In this paper, a numerical study is carried out to investigate the mixed convection flow and heat transfer in a parallel-plate channel with an anisotropic permeable porous medium. The principal axis of the porous medium is orientated in a direction which is oblique to the gravity vector. Both clear (Newtonian) fluid dissipation and Darcy viscous dissipation are considered in the heat transport equation. In this model, the temperature dependent fluid properties are considered and their influence on the flow and heat transfer characteristics is brought out. The governing non-linear equations (in non-dimensional form) are solved numerically by a second order finite difference scheme. The directional permeability ratio A1 is defined to combine the effects of the permeability ratio parameter K* = (K1 / K2) and the orientation angle Φ1. The effects of the anisotropic permeability ratio, the orientation angle of the principal axis, and the temperature dependent variable properties on the mixed convection flow and heat transfer are investigated. It is demonstrated that both the anisotropic permeability of the porous medium and the variable transport properties have strong effects on the flow and heat transfer characteristics.

In this work a numerical investigation has been conducted to study the unsteady oscillatory flow of a viscous fluid induced by a swirling disk. The disk stretches radially with the time-based sinusoidal oscillations. The governing equations for the three-dimensional boundary layer-flow are normalized using a suitable set of similarity transformations. The normalized partial differential equations are then solved numerically using a finite difference scheme by altering the semi-infinite domain to a finite domain. The effects of various imperative parameters on the oscillatory flow are discussed with graphs and tables.

The responses to an incident plane SH wave on or near a surface irregularity which is embedded in an elastic half-plane are investigated. The surface irregularity represents a canyon, an alluvial valley or a hill. The wave function expansion method has been employed to solve surface irregularities, such as a semi-cylindrical canyon, a semi-cylindrical alluvial valley, or a semi-elliptical canyon and a semi-elliptical alluvial valley. These solutions to the scattering problem of SH wave can be used to test the accuracy of the other numerical methods. But solutions for surface irregularities with arbitrarily shapes cannot be found easily. A hybrid method combines the finite element method with series expansion is applied to solve scattering problems in this study. A subregion encloses the surface irregularity with a semi-circular auxiliary boundary can be meshed by the finite element method. By using the transfinite interpolation (TFI) produces excellent grid mesh on the subregion. The advantage of TFI is the flexibility to facilitate modeling of the subregion. On the other hand, the boundary data can be formulated by using a series representation with unknown coefficients. The Lamb's solution which satisfies the traction free condition and the radiation condition at infinity is implemented to be the basis function. The unknown coefficients can be obtained by satisfying the continuity conditions of the semi-circular auxiliary boundary between the subregion and the half-plane. The hybrid method that combines TFI with series expansion is successfully herein to solve the scattering problem by a surface irregularity. Numerical results in this study for special cases agree well with those in the published literatures. In this study, the steps and skills of hybrid method are described systematically and completely to solve the surface irregularity.

Within the framework of linear piezoelectricity, the problem of two collinear electrically dielectric cracks in a piezoelectric layer is investigated under inplane electro-mechanical loadings. The energetically consistent crack-face boundary conditions are utilized to address the effects of a dielectric inside the cracks on the crack growth. The Fourier transform technique is applied to solve the boundary-value problem. Under the consideration of two-case electromechanical loadings, the electroelastic fields near the inner and outer crack tips are obtained through the Lobatto-Chebyshev collocation method. The special case of two collinear energetically consistent cracks in an infinite piezoelectric solid is analyzed and the closed-form solutions of the crack-tip electroelastic fields are further determined. Numerical results show the variations of stress intensity factors and energy release rates near the inner and outer crack tips on the applied electric fields, the geometry of cracks and the width of the piezoelectric layer in graphics. The observations reveal that the stress intensity factors are dependent not only on the adopted crack-face boundary conditions, but also on the applied mechanical loading.

In this paper, analytical simulations of the steel-laminated elastomeric bearing (SLEB) using a three-dimensional (3D) finite element model incorporating material, geometric nonlinearities, and a frictional contact algorithm in LS-DYNA code is conducted. In order to simulate the nonlinear responses of the elastomeric bearing under the compression and shear, a hyperviscoelastic rubber model such as The MAT_77_H (MAT_HYPERVISCOELASTIC_RUBBER) in LS- DYNA code is adopted. Based on the proposed material model for the SLEB, the interaction effects of the SLEB under compression, bending, and torsion are analyzed. Analytical results are compared with the test results of the SLEBs. A set of material parameters is proposed for 3D FEM analysis of SLEBs. The proposed material model demonstrates its accuracy.

Present paper is aimed at studying the effects of fractional order parameter, magnetic field, viscosity and diffusion on the thermoelastic interactions in an infinite body whose surface suffers a mechanical load. Body is assumed to be unstrained and unstressed initially and has uniform temperature. Formulation is applied to the fractional generalization of Lord-Shulman theory and the equations are tackled by employing Laplace and Fourier transforms. Expressions for different fields such as displacement, temperature, stress, concentration and chemical potential in physical domain are obtained using a numerical inversion technique. Finally, numerical solution is carried out for copper material and corresponding graphs are plotted to illustrate and compare theoretical results. Some particular cases of interest have also been deduced from the present study. Numerical results predict finite speeds of propagation for thermoelastic and diffusive waves.

A numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

This paper studies the buckling analysis for a ring-stiffened cylindrical shell consisted of functionally graded material (FGM) subjected to hydrostatic pressure and thermal loads. Material properties of the ring-stiffened FGM cylindrical shell are assumed to be temperature-dependent, and vary smoothly through the thickness direction of the structure according to a volume exponent. Based on the Donnell assumptions, buckling loads of the ring-stiffened FGM cylindrical shell are presented by utilizing the Galerkin method. Numerical results reveal that thermal loads, volume exponent and geometric parameters have significant effects on the buckling behavior of the ring-stiffened cylindrical shell.

The peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.

In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

Contact between hot objects and liquids occurs in many industries, such as nuclear reactors, metal casting industries and paper production. In such cases growth of vapour film leads to steam explosion that may cause human and financial damages. It is obvious that possibility of these phenomena can be judged by comparing vapour film radius growth and pressure inside vapour film. In this paper vapour film growth and pressure inside the vapour film formed, on hot sphere interaction with water, are investigated. The numerical simulation of problem is obtained and then validated using experimental test and other available results. The effects of the variations of different parameters such as hot sphere diameter, temperature, immersion depth into water and bulk water temperature are investigated on the vapour film radius, vapour pressure inside vapour film and the saturation temperature of phase interface surface. Finally, the overall results show that the effect of hot sphere interaction with water would be the same pressure inside vapour film suddenly increases up to 5 times more than initial pressure which would lead to hazard and put the safety of the system at risk.

Even though electro-magnetic wave can be calculated from Maxwell's equations, the cause of electro-magnetic waves has not been fully understood. This paper proposes a Newton's laws of motion based aether theory to derive identical results as those from Maxwell's equations for free field. The authors suggest that every aether particle has a mass and occupies a volume in space. Every aether particle has translational movement and particle spin movement. The translational movement is similar to the gas particle moving in the air and it does not produce an electro-magnetic wave. The particle spin movement generates shear and a spin wave that will be shown to have the same results as Maxwell's equations. Detailed derivation of electro-magnetic wave solutions from the proposed aether theory and Maxwell's equations is presented in this paper to show the validation of this model.