Showing papers in "Acta Mechanica in 2005"
TL;DR: In this article, the authors compared the performance of antifoam and CuO and Al2O3 nano particles in cooling engine oil with that of non-antifoams and made a comparison between their heat transfer performance and that of oil without adding such substances.
Abstract: This study adds CuO and Al2O3 nano particles and antifoam respectively into cooling engine oil. A comparison is made between their heat transfer performance and that of oil without adding such substances. The experimental platform is a real-time four-wheel-drive (4WD) transmisson system. It adopts advanced rotary blade coupling (RBC), where a high local temperature occurs easily at high rotating speed. Therefore, it is imperative to improve the heat transfer efficiency. Any resolution to such problems requires a thorough understanding of the thermal behavior of the rotating flow field within the power transmission system. The experiment measures the temperature distribution of RBC exterior at four different rotating speeds (400rpm, 800rpm, 1200rpm and 1600rpm), simulating the conditions of a real car at different rotating speeds and investigating the optimum possible compositions of a nanofluid for higher heat transfer performance.
132 citations
TL;DR: A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented.
Abstract: Active aeroelastic control is a recently emerging technology aimed at providing solutions to a large class of problems involving the aeronautical/aerospace flight vehicle structures that are prone to instability and catastrophic failures, and to oscillations that can yield structural failure by fatigue. In order to prevent such damaging phenomena to occur, the linear/nonlinear aeroelastic control technology should be applied. Its goals are among others: (i) to alleviate and even suppress the vibrations appearing in the subcritical flight speed range, (ii) to enlarge the flight envelope by increasing the flutter speed, and (iii) to enhance the post-flutter behavior by converting the unstable limit cycle oscillation to a stable one. A short review of the available control techniques and capabilities is presented first. Attention is focused on the open/closed-loop of 2D and 3D lifting surfaces as well as on panels exposed to supersonic flowfields. A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented. Emphasis is placed on theoretical and numerical results obtained with the various control strategies that are considered in a comparative way. Finally, conclusions and directions for further work are presented.
91 citations
TL;DR: This work deals with deep and ultra-deep waters installation by the so-called J-Lay method, which consists in laying submarine pipelines with a straight stinger at near-vertical angles with a novel approach for detecting the boundary layer phenomenon.
Abstract: This work deals with deep and ultra-deep waters installation by the so-called “J-Lay” method, which consists in laying submarine pipelines with a straight stinger at near-vertical angles. A hierarchy of simple analytical models is proposed starting from the classical catenary and enriching it to overcome its drawbacks. A novel approach for detecting the boundary layer phenomenon is proposed, and constitutes the base of two of the developed models. All models are compared with each other and with the results of refined numerical simulations in a case of practical interest. In the considered examples the stiffness of the soil has scarce influence, while the boundary layer phenomenon is very important and detected correctly, both from a qualitative and quantitative point of view, by the second class of proposed models.
90 citations
TL;DR: In this paper, the role of the initial material structure of a body, or its developing structure in the course of deformation, is accounted for in the constitutive equation of the material.
Abstract: In this paper, we present a framework within which the role of the initial material structure of a body, or its developing structure in the course of deformation, is accounted for in the constitutive equation of the material. The problem is dealt with at the local level, i.e., at the material neighborhood. If a neighborhood has structure then its geometry cannot be represented by a Euclidean metric. The entire body may thus be non–Euclidean. We formulate the constitutive equation for large deformation in the case where either a neighborhood is non–Euclidean because of its initial structure, or it becomes so by virtue of irreversible internal motion and/or induced dislocation fields, which we discuss at some length. In the formulation of the theory, questions of connectivity arise and are dealt with in the text.
89 citations
TL;DR: In this article, the authors carried out a perturbation analysis for steady gravity-driven film flow over undulations of moderate steepness that are long compared to the film thickness and study the linear stability of the flow in the framework of Floquet analysis.
