Volume 23 (2018): Issue 3 (August 2018)

Elastic waves in fluid-saturated granular media depend on the grain rheology, which can be complicated by the presence of gas bubbles. We investigated the effect of the bubble dynamics and their role in rheological scheme, on the linear Frenkel-Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum and bubbles surrounded by the fluid. We derived the Nikolaevskiy-type equation describing the velocity of the solid matrix in the moving reference system. The equation is linearized to yield the decay rate λ as a function of the wave number k. We compared the λ (k) -dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For both the cases, the λ(k) curve lies entirely below zero, which implies a global decay of the wave. We found that the increase of the radius of the bubbles leads to a faster decay, while the increase in the number of the bubbles leads to slower decay of the wave.

Laminar natural convection in a trapezoidal porous vertical cavity has been investigated in this work. It is assumed that the porous enclosure is filled up with a permeable material subject to hydrodynamic and thermal anisotropy, the flow being governed by the Darcy law as applicable to a non-isotropic medium. It is further assumed that (i) there is heating at the left vertical wall and cooling at the right wall of the enclosure and (ii) the flow domain is subject to the presence of heat source or heat sink. The partial differential equations governing the resulting free convection have been solved numerically in the non-dimensional forms. There arises a number of parameters relating to buoyancy, internal heating, cavity aspect ratio and inclination of the upper surface to the horizontal. The influence of these parameters has been illustrated and analyzed through contours of streamlines and isotherms. We have also discussed the role of internal heating as well as anisotropy on the heat transfer characteristics.

In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.

The unsteady flow of a viscous incompressible electrically conducting fluid due to non-coaxial rotations of a porous disk subjected to a periodic suction and the fluid at infinity in the presence of applied transverse magnetic field has been studied. The fluid at infinity passes through a fixed point. The velocity field, shear stresses are obtained in a closed form.

The effect of vertical throughfow and temperature modulation on a viscoelastic fluid saturated porous medium has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non autonomous complex Ginzburg- Landau equation, is calculated. The effect of vertical through flow is found to stabilize the system irrespective of the direction of through flow in the case of permeable boundary conditions. The time relaxation has a destabilizing effect, while the time retardation parameter has a stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study shows that the heat transport can be controlled effectively by a mechanism that is external to the system. Further, it is also found that heat transfer is more in oscillatory mode of convection rather than in stationary mode of convection.

This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.

Tapered beams are more efficient compared to uniform beams as they provide a better distribution of mass and strength and also meet special functional requirements in many engineering applications. In this paper, the linear and non-linear fundamental frequency parameter values of the tapered Timoshenko beams are evaluated by using the coupled displacement field (CDF) method and closed form expressions are derived in terms of frequency ratio as a function of slenderness ratio, taper ratio and maximum amplitude ratio for hinged-hinged and clamped-clamped beam boundary conditions. The effectiveness of the CDF method is brought out through the solution of the large amplitude free vibrations, in terms of fundamental frequency of tapered Timoshenko beams with axially immovable ends. The results obtained by the present CDF method are validated with the existing literature wherever possible.

A numerical model is developed to study the Soret and Dufour effects on MHD boundary layer flow of a power-law fluid over a flat plate with velocity, thermal and solutal slip boundary conditions. The governing equations for momentum, energy and mass are transformed to a set of non-linear coupled ordinary differential equations by using similarity transformations. These non-linear ordinary differential equations are first linearized using a quasi-linearization technique and then solved numerically based on the implicit finite difference scheme over the entire range of physical parameters with appropriate boundary conditions. The influence of various governing parameters along with velocity, thermal and mass slip parameters on velocity, temperature and concentration fields are examined graphically. Also, the effects of slip parameters, the Soret and Dufour number on the skin friction, Nusselt number and Sherwood number are studied. Results show that the increase in the Soret number leads to a decrease in the temperature distribution and to an increase in concentration fields.

The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.

This paper is concerned with the problem of reflection and transmission of elastic waves due to an incident plane qSV-wave at a corrugated interface between two dissimilar monoclinic elastic half-spaces. Due to the corrugated nature of the interface, there exist regularly and irregularly reflected and transmitted elastic waves. Using Rayleigh’s method of approximation, the reflection and transmission coefficients of regular and irregular waves are obtained for the first order of approximation. We have found that these coefficients are functions of the angle of incidence, elastic constants, corrugation and the frequency parameter. These coefficients are obtained for a special type of interface, z =dcos py. We have computed these coefficients for a particular model and discussed the effects of corrugation and frequency parameter.

In this study, the influence of thermomechanical coupling effect - the effect of thermal expansion due to dissipation of the energy of plastic deformation, with and without taking into account the stored energy of plastic deformation (SEPD) for the distribution of stresses, strains, temperature, the applied pressure and the residual stresses is examined. The residual stresses remain in a thick-walled tube (a cylindrical thick-walled tank) after removing the internal pressure in the process of purely elastic unloading. The analysis is made on the example of an analitycal solution for a thick-walled tube subjected to a quasistatically increasing internal pressure for the case of adiabatic processes (without heat flow). Since the loading with internal pressure is quasi-static (monotonic), then neglecting the process of heat flow can lead to some different results in calculated stresses, deformations, temperature, internal pressure and residual stresses. The calculations for isothermal type of processes of deformations (without heat or ideal cooling) are also performed for the estimation of these differences. The results calculated for the process with heat flow should be intermediate between the values obtained for isothermal and adiabatic processes.

In this paper, we present the mathematical study of heat and mass transfer effects on an arterial blood flow under the influence of an applied magnetic field with chemical reaction. A case of mild stenosis is considered in a non-tapered artery which is inclined at an angle γ from the axis. The variable viscosity of the blood is considered varying with the hematocrit ratio. Governing non-linear differential equations have been solved by using an analytical scheme, homotopy perturbation method to obtain the solution for the velocity, temperature and concentration profiles of the blood flow. For having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted for wall shear stress, velocity, temperature and concentration profiles with varying values of the applied magnetic field, chemical reaction parameter and porosity parameter. The results show that in an inclined artery, the magnitude of the wall shear stress at stenosis throat increases as values of the applied magnetic field increase while it reduces as the values of both the chemical reaction and porosity parameters increase. Contour plots have been plotted to show the variations of the velocity profile of blood flow as the values of the height of the stenosis as well as the influence of the applied magnetic field increase.

This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

In the paper a nonlinear model of a lattice-boom crane with lifting capacity up to 700mT for static analysis is presented. The rigid finite element method is used for discretisation of the lattice-boom and the mast. Flexibility of rope systems for vertical movement and for lifting a load is also taken into account. The computer programme developed enables forces and stress as well as displacements of the boom to be calculated. The model is validated by comparison of the authors’ own results with those obtained using professional ROBOT software. Good compatibility of results has been obtained.

The thermosolutal stability of a layer of the Rivlin-Ericksen fluid in a porous medium is considered under varying gravity conditions. It is found that for stationary convection, medium permeability and suspended particles have a destabilizing/stabilizing effect when gravity increases/decreases. The stable solute gradient has a stabilizing effect on the system.