# International Journal of Mechanics

**E-**ISSN: 1998-4448

Volume 12, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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**Volume 12, 2018**

Title of the Paper: **Surface Quality of Injection Molds**

Authors: **Michal Stanek, Miroslav Manas, Martin Ovsik, Martin Reznicek, Vojtech Senkerik, Petr Fluxa**

Pages: **246-251**

Abstract: Polymer injection molding is one of the most used technology of polymer processing nowadays. It enables the manufacture of final products, which do not require any further operations. Working of shaping cavities is the major problem involving not only the cavity of the mold itself, giving the shape and dimensions of the future product, but also the flow pathway (runners) leading the polymer melt to the separate cavities. This paper shows the influence of cavity surface roughness, polymer material (with different flow properties) and technological parameters on the flow length of polymers into mold cavity. Application of the measurement results may have significant influence on the production of shaping parts of the injection molds especially in changing the so far used processes and substituting them by less costly production processes which might increase the competitiveness of the tool producers and shorten the time between product plan and its implementation.

Title of the Paper: **Ultra-nano Indentation Test of Crosslinked PBT Irradiated by Beta Rays**

Authors: **M. Ovsik, M. Stanek, A. Dockal, M. Manas, V. Senkerik**

Pages: **239-245**

Abstract: This article deals with the use of Ultra-nano indentation Tester UNHT3 for the measurement of (ultra nano) mechanical properties. The effect of electron beam (EB) radiation on Polybutylene terephthalate (PBT) was investigated. To clarify whether crosslinking could take place without or only with the presence of a crosslinking agent, special attention was paid to the incorporation of this agent into tested polymer. In this study we have investigated the effect of crosslinking agent, and instantaneously electron beam radiation-induced crosslinking in the presence of Triallyl cyanurate on various mechanical properties of PBT. The results show that the influence of radiation has improved the observed properties in the surface layer. The increase in ultra-nano properties was around 26% over the basic material. Engineering plastics like Poly (butylene terephthalate) due to their desirable properties have various industrial applications.

Title of the Paper: **Nano-indentation Test of Crosslinking Polyamide 11 by Electron Beam**

Authors: **M. Ovsik, M. Stanek, A Dockal, M. Reznicek, A. Skrobak**

Pages: **232-238**

Abstract: This article deals with the influence of electron beam radiation on nano-mechanical properties and the structure of polyamide 11. Crosslinking of polymers is a process, during which macromolecular chains start to connect to each other and the spatial network creates in the structure. During the action of the ionizing radiation two actions can occur: crosslinking and scission of macromolecules – degradation. Both these processes run parallel. Using the crosslinking technology the standard and construction polymer can obtain the more “expensive” high-tech polymeric materials properties and thus replace these materials in many applications. Tested material was irradiated by different doses of beta radiation (33, 66 and 99 kGy). The nano-mechanical properties were measured using DSI method, which fluently records the change of the indentation in time. From this dependence it is possible to determine nano-mechanical properties such as indentation hardness, indentation modulus etc. During results consideration it is obvious that irradiation acts on each polymer differently, but always when the optimal dose was found, nano-mechanical properties increased up to 34 %. The changes of nano-mechanical properties were confirmed by structural measurement when the change of hardness and modulus corresponded to gel content.

Title of the Paper: **Hall Current and Ion-Slip Effects on the Entropy Generation of Couple Stress Fluid with Velocity Slip and Temperature Jump**

Authors: **A. A. Opanuga, O. O. Agboola, H. I. Okagbue, A. M. Olanrewaju**

Pages: **221-231**

Abstract: In this work, analytical study of Hall current and Ion-slip effects on the rate of entropy generation of couple stress fluid is considered. The obtained partial differential equations governing the flow are reduced to ordinary differential equations by similarity variables, semi-analytical solution of the dimensionless nonlinear coupled differential equations for velocity, temperature, entropy generation and Bejan number are constructed using Differential Transform Technique. Effects of Hall current, Ion-slip, couples stress and magnetic parameters are presented and discussed graphically. From the results it is observed that Hall current and rotation parameters enhance secondary velocity, fluid temperature and entropy generation. In addition rarefaction and Hartman number reduce fluid temperature and entropy generation.

