For an endoreversible heat engine operates steadily between two fixed temperatures, Bejan found the engine's best performance can be obtained if the total thermal conductance is evenly divided for hot-end and cold-end heat exchangers. In this study, a heat by-pass model is used to represent the losses due to internal irreversibilities, and the more general formulations are derived for both the optimal area allocation and the maximum thermal efficiency. The results calculated from the present formulations when there is no internal irreversibility(a special case) are consistant with that obtained by Bejan.

This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a fluid-filled viscoelastic spherical membrane immersed in an unbounded viscous heat-conducting compressible fluid. The thermoviscous effects in the fluid are incorporated by application of a thin boundary layer model. The dynamic viscoelastic properties of the spherical membrane are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak-Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the basic acoustic quantities, such as the scattered far-field pressure directivity pattern, and the scattering cross section are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid thermoviscosity-related mechanisms, dynamic viscoelastic properties of the obstacle can be of significance in sound scattering. The presented analysis is of practical interest in development of contrast agents for echocardiographic research with potential clinical applications.

A compressively strained pseudomorphic Si1−xGex film being debonded from Si substrate by selective etching forms wrinkles with a uniform space periodicity. The present study provides experimental evidences and a theoretical model for the wrinkling process. To allow large deflection, non-linear Von Karman plate theory is employed. The amplitude and wavelength of wrinkles are determined by minimizing the total free energy of a debonded wrinkled film. The wrinkling analysis has shown that the amplitude and wavelength of wrinkled film are an outcome of a subtle compromise between bending energy, and normal and shearing components of the stretching energy. The wave number nondimentionalized over the depth of etch is a function of the membrane strain of a bonded film, Poisson's ratio, and the nondimensional film thickness.

To model the viscous effect, the core area of particles in Leonard's core spreading vortex method must grow linearly in time, which however results in growing convective errors and consequently causes the failure of a correct convergence of the method to the Navier-Stokes equations. The so-called diffusion vortex method was proposed and claimed to have smaller core-area growth rates because part of the viscous effect is modeled into the movement of particles. The growth rates however are non-uniform and an additional diffusion error arises due to the nonzero divergence of the diffusion velocity. The goal of this work is to analyze the associated errors of several existing versions of the diffusion vortex method and compare them with that of Leonard's. Simulations of two axisymmetric flows are performed to measure the involved diffusion errors and consequently distinguish these diffusion vortex methods. The results show that the circulation conservation is important, besides a small core-area growth rate, in obtaining a good accuracy. Under the consideration of both efficiency and accuracy, the diffusion vortex method in which each vortex particle conserves its own circulation on its core area alone is recommended.

Novel electrohydrodynamic (EHD) pump driven micro mixers are fabricated to study fluidic mixing in micro channels experimentally. Microscopic flow visualization experiments are presented to visualize microscale mixing in micro mixers. Mixing is achieved in a laminar flow by perturbing the main flow with EHD pumps in a micro channel. EHD pumps operate in a way to form cross-stream mixing mechanism by using either dc voltage or traveling wave signals. Experimental results show transverse or vortical cross-stream flows are generated within hundreds microns distance in the micro mixers, thereby increasing mixing.

In this paper, Valanis' steady creep theory with four creep parameters was derived from a liaison of the theory of deformation kinetics with internal isotropy and the theory of irreversible thermodynamics of continuous media with only one internal state variable.

According to the theory, steady creep rates under simple shear and simple tensile conditions are related and allow one to construct creep-parameters maps of high lead Pb/Sn solders (from 90% to 100% Pb). When testing temperatures are higher than solder's solvus temperature, microstructural transformation from lamellae α + β phase to solid solution α phase in the bulk specimens are considered in the construction of maps. Applications of maps in the 97.5Pb/2.5Sn solder joints creep tests need minor modifications due to dispersive precipitation of tin particles in lead matrix. As a result, the maps may provide estimated steady creep rates for the usage of finite elements analysis in the microsystem or electronic packaging analysis.

The solutions for flow and heat transfer in a steady laminar boundary layer flow are presented analytically for an electrically conducting viscoelastic fluid, subject to a transverse uniform magnetic field, past a semi-infinite stretching sheet. The temperature profiles and thermal characteristics at the wall are drawn and tabulated for selected parameters with prescribed surface temperature (PST) and prescribed surface heat flux (PHF) conditions. We also give the asymptotic solutions for temperature when the Prandtl number is very large. It is found that the inclusion of Joule heating has a significant influence on the thermal characteristics at the wall and the wall heat transfer strongly depends on the Prandtl number Pr as well as the Eckert number Ec. The heat flow may transfer from the fluid to the wall when Ec is large rather than from wall to the fluid when Ec is small. A physical argument about the thermal characteristics at the wall is proposed.

