The unsteady motion of a fully immersed solid sphere at low to moderate particle Reynolds number, from 1 to about 1600, has been modeled by considering the quasi-steady viscous drag, the added mass force, and the history force. The last force results from unsteady boundary layer growth and is often neglected in multiphase flow applications due to its complex formula. However, it has been shown that this unsteady viscous force is more crucial than the widely employed added mass force to describe an unsteady sphere motion. Thus, targeting the flow regime when the quasi-steady viscous drag is dominating, this work proposes two simple formulae to approximate the errors of neglecting either the history force or the added mass force in describing a fully immersed spherical pendulum motion. The proposed formulae are shown to capture the actual error when the numerical solution of a partial model that omits one force component is compared to the full model prediction when the sphere density is not too close to the ambient liquid.

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.

A systematic procedure is developed to calculate ground vibration at any specific location in layered medium due to harmonic loadings applied at a circular plate on the medium. In the procedure, the technique decomposing the interaction tractions between excited plate and layered medium will be employed. The decomposed tractions will automatically match boundary values of general solutions of three dimensional wave equations in cylindrical coordinates. In numerical results, the effect of layered stratum on ground vibration will be investigated and how ground vibration in layered medium decreases with depth will be presented. Also, from the numerical results, one can observe ground vibration may not decay monotonically along distance away from vibration source. The presented scheme is proved to be effective and efficient for accurately predicting near-field ground response to harmonic loadings applied at a rigid circular plate on layered medium. Comments on the presented scheme and numerical results will be given.

A nonlinear stability of two superposed semi-infinite Walters B′ viscoelastic dielectric fluids streaming through porous media in the presence of vertical electric fields in absence of surface charges at their interface is investigated in three dimensions. The method of multiple scales is used to obtain a Ginzburg-Landau equation with complex coefficients describing the behavior of the system. The stability of the system is discussed both analytically and numerically in linear and nonlinear cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the surface tension and medium permeability have stabilizing effects, and the fluid velocities, electric fields and kinematic viscoelastici-ties have destabilizing effects, while the porosity of porous medium and kinematic viscosities have dual role on the stability. In the nonlinear case, it is found that the fluid velocities, kinematic viscosities, kinematic viscoelasticities, surface tension and porosity of porous medium have stabilizing effects; while the electric fields and medium permeability have destabilizing effects.

Shell theory solutions for radial buckling of multiply-concentric hollow cylinders are presented. Multi-cylindrical systems are those composed of two or more concentically mounted hollow tubes, wherein the annular space mediates inter-tube forces, attractive or repulsive depending on structural details of composites. Reflecting the multiple core-shell structures, the systems often exhibit peculiar radial buckling modes, which should be relevant to macro scale applications for deep water oil and gas transportation andmicroscale realization in lipid bilayer tubes. In this article, we focus on an illustrative example of such the multiply-tubular systems with nanometric dimension, the so-called multiwalled carbon nanotubes (MWNTs). Theoretical analysis based on a thin shell theory allows us to find anomalous radial buckling behaviors of MWNTs driven by hydrostatic pressure. The obtained buckling modes are characterized by petal-like wavy cross sections, which is what we call the radial corrugation of MWNTs. An important observation is the mechanical consequence of stiff core-tube insertion into the innermost hollow region of a given MWNT. The insertion results in a significant variance in the critical buckling pressure, above which the MWNT undergoes radial corrugation. The insertion-induced-variance in the critical pressure is due to the primary role of inter-tube interaction between adjacent constituent tubes, as explained within our theoretical model.

This paper extends the recently developed method of reverberation-ray matrix for planar structures to three-dimensional framed structures. The propagation of steady state axial, flexural and torsional waves, as well as the mode conversions through scattering of all three waves at connecting joints are evaluated in the frequency domain. The transient waves in all members are then determined by the Fourier synthesis. The transient responses of a two-storey framed building subject to a step time loading are calculated in detail. Numerical results are obtained for early time as well as moderately long time records. The results are shown to be accurate in arrival times of all three types of waves and in asymptotic values at times.

This paper studies the behavior of second grade viscoelastic fluid past a cavity in a horizontal channel. The effects of Reynolds number, fluid elasticity and the aspect ratio of the cavity on the flow field are simulated numerically. The equations are converted into the vorticity and stream function equations. The solution is obtained by the finite difference method.

The behavior of viscoelastic fluids is quite different from the Newtonian fluid, due to the effects of fluid elasticity. Only one flow pattern appears when the Newtonian fluid past the cavity. However, three kinds of flow patterns appear while the viscoelastic fluids past the cavity by increasing Reynolds number from 20 to 300. The flow field is affected by the fluid elasticity as well as the aspect ratio of the cavity. The transitional flow pattern appears at lower Reynolds number as the higher elasticity fluid past the cavity with larger aspect ratio.

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 boundary layer flow of an Eyring-Powell fluid over a stretching surface subject to the convective boundary condition is investigated. Nonlinear problem is computed and a comparative study is presented with the existing results in viscous fluid. The constructed differential systems have been solved for homotopic solutions. Convergence of series solutions has been discussed. Special emphasis has been given to the effects of material parameters of fluid (ε), (δ), Biot number (γ) and Prandtl number (Pr) on the velocity and temperature profiles. Tabulated values of Nusselt number and skin friction for different emerging parameters are also illustrated. It is noted that the boundary layer thickness is an increasing function of (ε) and decreasing function of (δ). However the temperature and thermal boundary layer thickness decrease when the values of (ε) and (δ) are increased.