Abstract: We carry out a perturbation analysis for steady gravity-driven film flow over undulations of moderate steepness that are long compared to the film thickness and study the linear stability of the flow in the framework of Floquet analysis. The effect of geometric nonlinearities on the instability becomes relevant for moderate bottom variations. We find that the critical Reynolds number for the onset of surface waves is higher than that for a flat bottom. At higher inclination angles, the theoretical results are in good quantitative agreement with experiment. At inclination angles where the flat part of the undulation is close to being horizontal, the basic solution for the steady flow fails to describe the flow in the flat part, and the linear stability analysis overestimates the critical Reynolds number.
84 citations
TL;DR: In this article, the effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented.
Abstract: The effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The velocity profiles are compared with previously published works and are found to be in good agreement. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite element method. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first-order chemical reaction the concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.
77 citations
TL;DR: In this article, the authors proposed modified relations along with the Zerilli-Armstrong (Z-A) physical based relations that are used in polycrystalline metals at low and high strain rates and temperatures.
Abstract: The Zerilli-Armstrong (Z-A) physical based relations that are used in polycrystalline metals at low and high strain rates and temperatures are investigated in this work. Despite the physical bases used in the derivation process, the Z-A model exhibits certain inconsistencies and predicts inaccurate results when applied to high temperatures-related problems. In the Z-A model, the thermal stress component vanishes only when T→∞. This contradicts the thermal activation mechanism that imposes an athermal behavior for the flow stress at certain finite critical temperatures. These inconsistencies, in fact, are attributed to certain assumptions used in the Z-A model formulation that causes the model parameters to be inaccurately related to the microstructural physical quantities. New relations are, therefore, suggested and proposed in this work using the same physical bases after overcoming any inappropriate assumptions. The proposed modified relations along with the Z-A relations are evaluated using the experimental results for different bcc and fcc metals. Comparisons are also made with the available experimental results over a wide range of temperatures and strain rates. The proposed model simulations, in general, show better correlation than the Z-A model particularly at temperatures values above 300K∘. Numerical identification for the physical quantities used in the definition of the proposed model parameters is also presented.
71 citations
TL;DR: In this article, a generalized thermo-viscoelastic plane wave model was proposed for a half-space whose surface is subjected to a thermal shock under the effect of rotation with one relaxation time.
Abstract: In this article, we propose a model of generalized thermo-viscoelastic plane waves for a half-space whose surface is subjected to a thermal shock under the effect of rotation with one relaxation time. The normal mode analysis is used to obtain the exact expressions for the considered variables. The resulting formulation is applied to two kinds of boundary conditions. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with one relaxation time in the absence of rotation.
69 citations
TL;DR: In this paper, the Dirichlet-Eshelby tensor is used to characterize the elastic fields due to inclusions embedded in a finite elastic medium, which is the first paper in a series concerned with the precise characterization of elastic fields.
Abstract: This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, self-similarity, and invariant group arguments. In this paper, we consider a two-dimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the so-called Dirichlet-Eshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the Dirichlet-Eshelby tensor are discussed briefly.
60 citations
TL;DR: In this paper, a theory is developed qualitatively and quantitatively describing the paradoxical behavior of general non-conservative systems under the action of small dissipative and gyroscopic forces.
Abstract: In the present paper, a theory is developed qualitatively and quantitatively describing the paradoxical behavior of general non-conservative systems under the action of small dissipative and gyroscopic forces. The problem is investigated by the approach based on the sensitivity analysis of multiple eigenvalues. The movement of eigenvalues of the system in the complex plane is analytically described and interpreted. Approximations of the asymptotic stability domain in the space of the system parameters are obtained. An explicit asymptotic expression for the critical load as a function of dissipation and gyroscopic parameters allowing to calculate a jump in the critical load is derived. The classical Ziegler–Herrmann–Jong pendulum considered as a mechanical application demonstrates the efficiency of the theory.
60 citations
TL;DR: In this paper, the authors proposed a method to install a baffle onto the channel wall to enhance the heat transfer characteristics of backward-facing step flow in a channel, and compared the results of the cases with or without the installation of baffle, the maximum augmentation on average Nusselt number is about 190% for the heating step.
