Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Stokes' First Problem for an MHD Burgers Fluid

This work is related to the flow of a magnetohydrodynamic Burgers fluid.The flow of an incompressible conducting Burgers fluid in the presence of a uniform transverse magnetic field over a plate that is moved suddenly is considered.By the application of the Laplace and Fourier sine transforms techniques,the exact analytical expressions for the velocity field and associated shear stress are determined in simple forms.They are written as a sum of steady-state and transient solutions.The graphical results are plotted for different values of indispensable parameters and some interesting results are concluded.The corresponding solutions for the hydrodynamic Burgers fluid appear as the limiting cases of the obtained solutions.     

Flutter of Finite-Span Flexible Plates in Uniform Flow

The flutter instability and response of finite-span flexible plates in uniform flow are investigated experimentally. The effects of the plate aspect ratio on its dynamic responses are mainly analyzed. A hysteretic phenomenon is observed and can be described such that the plate flutters spontaneously as the flow velocity is greater than a critical value UC and the plate returns to its stable state as the flow velocity is slowly decreased to another critical one UD. We find that the aspect ratio has a greater effect on UC than on UD. The flutter frequency decreases and the amplitude increases with the increase in the flow velocity. When the flutter instability of the plate occurs, three typical flutter modes are identified and are associated with the aspect ratio and the flow velocity.     

A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity

The steady flow and heat transfer of an electrically conducting fluid with variable viscosity and electrical conductivity between two parallel plates in the presence of a transverse magnetic field is investigated. It is assumed that the flow is driven by combined action of axial pressure gradient and uniform motion of the upper plate. The governing nonlinear equations of momentum and energy transport are solved numerically using a shooting iteration technique together with a sixth-order Runge-Kutta integration algorithm. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that the combined effect of magnetic field, viscosity, exponents of variable properties, various fluid and heat transfer dimensionless quantities and the electrical conductivity variation, have significant impact on the hydromagnetic and electrical properties of the fluid.     

The stability of partially rigid two-dimensional surfaces in uniform incompressible flow

A theoretical analysis is made of the stability of a partially rigid two-dimensional surface embedded in the uniform flow of an incompressible inviscid fluid. Membranes, simply supported panels and clamped panels, attached at their leading and trailing edges to rigid flat extensions aligned with the undisturbed flow direction, are considered and numerical results are obtained, by using the Galerkin method, showing how the stability varies with the change in length of the upstream and downstream rigid elements. Similar results are obtained for a cantilever panel attached to a leading edge rigid surface modelling the aerofoil or splitter plate used in experiments. The effects of structural damping are included where appropriate and comparisons made with other relevant theoretical and experimental results.     

Free convective MHD flow of visco-elastic fluid past a vertical porous plate in the presence of heat source and chemical reaction

Magnetohydrodynamics flow of a visco-elastic incompressible fluid (Walter’s B′ model) past an infinite porous plate in porous medium under the action of transverse uniform magnetic field in the presence of heat source and chemical reaction is investigated. The governing equations of the motion, energy and concentration are solved by a successive perturbation technique. The flow phenomenon is characterized by suction parameter, magnetic parameter, porosity parameter, Grashoff number, modified Grashoff number, Prandtl number, heat source parameter, chemical reaction parameter and Schmidt number. The expressions for skin friction coefficient, Nusselt number, and Sherwood number on the surface are also discussed.     

The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet

The flow and heat transfer problem of a second grade fluid film over an unsteady stretching sheet is considered. The fluid is incompressible and electrically conducting in the presence of a uniform applied magnetic field. The series solutions of the governing boundary value problems are obtained by employing homotopy analysis method (HAM). The convergence of the developed solutions is discussed explicitly. The dependence of velocity and temperature profiles on various parameters is shown and discussed through graphs. The values of skin-friction coefficient, Nusselt number and free surface temperature are given in tabular form for various emerging parameters.     

On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.     

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.     

Unsteady MHD Non-Darcian Flow over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model

An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.     

Effects of Hall current on unsteady MHD flows of a second grade fluid

The aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B ₀ → 0 and for a Newtonian fluid when α ₁ → 0.     

Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient

In the present study, the unsteady Hartmann flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

Experimental Study on Physical Mechanism of Drag Reduction of Hydrophobic Materials in Laminar Flow

We experimentally study the physical mechanism of the drag reduction of hydrophobic materials in the macroscopic scale. The experiment includes the drag and velocity measurements of laminar boundary layer flow over flat plates, and the observation of air bubbles on the surfaces. The plate surfaces have different wetting and roughness properties. In the drag measurements, the plates with bubbles on the surfaces lead to drag reduction, but not for those without bubbles. Velocity measurement confirms that the flow is laminar and gives apparent fluid slip on the plate wall with bubbles. In observation, air bubbles in macroscopic size emerge and enlarge on hydrophobic surfaces but not on hydrophilic surfaces. Therefore, the drag reduction of hydrophobic materials is explained by the generation of air bubbles of macroscopic size that cause the apparent velocity slip.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction

The modified ghost fluid method (MGFM) provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction (FSI) simulations. However, this methodology for one specific class of FSI problems, where the structure is plate, remains to be developed. This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate. In order to take into account the influence of simultaneous interaction at the interface, a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states. Then, ghost fluid states and plate load can be defined by utilizing the obtained interfacial states. A type of acceleration strategy in the coupling process is presented to pursue higher efficiency. Several one-dimensional examples are used to highlight the utility of this method over loosely-coupled method and validate the acceleration techniques. Especially, this method is applied to compute the underwater explosions (UNDEX) near thin elastic plates. Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated. Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.     

Mixed convection of a conducting third-grade fluid past an oscillating porous plate

We study heat transfer in the incompressible flow of a conducting third-grade fluid subject to a uniform magnetic field past an oscillating porous vertical plate.We obtain the analytical form of the boundary-layer velocity profile, the temperature profile, and the skin friction coefficient for small deviations from the Newtonian rheology. We examine the dependence of these quantities on the Prandtl number, the mixed convection parameter, the Hartmann number, and the suction parameter.     

Magnetic fluid based squeeze film between porous annular curved plates with the effect of rotational inertia

The squeeze film behaviour between rotating annular plates was analysed theoretically when the curved upper plate with a uniform porous facing approached the impermeable and flat lower plate, considering a magnetic fluid lubricant in the presence of an external magnetic field oblique to the plates. Expressions were obtained for pressure and load capacity; and response time is given by a differential equation. The increases in pressure and load capacity depended only on the magnetization. However, the increase in response time depended on magnetization, fluid inertia and speed of rotation of the plates.     

Experimental observation and numerical analysis of arc plasmas diffused by magnetism

At atmospheric pressure, an intensified charge-coupled device (ICCD) camera with a narrow-band filter is used to capture the unsaturated images of a magnetically rotating arc. Comparison of its configurations with different arc current and external axial magnetic field (AMF) strength shows that the strong electromagnetic force may impel the arc to diffuse. Under the fully diffuse mode, the plasma is distributed throughout the electrode gap and no anode attachment can be seen in the cross-section of the torch. The fully diffuse plasma runs more steadily and its intensity distribution is more uniform, while its voltage fluctuation is reduced significantly. Using a commercial CFD (computational fluid dynamics) code FLUENT, the fluid flow and heat transfer of the fully diffuse plasma in an assumed magnetron torch have been simulated for qualitatively discussing the AMF effects. Numerical results show that the AMF significantly impels the plasma to retract axially and expand radially. As a result, the plasma intensity distribution on the cross section of the torch gets to be more uniform.