On Stoke's problem in magnetohydrodynamics

Stoke's classic problem involving the impulsive motion of an infinite flat plate in an unbounded viscous incompressible fluid is investigated under the additional specification that the fluid is electrically conducting and the motion is developed in the presence of uniform transverse magnetic field. For the fluids with arbitrary magnetic Prandtl number, the compact expression for the skin friction coefficient at the plate is given in terms of exponential and error functions of complex arguments. For the fluids with unit magnetic Prandtl number, expressions for the induced magnetic field, velocity, current density and induced electric field in the viscous boundary layer region set up near the plate are obtained. The effect of the magnetic field on the skin friction is to make it approach the steady state faster than in nonmagnetic case.     

Computer extension and analytic continuation of problems of porous thrust bearings

Summary In this paper we propose new type of series solution, the semi-analytical, semi-numerical technique for the steady flow of a viscous fluid between two parallel disks in which the fluid is injected through the lower porous disk. We develop a double series expansion of the solution function and sufficiently large number of terms (30 terms-universal coefficients) in the expansion are obtained by delegating routine complex algebra to computer. The expression obtained in the form of power series for the normalized lift is analysed by means of Padé approximants. The change of roles of dependent and independent variables and the use of bilinear Euler transformation increases the region of validity of the corresponding power series. The results obtained from double series expansion method for small as well as moderately large values of cross-flow Reynolds number,R are more accurate and the computing time required in this method is negligible compared with pure numerical methods [1]. Besides this, we find that the method proposed by Phan-Thien and Bush [2] has to be implemented for each value ofR separately, whereas the one proposed by us has advantage of yielding, at a stretch, the results for larger range ofR which agree with exact values and at the same time requires less computer time. It is of interest to note that the pure numerical results in respect of normalized lift coefficient agree closely with the analytic continuation of our findings. In addition various Padé approximants are found to bracket the numerical results.     

Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface

Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations. The numerical results obtained from the above methods for various problems are given in terms of skin friction. Our study revealed that the results obtained from these methods agree well with those of direct numerical simulation of ordinary differential equations. Also, these methods have advantages over pure numerical methods in obtaining derived quantities such as velocity profile accurately for various values of the parameters at a stretch.     

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

Exact Analytic Solution of a Boundary Value Problem for the Falkner–Skan Equation

The Falkner–Skan equation, subject to appropriate physical boundary conditions arising from boundary layer theory, is exactly solved. The results obtained from this solution are compared with the numerical solution. The Blasius equation, subject to the same boundary conditions, is also solved exactly; the solution is compared with the earlier work on this equation. The analytic solution presented here agrees closely with the corresponding numerical results.     

Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid

The effect of surface roughness on squeeze film behavior between two circular disks with couple stress lubricant is analyzed when the upper disk has porous facing which approaches the lower disk with uniform velocity. The modified Stochastic Reynolds equation is derived on the basis of Stokes micro-continuum theory for couple stress fluid and Christensen Stochastic theory for the rough surface. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier–Bessel series. The importance of roughness and couple stress on bearing characteristics are presented in terms of load carrying capacity, squeeze time, and relative percentage of the load. It is observed that, effect of couple stress fluid, and surface roughness is more pronounced compared to classical case. These predictions enable design engineers to choose suitable parameters.     

Computation of eigenvalues and solutions of regular Sturm–Liouville problems using Haar wavelets

The paper presents a novel method for the computation of eigenvalues and solutions of Sturm–Liouville eigenvalue problems (SLEPs) using truncated Haar wavelet series. This is an extension of the technique proposed by Hsiao to solve discretized version of variational problems via Haar wavelets. The proposed method aims to cover a wider class of problems, by applying it to historically important and a very useful class of boundary value problems, thereby enhancing its applicability. To demonstrate the effectiveness and efficiency of the method various celebrated Sturm–Liouville problems are analyzed for their eigenvalues and solutions. Also, eigensystems are investigated for their asymptotic and oscillatory behavior. The proposed scheme, unlike the conventional numerical schemes, such as Rayleigh quotient and Rayleigh–Ritz approximation, gives eigenpairs simultaneously and provides upper and lower estimates of the smallest eigenvalue, and it is found to have quadratic convergence with increase in resolution.     

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet‐multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Correlation between biological activity and energies of electronic transitions in benzodiazepines. Negative ion mass spectrometry and ultraviolet absorption spectroscopy study of some derivatives

A correlation between the energies of electronic singlet transitions in benzodiazepines and their biological activity, which was revealed earlier by means of negative ion mass spectrometry with resonance electron capture, has been verified with a UV absorption spectroscopy investigation. Also, it has been noted that the energies of electronic singlet transitions in benzodiazepines are close in value to the ionization energies of atoms Cs, Rb, K, Na, Li and Tl, the cations of which are known to play an important role in nerve cell excitation processes. Copyright 1999 John Wiley & Sons, Ltd.     

Analysis of steady viscous flow in slender tubes

The computer extended perturbation series method is used to analyze the problem of steady viscous flow in slender tubes. The objective is to obtain an expansion in a power series of λ (= ɛ R, ɛ is a small parameter and R = \fracMLnR = \frac{M}{{L\nu }} is a streamwise Reynolds number) and look for its analytic continuation. Such an expansion was usually terminated at the second or third order term and consequently they have a very limited utility. Sufficiently large number of terms in the series, representing physical quantities are, generated for the detail analysis which enables to get converging Pade’ sums for large λ. Domb-Sykes plot enables in finding singularity restricting the convergence of the series. Useful results valid up to λ = 15 are obtained for different derived quantities whereas in earlier findings [6], analysis could be done only up to λ = 10 resulting into a substantial improvement in the present study.