Title of the Paper: **The Multiaxial Behaviour Comparison of Virgin Polypropylene and Polypropylene Reinforced with 30 % Glass Fibres**

Authors: **Hylova L., Mizera A., Manas M., Stoklasek P., Fiala T.**

Pages: **216-220**

Abstract: This study is concentrated on the multiaxial behaviour comparison of pure polypropylene to polypropylene reinforced with 30 % of glass fibre (PP30GF), both materials were subjected to the drop-weight test. PP is a semi-crystalline thermoplastic polyolefinic polymer which has a good resistance to the impact load and is commonly used in the wide area of the plastics industry to production of many application. In this study PP samples and PP samples with 30 % glass fibres were injection moulded and subsequently subjected to the penetration test at various potential energies. The results were evaluated and discussed. The results show that reinforced PP has a better behaviour at the multiaxial stress in comparison to the virgin one.

Title of the Paper: **Study of Mixing Reprocessed Polycarbonate on Charpy Impact Properties at Increased and Decreased Temperature**

Authors: **Vojtech Senkerik, Michal Stanek, Martin Ovsik**

Pages: **210-215**

Abstract: The feasibility of reprocessing has been studied as a possible alternative to polycarbonate recycling. The reprocessed polycarbonate was mixed in different proportions with the virgin polycarbonate, and several mixtures were made which were subjected to measurement. The ascertained properties were compared with the virgin material. Polymeric waste from polycarbonate was grinded. The prepared mixtures were subjected to Charpy Impact Properties. This measurement was carried out at two different temperatures, a low temperature minus 23 °C and an elevated temperature of 60 °C. These two temperatures were selected because polycarbonate products are often used in the automotive industry when such temperatures may occur. At low temperature, the results show that the mixtures show less influence on the reprocessed material for the measured properties. At higher temperatures, the effect of reprocessing can be observed, especially the impact of Charpy notch strength.

Title of the Paper: **The Uncovered Interest Rate Parity Assumption in a Hyperchaotic System**

Authors: **Ourania I. Tacha, Ioannis N. Stouboulos, Efthymia Meletlidou, Ioannis M. Kyprianidis**

Pages: **205-209**

Abstract: In this paper, the uncovered interest rate parity (UIP) assumption, using a well-known 3D chaotic dynamical system, which describes the variations of the interest rate, is studied. More specifically a 4D novel hyperchaotic financial system is proposed by introducing the exchange rate, due to the fact that the difference in interest rates between two countries is equal to the relative change in currency foreign exchange rates over the same period. The novel 4D financial dynamical system is investigated in two different cases with and without a base interest rate. The system’s hyperchaotic behavior and a route to chaos through a crisis phenomenon and quasiperiodic behavior are observed through the simulation results.

Title of the Paper: **An Improved Motion Controller of a Mobile Robot based on a Hyperchaotic System**

Authors: **Eleftherios K. Petavratzis, Christos K. Volos, Hektor E. Nistazakis, Ioannis N. Stouboulos, Ioannis M. Kyprianidis**

Pages: **200-204**

Abstract: In this paper, an improved technique of a mobile robot’s motion control, which is based on a hyperchaotic system, is studied. The proposed motion control strategy of the mobile robot is based on a chaotic path planning generator in order to cover a terrain faster, in regard to other previous works, and also with unpredictable way. The simulation results for the proposed motion control strategy prove that greater terrain coverage can be achieved.

Title of the Paper: **Natural-frequency Analysis of Laminated Composite Shell**

Authors: **E. Kormanikova**

Pages: **192-199**

Abstract: The paper deals with a numerical approach of modefrequency analysis of a simply-supported laminated doubly curved shell. For laminated shell the first-order shear deformation theory is capable of accurately predicting the shell behaviour. Transverse displacement field leads to using shear correction factor. Theory is also based on the assumption that the thickness to radius ratio of shell is small compared to unity and hence negligible. The governing equations are derived in orthogonal curvilinear coordinates and than these equations are rediced to those of doubly curved shell. Linear layered structural shell elements are used in FEM analysis. The natural frequencies of laminated orthotropic doubly curved shell with simply supported ends are solved. The numerical analysis is conducted to determine the effect of symmetry with respect to midplane, fibre orientation and width-to-thickness ratio to change of resonant frequencies.

Title of the Paper: **On Simple Algebraic Control Design and Possible Controller Tuning for Linear Systems with Delays**

Authors: **Libor Pekař**

Pages: **178-191**

Abstract: This paper is aimed at possible controller tuning of infinite-dimensional controllers of a predictor (compensator) type obtained from an algebraic-based controller structure design method for linear systems with delays. The design procedure is simple enough so that it can attract practitioners. The controllers are of a generalized proportional-integral(-derivative) (PI(D)) type after a trivial limit approximation, and those obtained for stable controlled processes can be compared to the well-known Smith predictor scheme. Some well-established tuning rules for three study cases are then used and compared; namely, the Chien-Hrones-Reswick and the equalization methods are applied for first and second order plants with input and state delays, and the quasi-continuous shifting procedure with the spectral abscissa minimization versus the tripledominant-root setting are used to the unstable first-order case. These tuning rules are directly applied to PI(D) laws in the simple feedback structure as well, which is compared to the results for the compensation controllers. The robustness of designed controllers is simply benchmarked via some selected perturbations in the static gain and both delays. Simulation outputs and performance measures are given to the reader to display and quantify the obtained results for clearer comparison.