Abstract: Aiming to enhance the heat transfer characteristics of backward-facing step flow in a channel, the present study proposes a method to install a baffle onto the channel wall. The effects of the dimensionless baffle height H b , baffle thickness W b , and distance between the backward-facing step and baffle D on the flow structure, temperature distribution and Nusselt number variation for the system at various Re and Gr/Re2 are numerically investigated. Comparing the results of the cases with or without the installation of baffle, the maximum augmentation on average Nusselt number is about 190% for the heating step and 150% for the heating section of the bottom plate when Pr=0.7, H s =0.5, L=5, H b =0.3, W b =0.2, 100 ≤Re ≤500 and 0≤Gr/Re2≤1. A slight movement of the baffle position could cause a drastic change in the transfer characteristics. In addition, as W b varies from 0.2 to 0.5, the difference in the average Nusselt number is within 3%.
TL;DR: In this article, a three-dimensional analysis of the static response of a clamped rectangular plate made of functionally graded material is presented, where the governing equation of the plate is derived by the Ritz energy method within the linear, small deformation theory of elasticity.
Abstract: A three-dimensional study for the static response of a clamped rectangular plate made of functionally graded material is presented. The governing equation of the plate is derived by the Ritz energy method within the linear, small deformation theory of elasticity. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent and thickness-side ratios are investigated. The developed three-dimensional elasticity solution by the multiterm Ritz method appears to be important because it can be used to assess the accuracy of both the two-dimensional theories as well as that of the numerical methods.
TL;DR: This work proposes a novel hybrid active damper which combines both, the advantages of active control devices, and the salient features of TLCD, e.g., cheap and easy implementation into civil engineering structures, simple modification of the natural frequency and damping properties, little maintenance costs, and a performance comparable to TMD as well as little additional weight if the TLP is used as water reservoir for fire fighting.
Abstract: Tuned liquid column dampers (TLCDs) are energy dissipating substructures, which can be used to improve the dynamics of structures. The basic operating principle is an energy transfer from the vibrating host structure to the TLCD. A TLCD consists of a rigid piping system which is integrated in a structure and partially filled with liquid, preferably water. Its dynamics can be derived using the extended instationary Bernoulli’s equation for moving reference systems. Although both the construction and working principle of TLCDs differ from tuned mass dampers (TMDs), an analogy between the different types of absorber is given. Extending the passive TLCD by an actively controlled air-spring setup, and applying a suitable control strategy results in a novel hybrid active damper which combines both, the advantages of active control devices, and the salient features of TLCD, e.g., cheap and easy implementation into civil engineering structures, simple modification of the natural frequency and damping properties, little maintenance costs, a performance comparable to TMD as well as little additional weight if the TLCD is used as water reservoir for fire fighting. In numerical simulations of dynamically excited structures the proposed TLCD shows a considerable vibration reduction for wind and earthquake loading.
TL;DR: In this paper, the influence of obstacles on granular flows was investigated by solving the hyperbolic Savage-Hutter equations with an appropriate integration technique, and the influence on the obstruction was graphically demonstrated and discussed for a finite mass and a steady inflow of granular material down an inclined plane.
Abstract: One means of preventing areas from being hit by avalanches is to divert the flow by appropriately constituted obstacles. Thus, there arises the question how a given avalanche flow is modified by obstructions and how the diverted flow depth and direction emerge. In this paper rapid gravity-driven dense granular flows, partly blocked by obstacles with different shapes, sizes and positions, are numerically investigated by solving the hyperbolic Savage-Hutter equations with an appropriate integration technique. The influences of the obstructions on the granular flows are graphically demonstrated and discussed for a finite mass and a steady inflow of granular material down an inclined plane, respectively. These flows are accompanied by shocks induced by both the presence of the obstacles and the transition of granular flows from an inclined surface into a horizontal run-out zone when the velocity transits from its supercritical to its subcritical state. The numerical results show that the theory is capable of capturing key qualitative features, such as shocks wave and particle-free regions.
TL;DR: In this article, the authors consider the Stokes flow of a semi-infinite viscous fluid against a liquid film resting on a plane wall and show that the film keeps thinning in time, while the rate of thinning decreases as the interface approaches the wall.