Bulk migration of particles towards regions of lower shear occurs in suspensions of neutrally buoyant spheres in Newtonian fluids undergoing creeping flow in the annular region between two rotating, coaxial cylinders (a wide-gap Couette). For a monomodal suspension of spheres in a viscous fluid, dimensional analysis indicates that the rate of migration at a given concentration should scale with the square of the sphere radius. However, a previous experimental study [12] showed that the rate of migration of spherical particles at 50% volume concentration actually scaled with the sphere radius to approximately the 2.9 power. In the current study, a series of experiments is performed to extend the previous study to two new concentrations, namely, 35% and 42.5%. The new study indicates that the power scaling decreases with concentration.

In this paper, an efficient macromodel extraction technique for dynamical MEMS gas damping effects is presented. The technique applies an Arnoldi-based model-order-reduction algorithm to generate low-order macromodels from a FEM approximation of the governing equation of the squeeze-film fluidic damping effect, the Reynolds equation. We demonstrate that this approach is more than 100 times efficient than previous approaches, which solve the Reynolds equation using transient finite-element/finite-difference methods. The generated gas-damping macromodels can be easily inserted into system-level modeling packages, such as SPICE, Saber and Simulink, for transient and frequency coupled-domain analysis. We also demonstrated that the simulated results are in good agreement with experimental results for various MEMS devices.

To study the cutting forces, the carbide tip's surface temperature, and the mechanism of secondary chip and main chip formation of face milling stainless steel with a chamfered main cutting edge has been investigated. Theoretical values of cutting forces were calculated and compared to the experimental results with SUS 304 stainless steel plate as a workpiece material. Force data from these tests were used to estimate the empirical constants of the mechanical model and to verify its prediction capabilities. A comparison of the predicted and measured forces shows good agreement. A preliminary discussion is also made for the design of special tool holders and their geometrical configurations. Next, the tips mounted in the tool holders are ground to a chamfered width and the tool dimensions are measured by using a toolmaker microscope.

This paper uses three lubrication models to explore the differential phenomenon in the status of thin film lubrication (TFL). According to the viscous adsorption theory, the modified Reynolds equation for thin film elastohydrodynamic lubrication (TFEHL) is derived. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and density of the lubricant vary with pressure in each layer. Under certain conditions, such as a rough or concentrated contact of a nominally flat surface, films may be of nanometer scale. The thin film elastohydrodynamic lubrication (EHL) analysis is performed on a surface forces (SF) model which includes van der waals and solvation forces. The results show that the proposed TFEHL model can reasonably calculate the film thickness and the average relative viscosity under thin film EHL. The adsorption layer thickness and the viscosity influence significantly the lubrication characteristics of the contact conjunction. The differences in pressure distribution and film shape between surface forces model and classical EHL model were obvious, especially in the Hertzian contact area. The solvation force has the greatest influence on pressure distribution.

As an essential foundation for the associated thermoelasticity analysis in the boundary element method (BEM), this article proposes an expedient, yet powerful, approach to analyze the heat conduction in multiply jointed anisotropic media with bonding defects/interface cracks. The direct domain mapping technique (DDM) is applied to treat a domain consisting of dissimilar anisotropic sub-regions in the potential theory of BEM. The heat transfer across a crack is modeled with a gap conductance equation specially formulated for the BEM analysis. Two numerical examples are provided as illustrations of the validity and the applicability of this proposed scheme.

A simple model has been developed for the study of turbulent film condensation from downward flowing vapors onto a horizontal circular tube with variable wall temperature. The interfacial shear at the vapor condensate film is evaluated with the help of Colburn analogy. The condensate film flow and local/or mean heat transfer characteristics from a horizontal tube with non-uniform temperature variation under the effect of Froude number, sub-cooling parameter and system pressure parameter has been conducted. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on the non-uniform wall temperature variation is almost negligible.

Recently, Shy and his co-workers developed a new turbulent flow system that used a pair of counter-rotating fans and perforated plates to generate stationary near-isotropic turbulence, as verified by LDV measurements, for the study of premixed turbulent combustion processes. This paper evaluates for the first time the correlations between spatial and temporal properties of small-scale intermittency in such a fan-stirred near-isotropic turbulence. These spatiotemporal properties are obtained simultaneously via high-speed digital particle image velocimetry together with wavelet analyses. It is found that the wavelet energy spectra in the inertial range of near-isotropic region all exhibit a slope of nearly −5/3 which spans at least from 3Hz to 100Hz. Characteristic scales, including the integral time and length scales, Taylor microscales, and viscous dissipation scales, are identified without the use of Taylor hypothesis. Thus, a direct evaluation of Taylor hypothesis in near-isotropic turbulence with zero mean velocity can be made. From variations of the flatness factor, equivalent to the 4th order velocity structure function, in the spatial and time domains, it is found that the characteristic spatial and temporal intermittent scales of intense vorticity structures in the dissipation range of the fan-stirred near-isotropic turbulence occur around 5 ∼ 8η and τk, respectively, where η and τk are the Kolmogorov length and time scales. These results are useful for further study of particle settling in turbulence, a problem of both engineering and geophysical interest.

