In the conventional boundary element analysis, near-singularities are present in the associated boundary integral equation for problems involving ultra-thin media. For this case, any conventional numerical schemes will fail to yield proper values for the integrals. In this paper, the boundary integrals of the boundary element method for 3D potential problems are fully regularized by the technique of integration by parts under the local coordinate system. The fully regularized integrands are expressed as very explicit formulations that can be easily programmed into a computer code. Numerical tests carried out for a typical case have verified the accuracy of the approach for any orders of small distance between the source and the element under integration.

Effects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.

A comprehensive study of MHD two dimensional stagnation point flow with heat and mass transfer characteristics towards a heated shrinking sheet immersed in an electrically conducting incompressible micropolar fluid in the presence of a transverse magnetic field is analyzed numerically. The governing continuity, momentum, angular momentum, mass concentration and heat equations together with the associated boundary conditions are first reduced to a set of self similar nonlinear ordinary differential equations using a similarity transformation and are then solved by a method based on finite difference discretization. Some important features of the flow, heat & mass transfer characteristics and chemical reaction for different values of the physical parameters are analyzed, discussed and presented through tables and graphs. The study may be beneficial in the flow and heat control of polymeric processing.

The unsteady laminar boundary layer flow of nanofluid caused by a linearly stretching sheet is considered. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into similar forms by using appropriate similarity transformations. The uniformly valid explicit expressions of velocity, temperature and nanoparticles volume fraction are derived. Convergence of the series solutions is carefully analyzed. It is observed that an increase in the strength of Brownian motion effect rises the temperature appreciably. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Brownian motion effect intensifies. It is also found that the temperature and nanoparticles concentration are increasing functions of the unsteady parameter.

An investigation with computational fluid dynamics of the ground effect on a small bird revealed quantitatively the obstruction of the vortex expansion resulting from the presence of the ground at varied distance. Preceding authors focused mainly on the bird's wings, generally neglecting the bird's body; we discuss specifically the distinction of the aerodynamic effect between cases with and without the presence of the bird's body. The results of simulation show that, considering only two wings, for a distance between the wing model and the ground smaller than a semi-span, the smaller is the ground clearance, the more significant is the ground effect. At clearance 0.37 times a semi-span, the drag is decreased 11%, and the lift is increased 5.6%. The ground effect for an intact bird model composed of both wings and body is less effective than that for a simplified model with body omitted, because a suction was observed on the lower surface of the intact bird's trunk at clearance 0.37 times a semi-span; for this reason the intact bird model benefits less from the ground effect than the model with body excluded, but increased lift and decreased drag remain observable. This research treating the ground effect on a gliding bird reveals the importance of the presence of the bird's body in both computational and experimental models.

Hall effects on the unsteady Couette flow between two infinite horizontal parallel plates in a rotating system under the boundary layer approximations have been studied. One of the plate is at rest and the other oscillates in its own plane with the velocity U(t). An exact solution of the governing equations has been obtained by the use of the Laplace transform technique. The numerical results for the velocity components and the shear stresses are depicted graphically. Asymptotic behavior of the solution has analyzed for large values of magnetic parameter, rotation parameter and frequency parameter to gain some physical insight into the flow pattern. It is observed that there exists thin boundary layer (s) is formed near the stationary plate for large values of rotation parameter, magnetic parameter and frequency parameter.

This paper studies the influence of mass transfer in the magnetohydrodynamic (MHD) boundary layer stagnation point flow of Burgers' fluid over a shrinking sheet. Analysis has been carried out in the presence of first order chemical reaction. The two-dimensional flow equations are modeled and then simplified using boundary layer approach. Similarity variables are used to transform the partial differential equations into nonlinear ordinary differential equation. The resulting system is computed using homotopy analysis method (HAM). It is noted that retardation time in Burgers' fluid enhances the magnitude of the flow. The gradient of mass transfer and surface mass transfer for various interesting parameters are also tabulated and analyzed.

This paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

The double side approach method combines the method of weighted residuals (MWR) with mathematical programming to solve the differential equations. Once the differential equation is proved to satisfy the maximum principle, collocation method and mathematical programming are used to transfer the problem into a bilateral inequality. By utilizing Genetic Algorithms optimization method, the maximum and minimum solutions which satisfy the inequality can be found. Adopting this method, quite less computer memory and time are needed than those required for finite element method.

