فهرست مطالب

  • Volume:51 Issue: 1, 2020
  • تاریخ انتشار: 1399/05/02
  • تعداد عناوین: 24
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  • Alireza Amiri, Hossein Rahmani *, Mohammad Ahmadi Balootaki Pages 1-21
    In this study, torsional wave propagation is investigated in a rod that are made of one and two dimensional functionally graded material. Firstly, the governing equations of the wave propagation in the functionally graded cylinder derived in polar coordinate. Secondly, finite difference method is used to discretize the equations. The Von Neumann stability approach is used to obtain the time step size. Two states are assumed for material distribution, in first state it’s considered that the material variation occurred only in radial direction(Ti6A14V and Al2O3) and in second state the material properties vary in radial and length directions(BN, Al 1100, Ti6A14V and Al2O3). Moreover, the effect of cutoff frequency and boundary condition in wave propagation is studied. The results was validated by comparing the analytical and numerical solutions for an isotropic rode subjected to a torsional impulsive load. The results show that the torsional wave propagation in FGM rod evidently effects by material composition variation.
    Keywords: Functionally Graded Materials, Finite Difference Method, Wave Propagation, torsional wave
  • Mohammad Reza Salehi Kolahi, Hossein Moeinkhah * Pages 21-29
    By the past two decades IPMCs have been intensively studied because of their special capabilities for actuation and sensing.This paper presents a theoretical physics based model for analyzing the behavior of IPMC sensors in fluid environments. The mechanical vibration of the IPMC strip is described by the classical Euler–Bernoulli beam theory. The model also takes in to account the physical properties of the surrounding fluid. The resulting model is an infinite-dimensional transfer function that relates the input tip displacement to the output sensing current. Further the original model is reduced to a finite-dimensional one, for pure sensing applications of IPMC sensors such as structural health monitoring. The proposed model is verified using existing experimental data. Then the effect of various parameters is investigated. The acoustics physics interface in COMSOL Multiphysics software is used for coupled modal analysis of the IPMC strip. It is shown that the effect of surrounding fluid cannot be neglected.
    Keywords: dynamic model, IPMC, Physical model, Smart Materials
  • Abbas Barati *, Saeed Norouzi Pages 30-36
    The microtubes are important structures in nano electromechanical system .in this study a nonlocal model is presented to investigate the static torsion behavior of microtubes made of bi-directional factionally graded material (BDFGM) subjected to a longitudinal magnetic field. Mechanical properties of BDFGM microtube varies in the radial and longitudinal direction according to an arbitrary function. The governing equation is obtained using the principle of minimum potential energy. a sinusoidal distributed torque and uniform magnetic field with clamped boundary condition are considered to capture the effects of nonlocal parameter, FGM indexes and intensity of longitudinal magnetic field on the torsional angle of BDFGM microtube. The numerical solution of generalized differential quadrature (GDQ) is compared with Galerkin method which a reasonable agreement is observed. Result indicates that intensity of longitudinal magnetic has important role on the torsional angle of microtubes such that when intensity of longitudinal magnetic field increases the torsional angle of microtubes decreases
    Keywords: Static torsion, magnetic field, Microtube, Nonlocal Elasticity Theory, Bi-directional functionally graded materials (BDFGMs), Generalized differential quadrature method (GDQM)
  • Ali Soleimani, Pedram Hanafizadeh *, Amirmohammad Sattari Pages 37-45
    Subcooled flow boiling in multi-microchannels can be used as an efficient thermal management approach in compact electrical devices. Highly subcooled flow boiling of HFE 7100 is studied in two microchannel heat sinks to choose a proper numerical model for simulating boiling flows in microchannels. Results of five different numerical models, including Volume of Fluid (VOF), Eulerian boiling, Eulerian Lee, Eulerian thermal phase change, and mixture models, were compared with experimental data. ANSYS Fluent was used as the numerical tool to solve three-dimensional governing equations. Results were obtained in the steady-state condition of the transient solution. The average wall temperature reached a steady state in all models except in Eulerian boiling and mixture models. It was found that Eulerian thermal phase change and VOF models predicted microchannel’s bottom wall average temperature with less than 2% error. VOF model predicted flow boiling regime as it was reported in the experimental research and boiling curves. Velocity distribution over microchannel height was investigated, and it was observed that after the onset of nucleate boiling, the velocity profile becomes asymmetrical. Also, in the two-phase regions, each phase had a different velocity magnitude and distribution. Based on flow regime and temperature results, which were compared with experimental data, VOF model was recommended as the best model to simulate flow boiling in microchannels at the working conditions of this research. Furthermore, subcooled flow boiling’s capability to be used in thermal management systems was proved while observing temperature distribution over computational domain.
