Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

The unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter lambda, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Effect of longitudinal surface curvature on boundary layers

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

Magnetic skin layer of NiO(100) probed by polarization-dependent spectromicroscopy

Using polarization-dependent x-ray photoemission electron microscopy, we have investigated the surface effects on antiferromagnetic (AFM) domain formation. Depth-resolved information obtained from our study indicates the presence of strain-induced surface AFM domains on some of the cleaved NiO(100) crystals, which are unusually thinner than bulk AFM domain wall widths (similar to 150 nm). Existence of such magnetic skin layer is substantiated by exchange-coupled ferromagnetic Fe domains in Fe/NiO(100), thereby evidencing the influence of this surface AFM domains on interfacial magnetic coupling. Our observations demonstrate a depth evolution of AFM structure in presence of induced surface strain, while the surface symmetry-breaking in absence of induced strain does not modify the bulk AFM domain structure. Realization of such thin surface AFM layer will provide better microscopic understanding of the exchange bias phenomena. (C) 2014 AIP Publishing LLC.

Supersonic flutter of composite skin panels of repeated-sublaminate layup

In high-speed aerospace vehicles, supersonic flutter is a well-known phenomenon of dynamic instability to which external skin panels are prone. In theory, the instability stage is expressed by the 'flutter critical parameter' Q(crit), which is a function of the stiffness-, and dynamic pressure parameters. For a composite skin panel, Q(crit) can be maximised by lay-up optimisation. Repeated-sublaminate lay-up schemes possess good potential for economical lay-up optimisation because the corresponding effort is limited to a family of sublaminates of few layers only. When Q(crit) is obtained for all sublaminates of a family, and the sublaminates ranked accordingly, the resulting ranking reveals not only the optimum lay-up, but also the near-optimum lay-ups, which are useful design alternatives, and the inferior lay-ups which should be avoided. In this paper, we examine sublaminate-ranking characteristics for a composite panel prone to supersonic flutter. In particular, we consider a simple supported midplane-symmetrical rectangular panel of typical aspect ratio alpha and flow angle psi, and for four-layered sublaminates, obtain the Q(crit)-based rankings for a wide range of the number of repeats, r. From the rankings, we find that an optimum lay-up can exist for which the outermost layer is oriented wide of, rather than along, the flow. Furthermore, for many lay-ups other than the optimum and the inferior, we see that as r increases, Q(crit) undergoes significant change in the course of converging. To reconcile these findings, eigenvalue-coalescence characteristics are discussed in detail for specific cases.

Surface chemical studies of Thiobacillus ferrooxidans with reference to copper tolerance

A strain of Thiobacillus ferrooxidans was adapted to grow at higher concentrations of copper by single step culturing in the presence of 20 g/L (0.314 mol/L) cupric ions added to 9K medium. Exposure to copper results in change in the surface chemistry of the microorganism. The isoelectric point of the adapted strain (pI=4.7) was observed to be at a higher pH than that of the wild unadapted strain(pI=2.0). Compared to the wild strain, the copper adapted strain was found to be more hydrophobic and showed enhanced attachment efficiency to the pyrite mineral. The copper adsorption ability of the adapted strain was also found to be higher than that of the wild strain. Fourier transform infrared spectroscopy of adapted cells suggested that a proteinaceous new cell surface component is synthesized by the adapted strain. Treatment of adapted cells with proteinase-K, resulted in complete loss of tolerance to copper, reduction in copper adsorption and hydrophobicity of the adapted cells. These observations strongly suggest a role played by cell surface modifications of Thiobacillus ferrooxidans in imparting the copper tolerance to the cells and bioleaching of sulphide minerals.

On the measurement of the surface energy budget over a land surface during the summer monsoon

The measurement of surface energy balance over a land surface in an open area in Bangalore is reported. Measurements of all variables needed to calculate the surface energy balance on time scales longer than a week are made. Components of radiative fluxes are measured while sensible and latent heat fluxes are based on the bulk method using measurements made at two levels on a micrometeorological tower of 10 m height. The bulk flux formulation is verified by comparing its fluxes with direct fluxes using sonic anemometer data sampled at 10 Hz. Soil temperature is measured at 4 depths. Data have been continuously collected for over 6 months covering pre-monsoon and monsoon periods during the year 2006. The study first addresses the issue of getting the fluxes accurately. It is shown that water vapour measurements are the most crucial. A bias of 0.25% in relative humidity, which is well above the normal accuracy assumed the manufacturers but achievable in the field using a combination of laboratory calibration and field intercomparisons, results in about 20 W m(-2) change in the latent heat flux on the seasonal time scale. When seen on the seasonal time scale, the net longwave radiation is the largest energy loss term at the experimental site. The seasonal variation in the energy sink term is small compared to that in the energy source term.

Surface chemical studies on mica and galena using dextrin

The interactions of dextrin with biotite mica and galena have been investigated through adsorption, flotation, and electrokinetic measurements. The adsorption densities of dextrin onto mica continuously increase with increase of pH, while those onto galena show a maximum at pH 11.5. It is observed that the adsorption density of dextrin onto galena is quite high compared to that on mica. Both the adsorption isotherms exhibit Langmuirian behavior. Electrokinetic measurements portray conformational rearrangements of macromolecules with the loading, resulting in a shift of the shear plane, further away from the interface. Dissolution experiments indicate release of the lattice metal ions from mica and galena. Coprecipitation tests confirm polymer-metal ion interaction in the bulk solution. Dextrin does not exhibit any depressant action toward mica, whereas, with galena, the flotation recovery is decreased with an increase in pH beyond 9, in the presence of dextrin, complementing the adsorption results. Differential flotation results on a synthetic mixture of mica and galena show that mica can be selectively separated from galena using dextrin as a depressant for galena above pH 10. Possible mechanisms of interaction between dextrin and mica/galena are discussed.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Genesis of workpiece roughness generated in surface grinding and polishing of metals

Assuming the grinding wheel surface to be fractal in nature, the maximum envelope profile of the wheel and contact deflections are estimated over a range of length scales. This gives an estimate of the 'no wear' roughness of a surface ground metal. Four test materials, aluminum, copper, titanium, and steel are surface ground and their surface power spectra were estimated. The departure of this power spectra from the 'no wear' estimates is studied in terms of the traction-induced wear damage of the surfaces. The surface power spectra in grinding are influenced by hardness and the power is enhanced by wear damage. No such correlation with hardness was found for the polished surface, the roughness of which is insensitive to mechanical properties and appears to be influenced by microstructure and physical properties of the material.