Impulsive motion of a flat plate in a Rivlin-Ericksen fluid

The problem of the impulsive motion of a flat plate in a Rivlin-Ericksen fluid is reconsidered. An exact solution for the velocity distribution is found in terms of a definite integral. It is shown that a solution obtained earlier does not satisfy the boundary condition at the plate in the sense of generalized functions.     

Moving wedge and flat plate in a power-law fluid

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving wedge in a moving fluid is studied in this paper. The transformed boundary-layer equation is solved numerically for some values of the involved parameters. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that multiple solutions exist when the wedge and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids.     

Impulsive motion of a semi-infinite flat plate in a viscous fluid

The unsteady laminar boundary layer flow is investigated for a semi-infinite flat plate subjected to impulsive motion. An approximate solution is obtained by utilizing Meksyn's method. These results vary smoothly from Rayleigh's unsteady solution to the steady state solution of Blasius. Results are compared to those of Lam and Crocco.Nomenclature A expansion coefficient, see eq. (13) - a expansion coefficient, see eq. (10) - B expansion coefficient, see eq. (14) - b expansion coefficient, see eq. (12) - G function defined by eq. (6) - U free stream velocity - u velocity in x direction - v velocity in y direction - x coordinate along plate - y coordinate normal to plate Greek symbols (l, ) incomplete gamma function - function defined by eq. (15) - y(U/x) ^1/2 - kinematic viscosity - x/Ut - (Uvx)^1/2 f(, )     

Non-linear vibration analysis of an elastic plate subjected to heavy fluid loading in magnetic field

In the present study, the non-linear vibration of an elastic plate subjected to heavy fluid loading in an inclined magnetic field is investigated. The structural non-linearity, fluid non-linearity, and the effects of magnetic field are all incorporated in the formulations to derive the governing equation of the plate. The method of multiple scales is adopted to determine the eigenvalues and mode shapes of the linear vibration, and then the amplitude of the non-linear vibration response of the plate is calculated. Based on the assumptions of ordering and formulations of multiple scales, it can be concluded that the linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is influenced by the effects of the fluid loading, linear structural rigidity and linear magnetic field, furthermore, the non-linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is dominated and controlled by the effects of the fluid loading, non-linear structural rigidity and non-linear magnetic field. Both thick and thin plates are investigated; the contributions due to the structural non-linearity and acoustic linear radiation damping are of the same order for a rather thick plate. For a thin plate, the structural non-linearity completely controls the behavior of the plate, which implies that in this case the effect of fluid loading is considerably negligible. In general, it can be concluded that both the effects of magnetic field and structural non-linearity play important roles only on the first few modes of the plate.     

Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid

A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced \(\hbox {BaTiO}_{3}\)–\(\hbox {CoFe}_{2}\hbox {O}_{4}\) composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.     

A nonlinear vibration isolator supported on a flexible plate: analysis and experiment

Nonlinear Dynamics - To address low-frequency vibration isolation, an issue that engineers often face, this paper first studies the nonlinear energy transfer of a flexible plate, with arbitrary...     

The experimental study on flat plate heat pipe of magnetic working fluid

An effective thermal spreader can achieve uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Flat plate heat pipe is one of the highly effective thermal spreaders. Magnetic fluid is liquid and can be moved by the force of magnetic field. Therefore, the magnetic fluid is suitable to be used as the working fluid of flat plate heat pipes which have a very small gap between evaporation and condensation surfaces. We prepared a disk-shaped wickless flat plate heat pipe, and the distance between evaporation and condensation surfaces is only 1 mm. From experimental study, the effect of heat flux and working fluid ratio on the performance of flat plate heat pipe is presented. Also we compared the experimental results between the performance of water and magnetic fluid as working fluids.     

Free vibration analysis of a flat stiffened plate with side crack through the Ritz method

Archive of Applied Mechanics - The free vibration of a flat plate with a side crack of Mode I fracture, reinforced by one stiffener parallel to the edges of the plate, is studied in this paper....     

The analogy between fluid friction and heat transfer of laminar forced convection on a flat plate

This paper has examined the validity of the analogies between heat transfer and fluid friction when they are applied to laminar forced convection on a flat plate. For the case of uniform wall temperature, all the analogies are valid for Prandtl number do not differ greatly from 1, and the Colburn analogy is consistent with numerical data forPr1. However, the previous analogies are not valid for the case of uniform wall heat flux. For fluids ofPr1 under uniform heating, the Colburn analogy factor is 0.72. In addition, these analogies are not applicable to the fluids of small Prandtl number. For the sake of completeness, this work has developed the analogies between heat and momentum transfer over the range of 0.001 Pr 0.1 for both the cases of constant wall temperature and heat flux.Die Gültigkeit der Analogien zwischen Wärmeübergang und Flüssigkeitsreibung wird für den Fall der erzwungenen Konvektion an einer ebenen Platte überprüft. Unter der Randbedingung gleichförmiger Wandtemperatur sind alle Analogien für Prandtl-Zahlen in der Nähe von 1 gültig und die Colburn-Analogie stimmt mit numerisch gewonnenen Ergebnissen fürPr1 überein. Die vorgenannten Analogien sind allerdings nicht gültig, wenn als Randbedingung gleichförmiger Wandwärmefluß unterstellt wird. Für Fluide mitPr1 und gleichförmigem Wärmefluß ist der Analogiefaktor nach Colburn gleich 0,72. Auch für Flüssigkeiten mit kleinen Prandtl-Zahlen gelten die Analogien nicht. Der Vollständigkeit halber wurden in dieser Arbeit die Analogien zwischen Wärme- und Impulsaustausch für den Bereich 0,001 Pr 0,1 entwickelt, und zwar sowohl für gleiche Temperatur wie gleichen Wärmefluß an der Wand.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary and non-uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed from the physical point of view.     

