Volume 18 (2013): Issue 1 (March 2013)

The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.

An analysis is made on a steady flow of an incompressible visco-elastic fluid (of small memory) past a porous plate subject to uniform suction or blowing. The fluid and the plate rotate in unison with uniform angular velocity about an axis perpendicular to the plate. It is shown that for a visco-elastic fluid of small memory, a boundary layer is formed for uniform suction or blowing at the plate. It is found that the primary velocity increases whereas the secondary velocity increases near the plate and decreases away from the plate with an increase in the elastic parameter. The secondary flow shows flow reversal for a large elastic parameter. It is found that both primary and secondary velocities increase near the plate and decrease away from the plate with an increase in the rotation parameter. It is also found that the shear stress due to primary flow increases with an increase in either the elastic parameter or rotation parameter. On the other hand, the shear stress due to secondary flow decreases with an increase in the elastic parameter while it increases with an increase in the rotation parameter. The temperature distribution in the boundary layer is also determined. It is shown that elasticity leads to an increase in heat transfer at the plate.

The paper deals with an unsteady two dimensional laminar slip flow of a viscous incompressible magnetomicropolar fluid past a semi infinite porous plate embedded in a porous medium. The flow is under the influence of a transverse magnetic field and heat source/sink. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. The porous surface absorbs the fluid with time varying suction velocity. Expressions are obtained for velocity and temperature fields, mean angular velocity, skin friction and the Nusselt number.

The objective of this paper is to present and compare the results of numerical solutions of contact problem for two types of seats subjected to typical sitting loadings. The first seat is made of a typical hyperelastic foam, the other is designed with an auxetic polyamid spring skeleton. Computer simulations of the seat structure under a typical static loading exerted by a human body are performed by means of ABAQUS FEA. The model provides an insight into deformation modes and stress field in relation to geometric and material parameters of the seat structure.The other type of seat, due to the fact of global auxecity and progressive springs characteristics reduces contact stress concentrations, giving an advantegous distribution of pressure and provides the sensation of physical comfort. The proper seat skeleton shape leads to an improvement of ergonomic quality.

This paper presents both analytical and numerical analyses of a fully developed unsteady/steady natural convection flow of a reactive viscous fluid in an open ended vertical annulus. Analytical expressions for velocity, temperature, skin-friction and rate of heat transfer are obtained after simplifying and solving the governing differential equations with reasonable approximations. The interesting result found in this study is that an increase in non-dimensional time (t) , increases both temperature and velocity profiles until a steady-state value is attained. Subsequent results obtained by numerical calculations show excellent agreement with analytical results.

A complete three-dimensional and single phase model for proton exchange membrane (PEM) fuel cells was used to investigate the effect of using different channels geometry on the performances, current density and gas concentration. The proposed model was a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations were solved in a single domain; therefore no interfacial boundary condition was required at the internal boundaries between cell components. This computational fluid dynamics code was employed as the direct problem solver, which was used to simulate the three-dimensional mass, momentum, energy and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC. The results showed that the predicted polarization curves by using this model were in good agreement with the experimental results and a high performance was observed by using circle geometry for the channels of anode and cathode sides. Also, the results showed that the performance of the fuel cell improved when a rectangular channel was used.

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

An analysis of heat transfer for boundary layer forced convective flow past a moving flat surface parallel to a moving stream is presented. The power-law surface temperature at the boundary is prescribed. The surface temperature varying directly (or inversely) with power-law exponent is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with known results from the open literature for some particular cases of the present study. When the surface and the fluid move in the opposite directions, dual solutions exist.

Energy stability of a horizontal layer of a two-component Maxwell fluid in a porous medium heated and salted from below is studied under the Oberbeck-Boussinesq-Darcy approximation using the Lyapunov direct method. The effect of stress relaxation on the linear and non-linear critical stability parameters is clearly brought out with coincidence between the two when the solute concentration is dilute. Qualitatively, the result of porous and clear fluid cases is shown to be similar. In spite of lack of symmetry in the problem it is shown that non linear exponential stability can be handled.

The development of velocity, temperature and concentration fields of an incompressible viscous electrically conducting fluid, caused by impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid in a saturated porous medium is studied. The partial differential equations governing the unsteady laminar boundary layer flow are solved analytically. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stress in x and y directions and the surface heat transfer and surface mass transfer increase with the magnetic parameter and with permeability parameter and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

The aim of the present paper is to investigate surface waves in an anisotropic, elastic solid medium under the influence of gravity. First, a theory of generalised surface waves was developed and then it was employed to investigate particular cases of waves, viz., Stoneley and Rayleigh, Love type. The wave velocity equations were obtained for different cases and they are in well agreement with the corresponding classical result, when the effect of gravity, viscosity as well as parameters for fibre-reinforcement of the material medium are ignored.

Plane-strain vibrations in a fluid-loaded poroelastic hollow cylinder surrounded by a fluid are investigated employing Biot’s theory of wave propagation in poroelastic media. The poroelastic hollow cylinder is homogeneous and isotropic, while the inner and outer fluids are homogeneous, isotropic and inviscid. The frequency equation of the fluid-loaded poroelastic cylinder surrounded by a fluid is obtained along with several particular cases, namely, fluid-loaded poroelastic cylinder, fluid-loaded bore, poroelastic cylinder surrounded by a fluid and poroelastic solid cylinder submerged in a fluid. The frequency equations are obtained for axially symmetric, flexural and anti-symmetric vibrations each for a pervious and an impervious surface. Nondimensional frequency for propagating modes is computed as a function of the ratio of thickness to the inner radius of the core. The results are presented graphically for two types of poroelastic cylinders and then discussed.

The present investigation is concerned with the effect of two temperatures on reflection coefficients in a micropolar thermoelastic solid half space. With two relaxation times, reflection of plane waves impinging obliquely at a plane interface of the micropolar generalized thermoelastic solid half space with two temperatures is investigated. The incident wave is assumed to be striking at the plane surface after propagating through the micropolar generalized thermoelastic solid with two temperatures. Amplitude ratios of the various reflected waves are obtained in closed form and it is found that these are functions of angle of incidence, frequency and are affected by the elastic properties of the media. The effect of two temperatures is shown on these amplitude ratios for a specific model.

The paper presents an aproximate analytic method for determination of the stored energy of plastic deformation during cold bending of metal tubes at bending machines. Calculations were performed for outer points of the tube layers subjected to tension and compression (the points of maximum strains). The percentage of stored energy related to the plastic strain work was determined and the results were presented in graphs. The influence and importance of the stored energy of plastic deformation on the service life of pipeline bends are discussed.

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem

An exact solution of an unsteady flow past an exponentially accelerated infinite isothermal vertical plate with uniform mass diffusion in the presence of a transverse magnetic field has been studied. The plate temperature is raised to Tw and the species concentration level near the plate is also made to rise Cʹw . The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration profiles are studied for different physical parameters such as the magnetic field parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, time and a. It is observed that the velocity decreases with increasing the magnetic field parameter.