Abstract: Stagnation-point flow of a semi-infinite viscous fluid against a liquid film resting on a plane wall is considered under conditions of Stokes flow and for arbitrary Reynolds numbers. Assuming that the interface remains flat and parallel to the wall at all times, the lateral spatial coordinate is scaled out to yield a simplified system of governing equations in the transverse coordinate normal to the wall, describing the evolution of the flow and displacement of the interface. In this inherently unsteady flow the film keeps thinning in time, while the rate of thinning decreases as the interface approaches the wall. Orthogonal two-dimensional, axisymmetric, three-dimensional, and oblique two-dimensional flow are individually considered. In each case, exact solutions of a similarity form are constructed, and an evolution equation describing the film thickness is formulated and solved by numerical methods. Quasi-steady solutions compare favourably with full calculations of the unsteady flow, suggesting that the unsteady terms have only a minor effect on the rate of film thinning. Dual solutions are uncovered in the case of three-dimensional flow.
TL;DR: In this article, a numerical simulation is performed to investigate the viscous flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish.
Abstract: A numerical simulation is performed to investigate the viscous flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The objective of this study is to elucidate hydrodynamic features of the flow structure over the travelling wavy wall and to get physical insights to the understanding of fish-like swimming mechanisms in terms of drag reduction and optimal propulsive efficiency. The effect of phase speed, amplitude and Reynolds number on the flow structure over the wavy wall, the drag force acting on the wall, and the power consumption required for the propulsive motion of the wall is investigated. The phase speed and the amplitude, which are two important parameters in this problem, predicted based on the optimal propulsive efficiency agree well with the available data obtained for the wave-like swimming motion of live fish in nature.
TL;DR: In this paper, the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically.
Abstract: In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.
TL;DR: In this paper, an exact and closed form solution is obtained for the elastic fields of a circular inclusion embedded in a finite circular representative volume element (RVE), which is subjected to the traction (Neumann) boundary condition.
Abstract: This is the second paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. In this part, an exact and closed form solution is obtained for the elastic fields of a circular inclusion embedded in a finite circular representative volume element (RVE), which is subjected to the traction (Neumann) boundary condition. The disturbance strain field due to the presence of an inclusion is related to the uniform eigenstrain field inside the inclusion by the so-called Neumann-Eshelby tensor. Remarkably, an elementary, closed form expression for the Neumann-Eshelby tensor of a circular RVE is obtained in terms of the volume fraction of the inclusion. The newly derived Neumann-Eshelby tensor is complementary to the Dirichlet-Eshelby tensor obtained in the first part of this work. Applications of the Neumann-Eshelby tensor are discussed briefly.
TL;DR: In this article, the existence, uniqueness and dissipativity of a class of nonlinear dynamical systems including systems with fractional damping is established. But the authors do not consider the effect of damping on the dynamics of the nonlinear systems.
Abstract: Existence, uniqueness and dissipativity is established for a class of nonlinear dynamical systems including systems with fractional damping. The problem is reduced to a system of fractional-order differential equations for numerical integration. The method is applied to a non-linear pendulum with fractional damping as well as to a nonlinear pendulum suspended on an extensible string. An example of such a fractional damping is a pendulum with the bob swinging in a viscous fluid and subject to the Stokes force (proportional to the velocity of the bob) and the Basset-Boussinesq force (proportional to the Caputo derivative of order 1/2 of the angular velocity). An existence and uniqueness theorem is proved and dissipativity is studied for a class of discrete mechanical systems subject to fractional-type damping. Some particularities of fractional damping are exhibited, including non-monotonic decay of elastic energy. The 2:1 resonance is compared with nonresonant behavior.
TL;DR: In this paper, free undamped in-plane vibrations of shear unbounded curved beams around their highly buckled configurations are investigated neglecting rotary inertia effects, and the solutions of the associated eigenvalue problems are found employing two approaches: a semi-analytical method based on Galerkin discretization and a finite element method.