Disc rheological parameters regulate the mechanical and biological function of intervertebral disc. The knowledge of effects of degeneration on disc rheology can be beneficial for the design of new disc implants or therapy. We developed two material property identification protocols, i.e., inverse poroelas-tic finite element analysis, and biphasic closed form solution. These protocols were used to find the material properties of intact, moderate and severe degenerated porcine discs. Comparing these two computational protocols for intact and artificial degenerated discs showed they are valid in defining bi-phasic/poroelastic properties. We found that enzymatic agent disrupts the functional interactions of proteoglycans which decreased hydraulic permeability and aggregate modulus but increased the Poisson's ratio. The fatigue loading, which damages disc structure, and squeezes and occludes the matrix pores, further decreased the hydraulic permeability and the Poisson's ratio but increased the elastic modulus. The FE simulations showed the stress experienced during the creep test increases with severe degeneration but steady-state fluid loss decreases for the both moderate and severe degenerated discs. Discriminant analysis declared that the probability of correct classification using the FE analysis is higher than the results of the closed form solution. The specimen-specific models extracted from FE analysis can be additionally used for complimentary investigations on disc biomechanics.

The problem of magnetohydrodyanmic stagnation point flow and heat transfer of second grade fluid past a radially stretching sheet is investigated. The flow problems are examined in the presence of Newtonian heating and Soret and Dufour effects. The relevant mathematical problems are developed through equations of continuity, momentum, energy and concentration. The reduced differential equations are solved for the convergent series solutions. In order to validate the homotopy analysis method (HAM), a comparative study between the present and previous results is made. It is observed that Dufour and Soret effects on temperature and concentration distributions are different. Qualitatively, the influence of Prandtl number on temperature and Schmidt number on concentration is similar. It is further noted that the diffusion of solute in second grade fluid is increasing function of Soret number whereas it decreases when Dufour number increases.

Resistance training has been shown to be effective for developing musculoskeletal strength and is recommended by many major health organizations, such as the American College of Sports Medicine and the American Heart Association. This form of training is available for most populations, including adolescents, healthy adults, the elderly, and the clinical population. Resistance training equipment design relies heavily on the analysis of human movement. Dynamic models of human movement help researchers identify key forces, movements, and movement patterns that should be measured. An at-home resistance training upper limb exoskeleton has been designed with a three-degree-of-freedom shoulder joint and a one-degree-of-freedom elbow joint to allow movement of the upper limb at single and multiple joints in different planes. The exoskeleton can continuously increase the resistance as the spring length changes to train more muscle groups and to reduce the potential risk of muscle injury to the upper limb by free weights and training equipment. The objectives of this research were to develop a dynamic model of the spring-loaded upper limb exoskeleton and to evaluate this model by adopting an appropriate motion analysis system to verify our hypotheses and to determine the optimal configuration of a spring-loaded upper limb exoskeleton for further verification studies.

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.

Despite the analysis of muffler performance for many years, most works focus mainly on reducing inlet sound and fail to consider the flow effect. Most of their results correlate well with the experimental measurements. Subsequent works have considered the mean flow effect. Owing to Doppler's effect, transmission loss curve of the muffler will shift in its corresponding frequency. However, the correlation is worse than the experimental results since the flow induced noise does not include in the analysis. This work elucidates how flow induced noise affects muffler performance by analyzing a uniform flow that passes through perforated mufflers. The flow field is calculated with the CFD method, followed by evaluation of the aerodynamic noise based on the simulation results. Additionally, the procedure is simplified by computing and comparing only the total sound power induced by the flow in the muffler interior. Two muffler types, Helmholtz resonator and plug perforated tube muffler, are analyzed and discussed.

This article addresses peristaltic flow of third order fluid in an asymmetric channel. Channel walls are subjected to the convective boundary conditions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Long wavelength approximation and perturbation method give the series solutions for the stream function, temperature and longitudinal pressure gradient. Analysis has been further carried out for pressure rise per wavelength through numerical integration. Several graphs of physical interest are displayed and discussed.

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.

This study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

Analytical solutions are presented for time periodic EOF flow of linear viscoelastic fluids through a cylindrical micro-pipe. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluid and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. The velocity expressions of these two layers were obtained, respectively. By numerical computations, the influences of the periodic EOF electric oscillating Reynolds number Re, Deborah number De, depletion layer thickness δ and the viscosity ratio γ of Maxwell to Newtonian fluids on velocity profile are presented. For a prescribed De, the increasing Re will cause large changes of the EOF velocity with decreasing velocity magnitude. For a given Re, large De gives large EOF velocity magnitude. Increasing γ will lead to larger velocity amplitude for a given lower Re. However, at higher Re, the velocity amplitude decreases with the viscosity ratio γ, especially within the depletion layer. In addition, large depletion layer thickness gives small EOF velocity magnitude for fixed Re and De. Finally, the influence of De on energy dissipation is studied. These results provide a detail insight of the flow characteristic of this flow configuration.

This paper experimentally studies flow separation and aerodynamic performance of a NACA633018 wing using a series of piezoelectric-driven disks, which are located at 12% chord length from the leading edge to generate a spanwise-distributed synthetic jets to excite the passing flow. The experiment is conducted in an open-type wind tunnel with Reynolds numbers (Re) of 8 × 104 and 1.2 × 105, respectively, based on the wing chord. The oscillations of the synthetic jet actuators (SJAs) disturb the neighboring passage flow on the upper surface of the wing before the laminar separation takes place. The disturbances of energy influence the downstream development of boundary layers to eliminate or reduce the separation bubble on the upper surface of the wing. Significant lift increase and drag decrease are found at the tested Reynolds number of 8 × 104 due to the actuators excitation. Furthermore, the effect of drag also reduces dominant with increasing Reynolds number, but the increase on lift is reduced with the Reynolds number increased.