    Keywords: Subcooled flow boiling, Microchannel, Heat Sink, CFD, VOF model
  • Jafar Nejadali *, Alireza Riasi Pages 46-54
    Draft tube of Francis type hydraulic turbine usually consists of: cone, elbow and diffuser. On the contrary, in some power stations an extra pipe should be added to the draft tube at the bottom of cone because of installation limitation. In this paper, this special case has been numerically studied. To this end CFD analysis was applied to simulate all parts of hydraulic turbine. A homogeneous multiphase model with Rayleigh-Plesset cavitation model was applied for presence of cavitation. The results reveal that the additional tube causes pressure drop and severe cavitation at the trailing edge of runner blades. Also, results showed that the efficiency reduces in comparison with original hill-diagram of model test in which this extension was not considered. With the removal of the extension tube, the efficiency increased significantly. The comparison of pressure recovery factors along draft tube, and theoretical investigation showed that the height of the draft tube is an important parameter and addition of an extra pipe will cause reduction in draft tube performance and increases the probability of occurrence of cavitation under the runner.
    Keywords: CFD Simulation, Hydraulic turbine, Draft tube, Cavitation, Pressure recovery factor
  • Ghazal Etesami, Mohammad Ebrahim Felezi *, Nader Nariman-Zadeh Pages 55-65
    Four-bar mechanisms are widely used in the industry especially in rotary engines. These mechanisms are usually applied for attaining a special motion duty like path generation; their high speeds in the industry cause an unbalancing problem. Hence, dynamic balancing is essential for their greater efficiency. In this research study, a multi-objective differential evolution algorithm is used for Pareto optimization balancing of a four-bar planar mechanism while considering the shaking moment and horizontal and vertical shaking forces as objective functions. This is necessary since the high magnitude of shaking forces and moment affect the fatigue life of the mechanism. The design variables are both kinematic and dynamic parameters of the moving links. The Pareto charts of five-objective optimization exhibit a large number of non-dominated points, which provide more choices for optimal balancing design of the planar four-bar mechanism. A comparison of the results obtained from this study with those reported in the literature shows a significant decrease in shaking forces and shaking moment.
    Keywords: Multi-objective optimization, Balancing, Four-bar mechanism, Differential evolution algorithm, Pareto
  • Pezhman Taghipour Birgani * Pages 66-71
    In this paper, the reflection of ultrasonic guided waves from simple dent in pipes has been investigated using finite element method and the relationship between reflection coefficient of these waves and deformation rate has been determined. Also, the effect of the parameters of wave generation source on the generated wave field has been investigated using normal modes expansion method. At first, ultrasonic guided waves propagation has been studied in an intact pipe to obtain multiple modes using of displacement potential method. The characteristic equation has been solved using a matlab code in order to draw the dispersion curves of phase and group velocities in different frequencies for longitudinal modes, and it is observed that mode L(0,2) is a suitable mode for inspection in a range of frequency 200-300 kHz. The single sided dent is created in pipe using a plasticity analysis with the aid of finite element simulation and then L(0,2) mode is generated in pipe. By Investigation of the reflection of this mode from dent, the relationship between reflection coefficient and deformation rate is specified and it has been observed that this relationship is almost linear by curve fitting. Also, it has been observed in case of partial loading by wave generation source that is a transducer with a specified axial length and circumferential coverage angle, a combination of different modes such as L(0,2) mode is generated in pipe, if using a axisymmetric wave generation source including 8 segments 45 degree, only L(0,2) symmetric mode is generated.