Effect of heat transfer on a third grade fluid in a flat channel

The heat transfer analysis on the laminar flow of an incompressible third grade fluid through a porous flat channel is examined. The lower plate is assumed to be at a higher temperature than the upper plate. Analytical solution for temperature distribution is obtained for various values of the controlling parameters and discussed. The obtained analytical solution is also compared with the numerical solution. The comparison shows the fact that the accuracy is remarkable. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of glow discharge on hypersonic flat plate boundary layer

Glow discharge is introduced as an artificial disturbance to investigate the evolution of first-and second-mode instabilities in a hypersonic flat plate boundary layer.Experiments are conducted in a Mach 6.5 quiet wind tunnel using Rayleigh scattering visualization and particle image velocimetry(PIV). Detailed analysis of the experimental observations is provided. It is found that the artificially introduced 17 kHz disturbance,which belongs to the first-mode frequency band, can effectively enhance first-mode waves.Moreover, it can enhance second-mode waves even more intensely. Possible mechanisms to explain this phenomenon are discussed.     

Effect of loading conditions on regimes of solid-phase transformations in a plate

A two-dimensional mathematical model of propagation of chemical conversion in a plate under mechanical loading is proposed. The problem is numerically studied for three variants of loads and displacements on the plate surfaces: clamped plate, uniaxial tension, and shear. As the fields of temperatures, concentrations, and stresses are coupled, the conversion modes under different loading conditions are found to be different. By means of a parametric study of the model, it is demonstrated that the value of internal stresses may be substantially higher than the external load.     

Analysing flow and heat transfer of a viscoelastic fluid over a semi-infinite horizontal moving flat plate

This paper presents a numerical study of the flow and heat transfer of an incompressible homogeneous second grade type fluid above a flat plate moving with constant velocity U. Such a viscoelastic fluid is at rest and the motion is created by the sheet. The effects of the non-Newtonian nature of the fluid are governed by the local Deborah number K (the ratio between the relaxation time of the fluid and the characteristic time of the flow). When , a new analytical solution for this flow is presented and the effects of fluid's elasticity on flow characteristics, dimensionless stream function and its derivatives are analysed in a wide domain of K. A novel result of the analysis is that a change in the flow solution's behaviour occurs when the dimensionless stream function at the edge of the boundary layer, f_∞, equals 1.0. It is found that velocity at a point decreases with increase in the elasticity of the fluid and, as expected, the amount of fluid entrained diminishes when the effects of fluid's elasticity are augmented. In our heat transfer analyses we assume that the surface temperature has a power-law variation. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Local similarity heat-transfer solutions are given for PST case when s=2 (the wall temperature parameter) whereas when a similarity solution takes place in the case of prescribed wall heat flux. The numerical results obtained are fairly in good agreement with the aforementioned analytical ones.     

Magnetoelastic vibration of a plate

Summary The propagation of plane harmonic waves in a thin flat homogeneous isotropic plate of finite width and infinite length permeated by a constant magnetic field is examined. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained, and some limiting cases of the frequency equations are then discussed.     

Forced convection from a microstructure on a flat plate

In this work, a cooling of a flat microelectronic structure with single-phase forced convection is investigated. The axial conduction, usually neglected in boundary layer theory, is considered here since the length of the heated element is in the same order of magnitude as the thickness of the boundary layer. The microstructure represents a package of chips mounted flush with the surface of the plate, and uniformly heated with a constant heat flux. The differential method is used to reduce the governing partial differential equations to ordinary differential ones, which are solved numerically by the use of a computational code developed by the authors. This code is based on Keller–Box method. The temperature profiles and Nusselt numbers are plotted at several locations on the heated element and are given as functions of the Reynolds number at the beginning of heated microstructure and of the ratio of unheated to heated length. Furthermore, the average Nusselt numbers on the heated length are computed for Prandtl numbers in the range 0.7≤Pr≤7,000. The results are compared to the boundary layer solution of unheated starting length problem. The results will be used as a baseline for successively more complex situations of cooling in electronics.     

Effect of electrohydrodynamic interaction on the stability of a flat plate laminar boundary layer

The stability of a unipolarly charged electrohydrodynamic boundary layer on a flat dielectric plate along which an electric current flows between electrodes located on the plate is investigated within the framework of the linear theory. The solution of the steady-state problem is obtained on the basis of methods developed earlier for conditions typical of aerodynamical experiments and various electric currents and electrode voltages. The effect of the interaction between perturbations of the electric and hydrodynamic flow parameters on the flow stability is estimated within the framework of the locally homogeneous approximation. This effect turns out to be insignificant under the conditions considered. It is shown that steady-state electrohydrodynamic action on the main flow makes it possible to obtain “accelerating” velocity profiles with increased absolute values of the second derivative in the transverse direction. This ensures a significant increase in the critical Reynolds numbers of loss of stability and a narrowing of the growing perturbation wavenumber range.