In the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

This paper describes the applications of the method of fundamental solutions (MFS) as a mesh-free numerical method for the Stokes' first and second problems which prevail in the semi-infinite domain with constant and oscillatory velocity at the boundary in the fluid-mechanics benchmark problems. The time-dependent fundamental solutions for the semi-infinite problems are used directly to obtain the solution as a linear combination of the unsteady fundamental solution of the diffusion operator. The proposed numerical scheme is free from the conventional Laplace transform or the finite difference scheme to deal with the time derivative term of the governing equation. By properly placing the field points and the source points at a given time level, the solution is advanced in time until steady state solutions are reached. It is not necessary to locate and specify the condition at the infinite domain such as other numerical methods. Since the present method does not need mesh discretization and nodal connectivity, the computational effort and memory storage required are minimal as compared to the domain-oriented numerical schemes. Test results obtained for the Stokes' first and second problems show good comparisons with the analytical solutions. Thus the present numerical scheme has provided a promising mesh-free numerical tool to solve the unsteady semi-infinite problems with the space-time unification for the time-dependent fundamental solution.

The purpose of this work is to study the dynamic mechanical response of silicon wafer subjected to low-velocity impact loading. Transient finite element analysis was utilized to obtain the numerical simulated result and was used to check against the experimental findings. Good relationship between each other was observed. A pair of polysilicon microsensors manufactured by the micro-fabrication technique was directly fabricated on the surface of silicon wafer so as to detect the impact induced dynamic strain. A series of low-velocity impact tests utilizing the home-made drop-weight mini-tower tester was conducted. These test results were used to examine the accuracy and adequacy of the current micro strain sensors for stress wave propagation measurements. It is concluded that the difference between the present measured wave speed and the one-dimensional longitudinal wave speed under conditions of plane strain were determined to be within 5.6% for the present low-speed impact problem. A maximum of 10.9% deviation between the test determined elastic modulus and a reference value (16) of 130 GPa was found based on a series of impact test results. In addition, a difference of 2% error was reported when we compared the test detected peak stress value after impact initiated (before wave is reflected from the boundary) and the corresponding numerical simulated response.

Broadband dispersion behaviors of wedge waves traveling along large-angled wedges are investigated with a laser ultrasound technique. Wedge waves are guided acoustic waves propagating along wedge tips. Until now, no elasticity-based close-form solution is available for the prediction of dispersion behavior of wedge waves. By assuming the wedge as a thin plate with variable thickness, McKenna obtained a theoretical approximation for the prediction of dispersion relation of truncated wedges within limited apex angle and bandwidth. The current research provides experimental data on wideband dispersion spectra of wedge waves traveling along large-angled wedges. It is found that the thin plate theory is accurate only within a small wavenumber regime. Also, a limiting behavior in the large wavenumber regime the ASF dispersion spectra are found to approach the Rayleigh wave speed.

This investigation presents the solution of kinematic wave equations for overland flow, in which the lateral term is determined from unsteady rainfall and the infiltration φ index model [1], in which the rate of abstractions is constant, yielding an excess rainfall hyetograph with a total depth that equals the depth of direct runoff over the watershed. Lateral inflow is inferred by the unit step function to represent an unsteady rainfall event; the solution uses the method of characteristics. Part of the discharge hydrograph that satisfies the boundary condition is semi-analytically solved, by a reduced, simple procedure, which does not require the use of numerical method such as finite difference. The analysis presented herein this investigation deals with both rising and falling stages. Example calculations, water surface profiles, and discharge hydrographs are also presented.

An analysis is presented for wave propagation in infinite homogeneous elastic plates of piezoelectric materials. The analysis is an extension to the work by Shuvalov [1] on wave propagation in general anisotropic elastic plates. A real form of dispersion equation is provided for a piezoelectric plate subjected to different boundary conditions on the plate surfaces. Perturbation theory [2] is exploited to obtain long-wavelength low-frequency approximation for physical quantities of wave propagation, including wave amplitude, stress, electric potential, electric displacement and velocity.