    Keywords: Ultrasonic Guided Waves, Dent, Deformation Rate, Wave Reflection Coefficient, Source parameters
  • Alireza Zabihihesari, Farzad A. Shirazi *, Alireza Riasi, Mohammad Mahjoob, Erfan Asnaashari Pages 72-80
    In this paper, a simulation-based method is proposed for optimal placement of vibration sensors for the purpose of fault detection in a centrifugal pump. The centrifugal pump is modeled to investigate the effect of vane tip fault on fluid flow patterns numerically. Pressure pulsations are investigated at different locations at the inner surface of the pump before and after the presence of the fault to determine the best location for installing vibration sensors on the pump casing. Experiments are also conducted by mounting accelerometers at various locations on the pump casing. Simulation and experimental results are then compared and a direct correlation between changes in PSD amplitudes of pressure and acceleration signals was observed. The optimum location for placement of an accelerometer is determined to be near the volute tongue on the casing where the highest level of pressure pulsations in the simulation is also calculated in the presence of vane tip fault.
    Keywords: CFD Simulation, Vibration, Sensor Placement, Centrifugal Pump, Fault Detection
  • Amr Hassan *, Ahmed Abouelregal, Khalil-M Khalil, Mohamed Nasr Pages 81-90
    Generalized thermoelastic models have been developed with the aim of eliminating the contradiction in the infinite velocity of heat propagation inherent in the classical dynamical coupled thermoelasticity theory. In these generalized models, the basic equations include thermal relaxation times and they are of hyperbolic type. Furthermore, Tzou established the dual-phase-lag heat conduction theory by including two different phase-delays correlating with the heat flow and temperature gradient. Chandrasekharaiah introduced a generalized model improved from the heat conduction model established by Tzou. The present work treats with a novel generalized model of higher order derivatives heat conduction. Using Taylor series expansion, the Fourier law of heat conduction is advanced by introducing different phase lags for the heat flux and the temperature gradient vectors. Based on this new model, the thermoelastic behavior of a rotating hollow cylinder is analyzed analytically. The governing differential equations are solved in a numerical form using the Laplace transform technique. Numerical calculations are displayed tables and graphs to clarify the effects of the higher order and the rotation parameters. Finally, the results obtained are verified with those in previous literature.
    Keywords: Thermoelasticity, Higher-Order, Phase-lags, rotation, Hollow cylinder
  • Peyman Mashhadi Keshtiban *, Milad Regbat, Mohsen Mashhadi Keshtiban Pages 91-97
    The geometric optimization of orthopedic screws can considerably increase their orthopedic efficiency. Due to the high geometric parameters of orthopedic screws, a finite element simulation is an effective tool for analyzing and forecasting the effect of the parameters on the load-bearing capacity of different types of screws and bones. Thus, in the present study, the tensile strength of a typical cortical titanium screw was investigated by the finite element method, and experimental tests confirmed the obtained results. The behavior of the screw in the tensile test was discussed in terms of stress, force, and displacement. The maximum force results show a 14% difference between simulation and experimental works in tensile type loading. Moreover, it was suggested that the trend of force curves in both the experimental test and numerical simulation shows high similarity, and FEM predicts the process with acceptable accuracy. Furthermore, it was concluded that the stress values are higher while moving toward the top surface of the bone.
    Keywords: Finite element, tensile test, Femur Bone
  • Hamidreza Eipakchi *, Saeed Khadem Moshir Pages 98-106
    In this paper, the transient response of a viscoelastic annular plate which has time-dependent properties is determined mathematically under dynamic transverse load. The axisymmetric conditions are considered in the problem. The viscoelastic properties obey the standard linear solid model in shear and the bulk behavior in elastic. The equations of motion are extracted using Hamilton’s principle by small deformation assumption for the elastic condition and they are extended to the viscoelastic form by defining viscoelastic operators based on the separating the bulk and shear behaviors. The displacement field is defined with the first order shear deformation theory by considering the transverse normal strain effect. These equations which contain four coupled partial differential equations with variable coefficients are solved using the perturbation technique. The results are compared with those obtained from the classical plate theory and the finite element method. The presented formulation is useful for parametric study because it does not need to generate mesh and selecting time step for each model; also the running time is short with respect to the finite elements method. For sensitivity analysis, the effects of geometrical and mechanical parameters on the response are investigated by parametric study.