In this paper, the incompressible-Newtonian, fully-developed, steady-state laminar flow in equilateral triangular, rectangular, elliptical and super-elliptical ducts is studied. Based on the maximum principle of differential equations, the monotonicity of the Laplace operator can be proved and the double side approach method can be applied. Different kinds of trial functions are constructed to meet the no-slip boundary condition, and it was demonstrated that the results are in great agreement with the analytical solutions or the formerly presented works. The efficiency, accuracy, and simplicity of the double side approach method are fully illustrated in the present study to indicate that the method is powerful for solving boundary value problems.

A Plate Infinite Element Method (PIEM) formulation based on Reissner-Mindlin theory is proposed for the stress analysis of cracked plates under bending and tension. The validity of the proposed formulation is demonstrated by comparing the results obtained for the normalized Stress Intensity Factor (SIF) under various loading conditions with the solutions presented in the literature. Importantly, the proposed formulation enables the effects of different crack lengths to be analyzed without the need to re-mesh the computational domain for each simulation/analysis. Overall, the PIEM formulation provides an accurate and computationally-efficient means of analyzing a wide variety of plate bending problems.

In this paper, we studied the peristaltic flow and heat transfer of an incompressible, electrically conducting Bingham Non-Newtonian fluid in an eccentric uniform annulus in the presence of external uniform magnetic field with slip velocity and temperature jump at the wall conditions. The viscous and Joule dissipations are taken into account. The inner tube is rigid and moving with a constant axial velocity, while the outer tube has a sinusoidal wave traveling down its wall. Under zero Reynolds number condition with the long wavelength approximation, the axial velocity and the stream function are obtained analytically. A numerical solution for the governing partial differential equation of energy is performed in order to analyze the temperature distribution. The effects of all parameters of the problem are numerically discussed and graphically explained.

Many engineering problems are governed by partial differential equations which can be solved by analytical as well as numerical methods, and examples include the plasticity problem of a geotechnical system, seepage problem and elasticity problem. Although the governing differential equations can be solved by either iterative finite difference method or finite element, there are however limitations to these methods in some special cases which will be discussed in the present paper. The solutions of these governing differential equations can all be viewed as the stationary value of a functional. Using an approximate solution as the initial solution, the stationary value of the functional can be obtained easily by modern global optimization method. Through the comparisons between analytical solutions and fine mesh finite element analysis, the use of global optimization method will be demonstrated to be equivalent to the solutions of the governing partial differential equations. The use of global optimization method can be an alternative to the finite difference/ finite element method in solving an engineering problem, and it is particularly attractive when an approximate solution is available or can be estimated easily.

The linear problem of large deflection of a clamped and layered piezoelectric circular plate under initial tension due to lateral pressure is solved. Von Karman plate theory for large deflection is extended to a symmetrically laminated case including a piezoelectric layer. The thus derived nonlinear governing equations are simplified by neglecting the arising nonlinear terms, yielding a modified Bessel equation or a standard Bessel equation for the lateral slope. These equations are solved analytically by imposing boundary conditions for the clamped edge. For a 3-layered nearly monolithic plate with a low applied voltage upon the piezoelectric layer, the results are in a good agreement with those available in literature for a single-layered plate under pure mechanical loading, thus validates the present approach. Typical 3-layered piezoelectric plates are then implemented and the results show that, piezoelectric effect seems to be apparent only up to a moderate initial tension. For a relatively high pretension, the effect of initial tension appears to be dominant, yielding nearly the same results for the structural responses, regardless of the piezoelectric effect, i.e., the magnitude of voltage applied upon the piezo-electric layer.

