propagating growing waves can be generated in a certain range of parameters characterizing the plate properties. As a result, the flow becomes absolutely unstable in the conventional sense.     

On the stability of mixed convective motions in a vertical layer with wave-like boundaries

The stability of the stationary and oscillatory convective motions which develop in a vertical layer with periodically curved boundaries is studied for the case of longitudinal fluid injection. The amplitude of the boundary undulations and the flow of fluid along the layer are both assumed to be small, and methods of perturbation theory are used. The characteristic properties of the incremental spectrum of the spatially periodic motions are studied and the most dangerous types of perturbations as well as the forms of the stability regions are determined.

Theoretical investigations of the effect of spatial inhomogeneity of the boundary conditions on the stability of convection were sparse, and they deal mainly with horizontal layers of fluid /1–3/. Stationary, spatially periodic motions in a vertical layer with curved boundaries were investigated in /4/ for the case of free convection (when the flow was closed), and their stability was investigated in /5/. It was established that the presence of a small but finite flow of fluid along the layer leads to an increase in the number of different modes of flow, and to the appearance of non-stationary convective motions in the region near the threshold.     

Numerical study of mixed convection flow of a micropolar fluid towards permeable vertical plate with convective boundary condition

In this article, the mixed convective flow of a micropolar fluid along a permeable vertical plate under the convective boundary condition is analyzed. The scaling group of transformations is applied to get the similarity representation of the system of partial differential equations of the problem and then the resulting equations are solved by using Spectral Quasi-Linearisation Method. This study reveals that the dual solutions exists for certain values of mixed convection parameter. The outcomes are analyzed with dual solutions in detail. Effects of micropolar parameter, Biot number and suction/injection parameters on different flow profiles are discussed and depicted graphically.     

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis and a normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M ₁. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.     

纤维悬浮槽流空间模式稳定性分析

采用扰动的空间发展模式而非通常的时间发展模式,对含有悬浮纤维的槽流进行了线性稳定性分析。建立了适用于纤维悬浮流的稳定性方程并针对较大范围的流动Re数及扰动波角频率进行了数值求解。计算结果表明,纤维轴向抗拉伸力与流体惯性力之比H可以反映纤维对流动稳定性的影响。H增大使临界Re数升高,对应的扰动波数减小,扰动空间衰减率增加,扰动速度幅值的峰值降低,不稳定扰动区域缩小,长波扰动所受影响相对较大。纤维的存在抑制了流场的失稳。     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.