    Keywords: Viscoelastic annular plate, Mathematical solution, Perturbation Technique, Dynamic response, First order shear deformation theory
  • Charles C. Ike *, Clifford U. Nwoji, Benjamin O. Mama, Hyginus N. Onah, Michael E. Onyia Pages 107-121
    In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and the problem is expressed as a boundary value problem (BVP) represented by a non-homogeneous biharmonic equation. Airy’s stress functions are chosen in terms of one and three unknown parameters and coordinate functions that satisfy both the domain equations and the boundary conditions on the loaded edges. Least squares weighted residual integral formulations of the problems are solved to determine the unknown parameters and thus the Airy stress function. The normal and shear stress fields are determined for the one-parameter and the three-parameter coordinate functions. The solutions for the stress fields are found to satisfy the stress boundary conditions as well as the domain equation. The presented solutions for the Airy stress function and the normal stresses and shear stress fields are identical with solutions obtained by using variational Ritz methods, Bubnov–Galerkin methods and agree with results obtained by Timoshenko and Goodier.
    Keywords: Least squares weighted residual method, Airy stress potential function, Biharmonic equation, Beltrami – Michell stress compatibility equation, Normal stresses, Shear stress fields
  • Mohammad Fakhar *, Ahmad Fakhar, Hamidreza Tabatabaei, Hossein Nouri-Bidgoli Pages 122-128
    In this article, the instable fluid velocity in the pipes with internal nanofluid is studied. The fluid is mixed by SiO2, AL2O3, CuO and TiO2 nanoparticles in which the equivalent characteristic of nanofluid is calculated by rule of mixture. The force induced by the nanofluid is assumed in radial direction and is obtained by Navier-Stokes equation considering viscosity of nanofluid. The displacements of the structure are described by first order shear deformation theory (FSDT). The final equations are calculated by Hamilton's principle. Differential quadrature method (DQM) is utilized for presenting the instable fluid velocity. The influences of length to radius ratio of pipe, volume fraction, diameter and type of nanoparticles are shown on the instable fluid velocity. The outcomes are compared with other published articles where shows good accuracy. Numerical results indicate that with enhancing the volume fraction of nanoparticles, the instable fluid velocity is increased. In addition, the instable fluid velocity of SiO2-water is higher than other types of nanoparticles assumed in this work.
    Keywords: Instable fluid velocity, Nanofluid, pipe, Navier-Stokes, Hamilton's principle
  • Hossein Chehardoli *, Mohammad Eghtesad Pages 129-136
    In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF can be constructed by employing the back-stepping approach. The major shortcoming of the SDL is that this limitation cannot be satisfied for complicated switched nonlinear systems. Therefore, a CQLF cannot be constructed by employing the back-stepping approach. Moreover, if SDL is satisfied, only stabilization problem can be solved. In this paper, a new approach based on state transformation is introduced to solve the stabilization and control problems of switched nonlinear cascade systems without any limitation. Several simulation and experimental studies are provided to show the effectiveness of the proposed approach.
    Keywords: Switched nonlinear cascade systems, Backstepping, SDL, Common quadratic Lyapunov function, Globally asymptotically stable
  • Behrooz Attaran, Afshin Ghanbarzadeh *, Shapour Moradi Pages 137-143
    This paper presents a new Fast Kurtogram Method in the time-frequency domain using novel types of statistical features instead of the kurtosis. For this study, the problem of four classes for Bearing Fault Detection is investigated using various statistical features. This research is conducted in four stages. At first, the stability of each feature for each fault mode is investigated. Then, resistance to load changes as well as failure growth is studied. In the end, the resolution and fault detection for each feature using comparison with a determined pattern and the coherence rate is calculated. From the above results, the best feature that is both resistant and repeatable to different variations, as well as having suitable accuracy of detection and resolution, is selected. It is found that kurtosis feature is not in a good condition in comparison with other statistical features such as harmmean and median. This approach increases the fault identification accuracy significantly.