Abstract: Free undamped in-plane vibrations of shear undeformable beams around their highly buckled configurations are investigated neglecting rotary inertia effects. The beams are inertially nonuniform since a lumped mass is rigidly clamped along the span. Two mechanical models are considered depending on the boundary conditions in the post-buckling phases. First, the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end, a roller support, both in the buckling and post-buckling phases. In the second model, the beam is extensible in the post-buckling phase because the roller support boundary is changed into a fixed hinged end. Free undamped vibrations are governed, in the first case, by a homogeneous integral-partial-differential equation and, in the second case, by two coupled partial-differential equations with variable coefficients. The solutions of the associated eigenvalue problems are found employing two approaches: a semi-analytical method based on Galerkin discretization and a finite element method. A close agreement in the outcomes is found. The leading differences relating to the natural frequencies and linear normal modes of the two pre-stressed curved beam models are discussed; in particular, the occurrence of the veering phenomenon and the crossovers are outlined.
TL;DR: In this article, the experimental identification of the field-dependent hysteretic behavior of a magnetorheological (MR) fluid is presented, by adopting one of commercially available MR fluids, both the minor loop property and the wiping-out property are experimentally examined via the rotational rheometer.
Abstract: This paper presents the experimental identification of the field-dependent hysteretic behavior of a magnetorheological (MR) fluid. By adopting one of commercially available MR fluids, both the minor loop property and the wiping-out property are experimentally examined via the rotational rheometer. Subsequently, the Preisach model for the MR fluid is established in order to identify the field-dependent hysteretic behavior. The effectiveness of the identified hysteresis model is then verified in the time domain by comparing the predicted field-dependent shear stress with the measured one.
TL;DR: In this paper, Simo and Pister showed that the widely used hypoelastic equation fails to be exactly integrable to deliver finite elastic relations for several well-known objective stress rates, including Jaumann rate, Green-Naghdi rate, Truesdell rate and Lie derivative (upper Oldroyd rate), etc.
Abstract: In 1984, Simo and Pister [1] demonstrated that the widely-used hypoelastic equation fails to be exactly integrable to deliver finite elastic relations for several well-known objective stress rates, including Jaumann rate, Green-Naghdi rate, Truesdell rate and Lie derivative (upper Oldroyd rate), etc. Successfully treating complicated systems of nonlinear partial differential equations in the Cauchy stress, they proved that Bernstein’s integrability conditions for hypoelastic rate equations could not be fulfilled for each of the foregoing classical stress rates.
TL;DR: In this paper, the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow are performed.
Abstract: Direct numerical simulation of stably and unstably stratified turbulent open channel flow is performed. The three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method based on high-order accurate spatial schemes. The objective of this study is to reveal the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow. Here, fully developed weakly stratified turbulent open channel flows are calculated for the Richardson number ranging from 20 (stably stratified flow) to 0 (unstratified flow) and to −10 (unstably stratified flow), the Reynolds number 180 based on the wall friction velocity and the channel depth, and the Prandtl number 1. To elucidate the turbulent flow and heat transfer behaviors, typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations are analyzed.
TL;DR: In this article, a linear temporal instability analysis has been carried out for a viscous annular liquid jet moving in two swirling gas streams of unequal velocities with the gas stream swirling motion represented by free-vortex rotation.
Abstract: A linear temporal instability analysis has been carried out for a viscous annular liquid jet moving in two swirling gas streams of unequal velocities with the gas stream swirling motion represented by free-vortex rotation. It is found that two modes of unstable surface waves exist, the para-sinuous and para-varicose mode. The results of the two limiting flow situations, which are a cylindrical liquid jet in a swirling gas stream and a swirling gas jet in a liquid stream, indicate that their instabilities are associated with the para-varicose mode on the outer interface and para-sinuous mode on the inner interface of the annular liquid jet, respectively. It is shown that the centripetal force induced by the inner gas stream rotation is destabilizing and enhances the jet instability, while the centripetal force produced by the outer gas stream rotation is stabilizing and reduces the instability of annular liquid jets. It is interesting to find that for a para-varicose mode an increase in the outer gas rotation not only reduces the upper cut-off wave number, but also increases the lower cut-off wave number, leading to the significant reduction in the unstable wave number range. The stabilizing effect of the outer gas rotation is much more significant for para-varicose mode, and the destabilizing effect of the inner gas rotation is much more influential for para-sinuous mode. In general, the para-sinuous mode has a much larger growth rate and is predominant in the annular liquid jet breakup process. Therefore, increasing the inner gas stream rotation can significantly enhance the breakup of annular liquid jets for practical spray applications.