Title of the Paper: **Dynamic Behavior of Fluid Rectangular Container**

Authors: **K. Kotrasová**

Pages: **170-177**

Abstract: Liquid store tanks are used to store of fluid. This paper presents the theoretical background for fluid effect in moved container and Finite element method numerical simulation of response of fluid filled rectangular tank due to horizontal harmonic motion. The peak waves of fluid in fluid filled rectangular tank were analysed in depending of frequency and acceleration. The realised experiments confirm the 1th mode of circular frequency. The FEM numerical simulation of tank fluid filling was completed dynamic behaviour of fluid and its effect on tank solid domain.

Title of the Paper: **Orientation Robotic Mechanism Used in Industrial Operations**

Authors: **Paul Ciprian Patic, Gabriela Mantescu, Marin Mainea, Lucia Pascale**

Pages: **162-169**

Abstract: The robot is a complex automated system that has the role of manipulating the parts and tools, replacing the action of human. An industrial robot is a system that does not operate in isolation, it communicates with other robots and machine tools, conveyor belts, thus reaching the idea of a flexible manufacturing cell. One of the most important robot classes is manipulating robots for manufacturing operations, which include industrial robots. There are, undoubtedly, many definitions of the industrial robot, which is a universal machine, used to perform some intellectual activity, human jobs or to have the capacity to replace man in different actions. The goal of this paper is to make a study on the kinematics of the mechanisms involved in industrial robot composition, some data regarding the dynamics of industrial robotic systems and the structure of a robotic position system used in industrial operations in order to optimize and correct the performances.

Title of the Paper: **Design of a Reconfigurable Exoskeleton Used on Human Locomotion Recovery**

Authors: **Dumitru N., Copilusi C., Dumitru S., Rosu E.**

Pages: **150-161**

Abstract: This paper describes a reconfigurable leg exoskeleton designed for human locomotion system rehabilitation. The designed exoskeleton consists of two equivalent lower limbs, a special frame and a command and control unit. The research core was focused on the actuation mechanism, which this can be replaced by physician specific requirements. Thus, there were proposed two types of actuation systems, namely linear electric motors and cam mechanisms with rotational electric motors. The starting actuation system solution was represented by the linear electric motors and this needs to be improved. For this, a human gait experimental analysis was performed in order to obtain the input data for cam mechanism designs. Based on this, a mathematical model of the cam actuation mechanism was developed from where the cam profiles were obtained. The cam mechanism fits perfectly the human locomotion system especially for knee and ankle joints. Thus it will be elaborated and numerically processed mathematical models for cam mechanism design respectively linear motion laws identification for linear actuators. The obtained results, starting from theoretical analyses to a prototype, validate both actuation systems and certify the reconfigurable solution.

Title of the Paper: **Corrosion Impact on Mechanical Properties of AA6061-T6 under Friction Stir Welding Process**

Authors: **Kasim Mohammed Jawad**

Pages: **140-149**

Abstract: The technology of friction stir welding (FSW) has been developed about four decades ago as a very effective tool to replace the old fashion welding technique for certain alloys such as aluminum and magnesium alloys. Despite the effectiveness of FSW, there are very important challenges and difficulties for applying this technique mainly due to corrosion and erosion. In this report, the corrosion of the nugget zone area was thoroughly studied by showing microstructure, hardness, and the corrosion of AA6061-T6 alloy. A series of experiments were carried out using the same corrosive solution but the exposure corrosion time was taken after 24, 48, 72, and 96 h. areas of 200, 400, and 600 mm2, and slurry speed of 1, 2, and 3 m/s. The results have shown that the exposure time of 48 h was the most effective time while the slurry speed of 2 m/s was the most effective speed. The hardness of the AA6061-T6 has shown very close symmetric feature on the two sides of the sample. The unique results of exposure corrosion time of 48 h and the slurry speed of 2 m/s could be considered as a good guide for future work of corrosion-erosion of aluminum and other alloys.