    Keywords: Fast Kurtogram, Bearing fault detection, Statistical features, Time-Frequency Domain
  • Mohammad Parhizkar Yaghoobi, Mehdi Ghannad * Pages 144-156
    This research presents temperature distribution and thermal strain of functionally graded material cylinders with varying thickness and temperature-dependency properties that are subjected to heat fluxes in their inner and outer layers. The heterogeneous distribution of properties is modeled as a power function. Using first-order temperature theory and the energy method, governing equations are extracted. The system of governing differential equations is a system of nonlinear differential equations with variable coefficients, which are solved by using the analytical method of the matched asymptotic expansion of the perturbations technique. Results obtained from temperature distribution, heat flux, and thermal strain for different heterogeneous constants and temperature-dependency properties are discussed. They show that heterogeneity has a significant impact on the temperature field and thermal strain inside functionally graded cylinders. Moreover, it is observed that heterogeneity has no impact on the direction of heat flux vector inside the body; however, any changes in heterogeneity would change the magnitude of heat flux. The results obtained from the analytical method were compared with those of previous studies and FEM, which showed good agreement.
    Keywords: analytical solution, Temperature distribution, Thermal Strain, Cylinders with Varying Thickness, Temperature-Dependent Properties, Functionally graded Material (FGM), First-Order Temperature Theory (FTT), Perturbation Technique
  • Seyed Ali Ghazi Mirsaeed *, Vahidreza Kalatjari Pages 157-169
    In this paper, the finite element analysis of two-dimensional linear viscoelastic problems is performed using quadrilateral complex Fourier elements and, the results are compared with those obtained by quadrilateral classic Lagrange elements. Complex Fourier shape functions contain a shape parameter which is a constant unknown parameter adopted to enhance approximation’s accuracy. Since the iso-parametric formulation utilized in the finite element code, based on the experience of authors, it is proposed that a suitable shape parameter for each problem is adopted based on an acceptable approximation of the problem’s geometry by a complex Fourier element. Several numerical examples solved, and the results showed that the finite element solutions using complex Fourier elements have excellent agreement with analytical solutions, even though noticeable fewer elements than classic Lagrange elements are employed. Furthermore, the run-times of the executions of the developed finite element code to obtain accurate results, in the same personal computer, using classic Lagrange and complex Fourier elements compared. Run-times indicate that in the finite element analysis of viscoelastic problems, complex Fourier elements reduce computational cost efficiently in comparison to their classic counterpart.
    Keywords: Viscoelasticity, finite element method, Complex Fourier shape functions, Shape parameters, Complex Fourier Lagrange Elements
  • Hamid Haghshenas Gorgani *, Alireza Jahantigh Pak Pages 170-183
    Popular method for assessment of final exam answer scripts in university and among the engineering drawing answer scripts based on absolute true or false judgment and assigning a single number or letter to answer of each problem cannot be so fair. To obtain a fair assessment method, we considered “imagination”, “accuracy”, “drawing” and “innovation” that are objectives of engineering drawing course to be separately assessed for each problem. Flexibility and linguistic properties of fuzzy logic made us use it as the basis of our method. In addition, fuzzy variables and membership functions are easily linguistic explainable, and adjustable to different conditions. “Answering time” was added as a factor with only a positive effect on the final grade. Between these five factors, imagination has special importance because it supports one of seven human intelligences which is spatial ability Finally, however we applied the proposed method to engineering drawing course, it can be applied to other courses with considering their properties.
    Keywords: FAIR ASSESSMENT, ANSWER SCRIPT, ENGINEERING DRAWING, Fuzzy
  • Hyginus Nwankwo Onah, Michael Ebie Onyia, Benjamin Okwudili Mama, Clifford Ugochukwu Nwoji, Charles Chinwuba Ike * Pages 184-198
    In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The derived functions are used to solve the elasticity problem of finding stresses and displacement fields in a thick circular plate with clamped edges for the case of uniformly distributed transverse load over the plate domain. Superposition of second to sixth order Legendre polynomials which are biharmonic functions are used in the thick circular plate problem as the stress function with the unknown constants as the parameters to be determined. Use of the stresses and displacement fields derived in terms of the stress and displacement function yielded the stress fields and displacement fields in terms of the unknown constants of the biharmonic stress function. Enforcement of the boundary conditions yielded the unknown constants, leading to a complete determination of the stress and displacement function for the stress fields and the displacement fields. The solutions obtained are comparable to solutions in the technical literature.
