MHD stagnation flow of a micropolar fluid through a porous medium

The unsteady MHD boundary layer flow of a micropolar fluid near the forward stagnation point of a two dimensional plane surface is investigated by using similarity transformations. The transformed nonlinear differential equations are solved by an analytic method, namely homotopy analysis method (HAM). The solution is valid for all values of time. The effect of MHD and porous medium, non dimensional velocity and the microrotation are presented graphically and discussed. The coefficient of skin friction is also presented graphically.     

Flow past an impulsively started vertical plate with variable surface temperature and mass flux

Finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with variable surface temperature and mass flux is presented here. The Velocity profiles are compared with exact solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that there is a rise in the velocity due to the presence of a mass diffusion. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically. Received on 27 May 1998     

Rayleigh lamb waves in micropolar isotropic elastic plate

The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.     

Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium

 An approximate solution to the problem of flow of a viscous incompressible dissipative fluid past an infinite vertical porous plate embedded in a porous medium is presented here. The plate temperature is assumed to be oscillating about a constant mean temperature. Mean velocity and mean temperature, the transient velocity and temperature profiles are shown graphically. The mean skin-friction and the mean rate of heat transfer are also shown graphically. The expressions for the amplitude and the phase of the skin-friction and the rate of heat transfer are derived and their numerical values are listed in Tables. The effects of different parameters governing the unsteady flow are discussed. Received on 23 November 1998     

Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of a transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived after developing a mathematical model for welded and smooth contact boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficient via wave number are plotted graphically to depict the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction field, the normal stress, and the temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.     

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical(CD) coupled, the Lord-Shulman(LS), and the Green-Lindsay(GL) models.     

Thermophoresis particle deposition effects in a free convective doubly stratified medium over a vertical plate

An analysis is performed to study the thermophoresis effects in a transient free convective flow of a viscous, incompressible fluid past an isothermal vertical plate in a doubly stratified medium. The governing boundary layer equations are solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The influence of thermophoresis on particle deposition velocity and particle concentration in a doubly stratified medium are analyzed and illustrated graphically. As well the influence of thermal and mass stratification on velocity, temperature and concentration are also investigated and presented. The influence of the parameters on local as well as average skin-friction, the rate of heat and mass transfer are presented graphically and discussed. The results are compared with particular solutions available in the literature and are found to be in good agreement.     

Mechanical loads on a generalized thermoelastic medium with diffusion

The disturbance caused by the application of continuous mechanical source on the free surface of a homogeneous, isotropic elastic half space in the context of the theory of generalized thermoelastic diffusion with one relaxation time parameter is investigated in the Laplace-Fourier transform domain for a two dimensional problem using eigenvalue approach. The integral transforms are inverted by using a numerical technique. The expressions for displacement components, stresses, temperature field, concentration and chemical potential so obtained in the physical domain are computed numerically and illustrated graphically at different times, for copper like material. As a special case the effect of diffusion on various expressions has also been obtained analytically and depicted graphically.     

On theory of generalized thermoelastic solids with voids and diffusion

Governing equations of thermoelastic diffusion material with voids are modified with the help of Lord and Shulman theory of generalized thermoelasticity. These governing equations are then solved in two-dimension to show the existence of four coupled longitudinal waves and a shear wave. The complex absolute values of the speeds of the coupled longitudinal waves are computed numerically against the frequency for Magnesium material. The reflection of these plane waves from a stress free thermally insulated boundary is also studied, where the dependence of the reflection coefficients on angle of incidence is shown graphically for the incidence of coupled longitudinal wave only. The speeds and reflection coefficients of plane waves are also computed numerically in the absence of voids and diffusion parameters, which are shown graphically to observe the effects of voids and diffusion.     

Oscillating Convection of Nanofluid in Porous Medium

In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl?CDarcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ??PES?? and concluded that ??PES?? is not valid for the problem.     

Thermo-elastic interaction with energy dissipation in an unbounded body with a spherical hole

The distribution of stresses due to step input of temperature at the boundary of a spherical hole in a homogeneous isotropic unbounded body is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures for aluminum–epoxy composite material. The comparison among the theories i.e. classical thermo-elasticity (CTE), classical coupled thermo-elasticity (CCTE), temperature-rate-dependent thermo-elasticity (TRDTE(GL)) and thermo-elasticity with energy dissipation (TEWED(GN)) theory is presented graphically.     

Torsional oscillation of rigid disk in infinite transversely isotropic elastic cylinder

In the present analysis torsional oscillation of a rigid disk in an infinite transversely isotropic elastic cylinder is considered. The effects of anisotropy in the stress intensity factor are shown graphically.     

Viscous dissipative fluid flow past a semi‐infinite vertical plate with variable surface temperature

An analysis of the effect of viscous dissipative heat on two‐dimensional viscous incompressible fluid flow past a semi‐infinite vertical plate with variable surface temperature is carried out. The dimensionless governing equations are unsteady, two‐dimensional, coupled, and non‐linear governing equations. A most accurate, unconditionally stable and fast converging implicit finite‐difference scheme is used to solve the non‐dimensional governing equations. Velocity and temperature of the flow have been presented graphically for various parameters occurring in the problem. The local and average skin friction and Nusselt number are also shown graphically. It is observed that greater viscous dissipative heat causes a rise in the temperature. Copyright © 2007 John Wiley & Sons, Ltd.     

Interface slip between two half-planes caused by a steadily moving force

A computationally simple problem is devised to study the behavior of steadily moving slip zones. Results are presented graphically.     

A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source

This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).     

Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material (Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg). The effect of the body forces is also studied.     

Wave propagation in dual-phase-lag anisotropic thermoelasticity

The present paper is concerned with the propagation of plane waves in a transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The governing equations are solved in x–z plane to show the existence of three plane waves. Reflection of these plane waves from thermally insulated as well as isothermal stress-free surfaces is studied to obtain a system of three non-homogeneous equations in reflection coefficients of reflected waves. For numerical computations of speeds and reflection coefficients, a particular material is modeled as transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The speeds of plane waves are computed numerically for a certain range of the angle of propagation and are shown graphically against the angle of propagation for the cases of dual-phase-lag (DPL) thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity. Reflection coefficients of various reflected plane waves are computed numerically for thermally insulated as well as isothermal cases and are shown graphically against the angle of incidence for the cases of DPL thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity.     

Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation

The theory of diffusive stresses based on the time-fractional diffusion equation is formulated. The source problem is discussed as well as the Cauchy problem. The stresses are found in axially symmetric cases (for plane deformation). The numerical results for the concentration and stress distributions are presented graphically for various values of order of fractional derivative.     

Theory of scattering from a nearly transparent anomaly

Summary Recent advances in the design of uhf and microwave communication equipment, coupled with the increasing need for expanding the usable frequency spectrum, have generated considerable interest in making use of scattered signals which are propagated beyond the radio horizon. Although a large number of experimental measurements have been reported in the literature, much theoretical work in interpreting the basic scattering phenomena remains to be done. In order to gain a more detailed insight into the scattering mechanism, an approximate equation of propagation of electromagnetic energy in a nearly transparent medium is applied to the case in which the medium contains a dielectric inhomogeneity in the form of an isolated gaussian-shaped perturbation in the refractive index. Equations for the scattering caused by the perturbing blob are illustrated graphically. The energy extracted from the incident wave by the blob is illustrated graphically by a plot of the total scattering cross-section as a function of blob size.