Showing papers in "Applied Mathematics and Mechanics-english Edition in 2015"
TL;DR: In this paper, the effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, and the shear stress at the sheet surface were graphically and quantitatively discussed in detail.
Abstract: The unsteady laminar magnetohydrodynamics (MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-Kutta-Fehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.
164 citations
TL;DR: In this article, an analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.
Abstract: Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented. The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon. Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique. The effects of various physical parameters on the profiles of momentum, thermal energy, nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. It is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.
53 citations
TL;DR: In this article, the boundary layer flow problems are stated in the spatial domain from zero to infinity, and solution expressions for the velocity and the temperature are obtained and examined for the influential variables.
Abstract: The Newtonian heating effects in the stagnation point flow of a Burgers fluid are addressed in this paper. The boundary layer flow problems are stated in the spatial domain from zero to infinity. The solution expressions for the velocity and the temperature are obtained and examined for the influential variables. The tabulated values show comparison with the previous results. It is observed that the obtained results are in good agreement with the existing results in limiting sense.
53 citations
TL;DR: In this paper, the authors studied flow and heat transfer characteristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation.
Abstract: The aim of the present paper is to study flow and heat transfer characteristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The resulting similarity equations are solved numerically with a shooting method. Comparisons with previously works are made, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.
52 citations
TL;DR: In this paper, an integro-partial-differential equation governing the transverse vibration of an axially accelerating viscoelastic Timoshenko beam with the external harmonic excitation is established.
Abstract: This investigation focuses on the nonlinear dynamic behaviors in the transverse vibration of an axially accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincare map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable relationship between the dual-frequency excitations.
47 citations
TL;DR: In this article, the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated.
Abstract: The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al2O3, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.
47 citations
TL;DR: In this article, the authors explored the three-dimensional boundary layer flow of the Maxwell nanofluid, generated by a bidirectional stretching surface, through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects.
Abstract: The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlinear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.
45 citations
TL;DR: In this paper, the effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity was discussed, and the temperature dependent thermal conductivities of fluid in an asymmetric channel was taken into account.
Abstract: The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ ∈ [0, π/2] and θ ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field (θ ≠ π/2) than that for the case of the transverse magnetic field (θ = π/2). The heat transfer coefficient decreases when the constant thermal conductivity (Newtonian) fluid is changed to the variable thermal conductivity (Jeffrey) fluid.
43 citations
TL;DR: In this article, the plane piezoelasticity theory of onedimensional (1D) quasicrystals with all point groups is investigated systematically, including monoclinic, orthorhombic, tetragonal and hexagonal QCs, and closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained.
Abstract: Based on the fundamental equations of piezoelasticity of quasicrystals (QCs), with the symmetry operations of point groups, the plane piezoelasticity theory of onedimensional (1D) QCs with all point groups is investigated systematically. The governing equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the operator method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.
42 citations
TL;DR: In this article, the two-dimensional boundary layer flow of an Oldroyd-B fluid in the presence of nanoparticles is investigated, where the nonlinear partial differential equations are reduced into the ordinary differential equation (ODE) systems.
Abstract: The two-dimensional boundary layer flow of an Oldroyd-B fluid in the presence of nanoparticles is investigated. Convective heat and mass conditions are considered in the presence of thermal radiation and heat generation. The Brownian motion and thermophoresis effects are retained. The nonlinear partial differential equations are reduced into the ordinary differential equation (ODE) systems. The resulting ODE systems are solved for the series solutions. The results are analyzed for various physical parameters of interest. Numerical values of the local Nusselt and Sherwood numbers are also computed and analyzed.
40 citations
TL;DR: In this article, the authors investigated the two-dimensional flow of a viscous nanofluid with the slip effects of the velocity, the temperature, and the concentration in the presence of an applied magnetic field.
Abstract: The two-dimensional flow of a viscous nanofluid is investigated. The flow is caused by a nonlinear stretching surface with the slip effects of the velocity, the temperature, and the concentration. The fluid is electrically conducted in the presence of an applied magnetic field. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. The convergent solutions of the governing nonlinear problems are computed. The results of the velocity, the temperature, and the concentration fields are calculated in series forms. The effects of the different parameters on the velocity, the temperature, and the concentration profiles are shown and analyzed. The skin friction coefficient, the Nusselt number, and the Sherwood number are also computed and investigated for different embedded parameters in the problem statements.
TL;DR: A heuristic technique is developed for a nonlinear magnetohydrodynamics Jeffery-Hamel problem with the help of the feed-forward artificial neural network (ANN) optimized with the genetic algorithm (GA) and the sequential quadratic programming (SQP) method.
Abstract: A heuristic technique is developed for a nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel problem with the help of the feed-forward artificial neural network (ANN) optimized with the genetic algorithm (GA) and the sequential quadratic programming (SQP) method. The two-dimensional (2D) MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem (BVP) of ordinary differential equations (ODEs). The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the angles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.
TL;DR: In this paper, a mixed convection three-dimensional flow of Jeffrey fluid is studied in the presence of thermal radiation and thermophoresis, and series solutions are presented for velocities, temperature, and concentration.
Abstract: Mixed convection three-dimensional flow of Jeffrey fluid is studied in the presence of thermal radiation and thermophoresis. The relevant problems are formulated, and series solutions are presented for velocities, temperature, and concentration. Convergence of series solutions is obtained graphically and numerically. Effects of different emerging parameters on the velocities, temperature, and concentration fields are plotted and discussed.