    Keywords: stress function, displacement function, Biharmonic function, three dimensional elasticity problem, Legendre polynomial, thick circular plate problem, stress fields, displacement fields
  • Sina Jalili, Alireza Daneshmehr * Pages 199-212
    The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is implemented and nonlinear prediction error (NPE) is proposed as a geometrical feature to analyze the chaotic attractor of a centrally cracked plate. For this purpose using line spring method (LSM) a nonlinear multi-degree of freedom model of part through cracked rectangular plate is developed. Tuning of Lorenz type chaotic signal is conducted by crossing of the Lyapunov exponents’ spectrums of nonlinear model of the plate and chaotic signal and in the next step by varying the tuning parameter to find a span in which a tangible sensitivity in the NPE could be observable. Damage characteristics such as length, depth and angle of crack are altered and variation of proposed feature is scrutinized. Results show that by implementation of the tuned chaotic signal, tangible sensitivity and also near to monotonic behavior of NPE versus damage intensity are achievable. Finally, the superiority of the proposed method is examined through the comparison with the frequency-based method.
    Keywords: Crack, chaotic, nonlinear dynamics, plate, prediction error
  • Afshin Ashofteh *, Mahmoud Mosavi Mashhadi, Sana Seifollahpour Pages 213-230
    Hydroforming process is largely used for the production of tubular parts in various industries, and has advantages such as less weight, higher quality, more strength and fewer production cost compared to the conventional methods of production. The aim of this study is forming a tube-shaped part with a special geometry that has both bulge- and T-zones with tube hydroforming process. The forming operations were performed on 304 stainless steel and 70/30 brass tubes, and a finite element (FE) model was used to achieve the best forming conditions. To validate FE model, firstly, several experimental tests were performed with different process parameters, and then the results were compared with the FE model in terms of the formed profile and the distribution of thickness. After validation of FE model, various pressure paths were studied and the best one between them was chosen. Finally, the part was formed correctly by the selected pressure path without defects like wrinkling or tearing, and the desired geometry was fully filled.
    Keywords: Tube Hydroforming, FE simulation, pressure path, bulge zone, T-way
  • Majid Jamali, Taghi Shojaee, Bijan Mohammadi * Pages 231-238
    The effect of central opening on the buckling and nonlinear post-buckling response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on buckling and post-buckling behavior are analyzed. In order to derive the basic formulations of plate the Mindlin plate theory is applied. Furthermore, nonlocal elasticity theory is applied to consider the size-dependent effect. Analytical approach and Newton-Raphson iterative technique are utilized to calculate the impact of cut out on the buckling and nonlinear post-buckling response of micro composite plate. The variation of buckling and post-buckling of micro composite cut out plate based on some significant parameters such as volume fraction of CNTs, small scale parameter, aspect ratio, square cut out and elastic medium were discussed in details. According to the results, it is concluded that the aspect ratio and length of square cut out have negative effect on buckling and post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the buckling and post-buckling behavior of plate. Meanwhile, considering elastic medium increases the buckling and post-buckling load of system.
    Keywords: Buckling, nonlinear Post-buckling analysis, micro composite plate, Central opening, Elastic medium, Mindlin plate theory
  • Mohsen Javanmard, Mohammad Hasan Taheri *, Morteza Abbasi Pages 239-246
    In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.
    Keywords: Collocation Method, finite element method, FlexPDE, Magnetohydrodynamics, Permeable Stretching Sheet
  • Farzad Ebrahimi *, Ali Dabbagh Pages 247-252

    Invention of carbon nanotube (CNT) in the 1990s introduced a new class of materials whose extraordinary mechanical, thermal, and electrical properties seemed appealing enough to the research community to devote their time and effort for the purpose of analyzing composite materials reinforced by CNTs. Particularly, the marvelous stiffness of CNTs has made it possible to reach a high-modulus composite once such a nanomaterial is dispersed into various types of matrices. Among all of these products, CNT-reinforced (CNTR) polymer nanocomposites (PNCs) are used more than the others due to their incredible specific stiffness and fracture toughness. Although PNCs can bring a lot for the designer due to their inherent merits, it must be pointed out that some practical phenomena take place in the microstructure of such advanced materials whose neglecting can be resulted in negative outcomes. Motivated by this reality and based upon the authors broad researches in this area, present review is organized to show how can the mechanical behaviors of PNCs be affected by entanglement of the CNTs inside the inclusions and their wavy shape.

    Keywords: Carbon nanotube (CNT), Agglomeration, Waviness, Polymer nanocomposites (PNCs)