TL;DR: In this article, a preconditioned conjugate gradient approach is developed to solve structural modifications due to the removal of degrees of freedom, which can adaptively monitor the accuracy of approximate solutions.
Abstract: This paper deals with reanalysis of structural modifications due to the removal of degrees of freedom. A preconditioned conjugate gradient approach is developed to solve such problems. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which only depends on the existing decomposition of the stiffness matrix for the initial design. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that, compared with the condition number of the original matrix, the condition number of the preconditioned matrix is largely reduced. Fast convergence and accurate results can thus be achieved by the proposed approach.
TL;DR: In this article, the surface instability of a harmonic solid attracted by a rigid body through the influence of van der Waals forces was analyzed and it was shown that the surface of the solid is always unstable, and the parameter α, characterizing the solid, plays an important role in its surface instability.
Abstract: In this paper, we use complex variable techniques to analyze the surface instability of a harmonic solid attracted by a rigid body through the influence of van der Waals forces. Our results indicate that the surface of the solid is always unstable, and the parameter α, characterizing the solid, plays an important role in its surface instability.
TL;DR: In this paper, a multiple-scale method of averaging is applied to the study of dispersion in oscillatory Couette flow where the solute may undergo reversible sorptive phase exchange with the boundary walls.
Abstract: A multiple-scale method of averaging is applied to the study of dispersion in oscillatory Couette flow where the solute may undergo reversible sorptive phase exchange with the boundary walls. On assuming that the oscillation period and the sorption reaction time are comparable with the transverse diffusion time, which is much shorter than the axial transport time scales, an effective advection-dispersion transport equation in terms of the mean concentration is deduced at the second order. Analytical expressions are obtained for the two dispersion coefficients due to the steady and oscillating components of the Couette flow, incorporating the coupling effects between the flow oscillation, sorption kinetics, and the retardation due to phase partitioning.
TL;DR: Based on the refined plate theory, a refined theory of rectangular beams is derived by using the Papkovich-Neuber solution and Lur'e method without ad hoc assumptions in this article, where the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface.
Abstract: Based on the refined plate theory, a refined theory of rectangular beams is derived by using the Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. The solutions based on the new theory are the same as the exact solutions of elasticity theory. In three examples it is shown that the new theory provides as good or better results than Levinson’s beam theory when compared to those obtained from the linear theory of elasticity.
TL;DR: In this paper, the steady flow of a fluid, called a fourth grade fluid, between two parallel plates is considered, and depending upon the relative motion of the plates, the nonlinear differential equation describing the velocity field is solved using perturbation technique and homotopy analysis method.
Abstract: The steady flow of a fluid, called a fourth grade fluid, between two parallel plates is considered. Depending upon the relative motion of the plates we analyze four types of flows: Couette flow, plug flow, Poiseuille flow and generalized Couette flow. In each case, the nonlinear differential equation describing the velocity field is solved using perturbation technique and homotopy analysis method. The pressure distribution is also found. It is observed that the homotopy analysis method is more efficient and flexible than the perturbation technique.
TL;DR: In this article, a recently developed model of dynamic wetting is applied to the spreading of a liquid over a smooth solid surface in the limit of weak viscosity effects, and experimentally observed deviations of the dynamic contact angle from the static one are attributed to non-equilibrium values of the surface tensions.
Abstract: A recently developed model of dynamic wetting (Shikhmurzaev [1]) is applied to the spreading of a liquid over a smooth solid surface in the limit of weak viscosity effects. In this model, experimentally observed deviations of the dynamic contact angle from the static one are attributed to non-equilibrium values of the surface tensions. The limiting case of small capillary numbers and large Reynolds numbers is considered, with the Reynolds number being based upon the relaxation length. The results are compared with experimental data. Reasonable agreement is only partially obtained, and possible sources of the discrepancies are discussed.