In the present study, the effect of the number of stages of Tesla Micro-Valve (TMV), as well as the dependency of Reynolds number, Re, on the valve performance has been analyzed. For this purpose, different layouts include one to four-stage with different sizes are investigated numerically. The main criterion for evaluation of valves performance is diodicity, Di. Unsteady and steady flow in valve have been simulated and compared. It is shown that although there are some difference but the trend is similar for both responses. Finally, 2-D and steady state computations of the fluid flow have been utilized that reveal a strong dependence of Di on Re and pressure drop, ΔP. The results showed that the maximum Di of the two-stage microvalve is approximately 1.45 times of that of one-stage. Additional stages increase the complexity, and they do not change Di appreciably. It is concluded that two-stage layout of Tesla type valve is the best option. Also, the two-stage valve performance for three different sizes is compared with Nozzle-Diffuser type Micro-Valve (NDMV). Comparisons, which are performed based on calculation Di in applicable range of Re, showed that Di as a function of Re is independent of the valve size. Also, the superiority of the Tesla type valve at higher Re and its weakness at lower Re is observed.

The influence of annealing temperature in the course of mechanical-thermal treatment on the steady-state creep of metals is discussed and modeled. The synthesis theory of irrecoverable deformation is taken as a mathematical apparatus. Results obtained in terms of the generalized synthetic theory give good agreements with experimental data.

In this article a two dimensional incompressible viscous flow past a square cylinder oscillating in cross flow with zero and 45 degree angles of attack is numerically studied by a Characteristics Based Splitter (CBS) finite element method. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for the body motion in the flow field. First, the accuracy of the numerical code is tested by comparing the numerical results obtained for the flow over the stationary square cylinder at the three different Reynolds numbers (Re = 100, 200, and 300) with the experimental data available. Then, the numerical results for the square cylinder undergoing transverse oscillations in the two angles of attack at different values of frequency and amplitude are investigated to determine the lock-on region. The results indicate physical similarity between circular and square cylinders concerning lock-on regions. Also the effect of lock-on phenomenon on the flow field pattern and time-averaged drag coefficient is investigated.

In this study, the fictitious time integration method (FTIM) is applied to investigate wave propagation over an arbitrary bathymetry with measured uncertainty. The FTIM is used to convert the higher-order elliptic mild-slope equation (EMSE) into a FTIM like EMSE (FTIMEMSE). It has the advantage to describe wave transformation from deep water to shallow water region in a large coastal area with numerical efficiency. The validity of the noise resistance for the measured uncertainty of the bathymetry is also studied. In addition, typical examples for waves propagating over an elliptic shoal rest on a horizontal and sloping bottom is presented. It is concluded that the FTIM is robust in the numerical stability and capable of against the noise of the measurement.

A non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

A method to simulate contact between two boundaries of structures which are not aligned to predefined axes when using Comsol Multi-physics (v3.3, Comsol Ltd, Cambridge, UK) is presented. This method was developed because of limitations in the existing default contact modelling. Some of these limitations were recently addressed in a separate study; however, the method exploited symmetry across an axis of the coordinate system. The method presented here enables contact modelling with arbitrarily aligned structures within such a coordinate system. The contact method presented is then applied to a simple model with two deformable structures that come into contact, and compared over a range of positions. Results show a minimal variation in peak stress and contact pressure with model orientation, demonstrating that results are independent of orientation. Therefore, the contact method enables contact simulations in Comsol Multi-physics without assuming symmetry about an axis for contract. The method is compatible with the true transient contact method defined.

This research experimentally investigates the rotor aerodynamics of horizontal-axis, micro-wind turbines. Specifically, the aerodynamic characteristics of large-tip, non-twisted blades are studied. The study is conducted in a wind tunnel system to obtain the relations between the power coefficient (CP) and tip speed ratio (TSR), the torque coefficient (CT) and TSR. Effects of rotor position inside a flanged diffuser, rotor solidity and blade number on rotor performance are investigated. The blade cross-section is NACA4415 airfoil. The pitch angle of the blades is fixed at 30°, and the chord length ratio between the blade root and tip (Cr / Ct) is fixed at 0.3. Results show that larger power output is obtained when the rotor placed closer to the diffuser inlet. The 60%-solidity rotor, in general, achieves better power and torque outputs among the test rotor solidities. The higher the blade number is, the larger the power output is, but the difference is small. Comparisons between the present and previous relatively short-tip blades (Cr / Ct = 0.5) show that the present blades have better power and torque outputs at lower rotor rotational speed. These results suggest that the large-tip blades are suitable for micro-wind turbine applications, and make rotor-generator matching more flexible.