TL;DR: In this paper, the effects of a vertical magnetic field on the double diffusive nanofluid convection were investigated, and valid approximations were made in the complex expression for the Rayleigh number to get useful and interesting results.
Abstract: The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.
TL;DR: In this paper, a semi-analytical approach named the state space based differential quadrature method (SSDQM) is used to provide an analytical solution along the thickness using the SSM and an approximate solution along a radial direction using the DQM. The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.
Abstract: The three-dimensional free vibration analysis of a multi-directional functionally graded piezoelectric (FGP) annular plate resting on two parameter (Pasternak) elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method (SSDQM) is used to provide an analytical solution along the thickness using the state space method (SSM) and an approximate solution along the radial direction using the one-dimensional differential quadrature method (DQM). The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.
TL;DR: In this paper, the effect of diffusion on thermoelastic thin plates is investigated and the governing equations for thin thermo-elastic diffusion plates under three different laws of heat and diffusion transmission are derived.
Abstract: The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C0-semigroup theory, the well-posedness of the proposed equations is shown.
TL;DR: In this article, the effects of different parameters such as nonlocal parameters, elastic media, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate.
Abstract: The nonlocal nonlinear vibration analysis of embedded laminated microplates resting on an elastic matrix as an orthotropic Pasternak medium is investigated. The small size effects of micro/nano-plate are considered based on the Eringen nonlocal theory. Based on the orthotropic Mindlin plate theory along with the von Karman geometric nonlinearity and Hamilton’s principle, the governing equations are derived. The differential quadrature method (DQM) is applied for obtaining the nonlinear frequency of system. The effects of different parameters such as nonlocal parameters, elastic media, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate. Results show that considering elastic medium increases the nonlinear frequency of system. Furthermore, the effect of boundary conditions becomes lower at higher nonlocal parameters.
TL;DR: In this paper, the unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. And the effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined.
Abstract: The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations (ODEs) by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.
TL;DR: In this paper, the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation is modeled with a thermo-electro-elastic constitutive law.
Abstract: This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini’s conditions and Tresca’s friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is derived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.
TL;DR: In this paper, the authors investigated the harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity, where wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant.
Abstract: Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method (GCTM). The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor (DSCF) becomes singular when the inhomogeneity parameter of medium is close to zero.
TL;DR: In this article, an analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs, where the flow regime is separated into two horizontal layers: a vegetation layer and a free water layer.
Abstract: An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers: a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.
TL;DR: In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically, and the results show that increasing the amplitude, A g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries.
Abstract: In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, A
g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when A
g increases.
TL;DR: In this article, an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material (FGPM) and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads is presented.
Abstract: This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material (FGPM) and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson’s ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.
TL;DR: In this paper, the static behavior of a functionally graded circu- lar plate made of magneto-electro-elastic (MEE) materials under tension and bending is investigated.
Abstract: This paper investigates the static behavior of a functionally graded circu- lar plate made of magneto-electro-elastic (MEE) materials under tension and bending. The analysis is directly based on the three-dimensional governing equations for magneto- electro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately (in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material (FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic (FG- MEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material het- erogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.
TL;DR: In this paper, the reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied and expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically.
Abstract: The reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied. The expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically. The piezothermoelastic solid half-space is assumed to have 6mm type symmetry and assumed to be loaded with water. The effects of angle of the incidence, the frequency, the specific heat, the relaxation time, and the thermal conductivity on the reflected and transmitted energy ratios are studied numerically for a particular model of cadmium selenide (CdSe) and water. Some special cases are also studied.
TL;DR: In this article, a non-autonomous complex Ginzburg-Landau equation (CGLE) is derived for the finite amplitude of convection, and a method is presented to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation.
Abstract: A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.
TL;DR: In this paper, the authors studied the traction characteristics of the grouser, cutting the simulative soil of deep-sea sediment, with different tooth widths, tooth heights, and ground pressures with traction characteristic test apparatus.
Abstract: The traction characteristics of the grouser, cutting the simulative soil of deep-sea sediment, with different tooth widths, tooth heights, and ground pressures are studied with traction characteristic test apparatus. A traction-displacement model is obtained by combining the analysis of the cutting mechanism. The results show that the traction-displacement curves of grousers with different tooth widths, tooth heights, and ground pressures have the same changing trend, which matches the Wong traction model. Their sensitivity coefficient and shear modulus are slightly fluctuated. Therefore, the average values can be used as the traction model parameters. The maximum traction of the grouser with a two-side edge and a 10mm tooth width increment changing with the tooth height and ground pressure can be determined according to the grousers with different tooth widths. By combining the traction model parameters, the traction-displacement curve of the grouser with a certain group values of tooth width, tooth height, and ground pressure can be predicted. Therefore, the slip of the mining machine can be prevented to improve the mining efficiency.
TL;DR: In this paper, a unified stress function for bi-modulus beams is proposed based on its mechanics sense on the boundary of beams, and elasticity solutions of stress and displacement are derived.
Abstract: A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ⩽ 5. The error also varies with the distributed load patterns.
TL;DR: In this paper, the dynamic behaviors of several moving cracks in a functionally graded piezoelectric (FGP) strip subjected to anti-plane mechanical loading and in-plane electrical loading are investigated.
Abstract: The dynamic behaviors of several moving cracks in a functionally graded piezoelectric (FGP) strip subjected to anti-plane mechanical loading and in-plane electrical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.
TL;DR: In this article, the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism, was analyzed by the Adomian decomposition method.
Abstract: The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method (ADM). The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile, and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.