Title of the Paper: **The Influence of Material and Geometric Parameters on the Design of Steel Mechanical Anchors to Concrete under Tension Loading**

Authors: **Michal Štrba, Marcela Karmazínová, Veronika Václavíková**

Pages: **131-139**

Abstract: This paper deals with some problems in case of the effective and efficient design of post-installed steel mechanical expansion anchors to concrete which are subjected to the tension loading using either static or cyclic loading force. Also the influence of some selected parameters and characteristics in case of the loadcarrying capacity determination and of the actual behaviour of these fastening members is discussed. All the presented information and results are mostly based on the previous theoretical and experimental research realized in last years on the authors’ workplace and oriented to a verification of these steel anchors to concrete using the effect of the mechanical interaction of both component materials (steel and concrete). Within the framework of mentioned research programme a large number of loading tests were performed for various loading cases and all the results were subsequently elaborated to get values of load-carrying capacity corresponding different failure mechanisms of these fasteners depending on the used material and geometric parameters as well as on the type of loading. They were also realized some additional loading tests for the verification of actual material properties of the selected members (especially in case of strength characteristics). All the data and test results obtained from the performed experiments were evaluated using statistic and probabilistic approaches to get the characteristic and design valuesof load-carrying capacity. Therefore, this article provides some additional information about the general principle of mentioned members for fastening as well as it complements some author’s previous publications in this field.

Title of the Paper: **Probabilistic Modelling of Fatigue Crack - Some Observations about Conditional Probability**

Authors: **Z. Kala**

Pages: **121-130**

Abstract: The article deals with time-dependent analysis of the failure probability of a load bearing element of a steel bridge. The theoretical model of fatigue crack propagation is based on linear fracture mechanics. The Latin Hypercube Sampling statistical method is used to calculate the unconditional and conditional probabilities. The conditional probability is calculated by excluding those random observations that have a detectable crack length observed during the inspection. The effect of included and excluded observations of input random quantities on the conditional failure probability is mapped and shown graphically. It is proven that the number of stress peaks per year can be considered as one random variable for any time interval of the life span of the bridge.

Title of the Paper: **On the Falls of Two Wheeled Vehicles**

Authors: **Andrea Bonci, Sauro Longhi, Emanuele Lorenzoni, Giuseppe Antonio Scala**

Pages: **109-120**

Abstract: The study and analysis of two-wheeled vehicle’s falls and critical situations are difficult tasks to perform due to the rather elaborate dynamics that come into play. However, to prevent such events, it is necessary a good understanding of the conditions that trigger them. To this purpose, suitable tools able to show how the vehicle's parameters may influence its dynamic behavior are required. In the present paper the analysis of the major falls relative to a two-wheeled vehicle is performed by means of dynamics simulations based on the motorcycle model presented by the authors in prior works. The simulations are also discussed in relation to alternative descriptions provided by theoretical instruments reported in the literature and the substantial consistency of the results is shown.

Title of the Paper: **A Interface Formation in Two-Phase Flow Problems**

Authors: **K. Fraňa, I. Nová**

Pages: **102-108**

Abstract: The objective of the paper is a numerical investigation of the multi-phase unsteady flow problem representing the formation and kinetic of bubbles. The mathematical model is given by the equation system used commonly for the three-dimensional viscous unsteady laminar flow problem. Shapes and forms of the phase-interface between gas-liquid depend strongly on the used grid resolution. Generally for various grid resolutions, different bubble formations were found. However, the volumetric fraction of the gas in the mixture was identical up to particular time. In advanced time, different progress of the gas decomposition was identified and the gas amount in the mixture was significantly lower in respect to the theoretical assumption. Furthermore, kinetic and bubble formations were investigated in liquids with various kinematic viscosity. It was found that kinematic viscosity could evidently influence the bubble formation, size and shape, but not a capability of the liquid to capture gas in the liquid as it can be assumed.

Title of the Paper: **Second Law Analysis of Ion Slip Effect on MHD Couple Stress Fluid**

Authors: **Abiodun A. Opanuga, Hilary I. Okagbue, Olasunmbo O. Agboola, Sheila A. Bishop**

Pages: **96-101**

Abstract: This paper is concerned with the numerical investigation of entropy generation in viscous incompressible MHD couple stress fluid in a rotating frame of reference. An approximate solution of the dimensionless velocity and temperature profiles are obtained and used to calculate the entropy generation rate and Bejan number. The influences of the governing parameters on velocity, temperature, entropy generation and Bejan number are presented with the aid of graphs.

Title of the Paper: **Flow Structure of the Transverse Jet Interaction with Supersonic Flow for Moderate to High Pressure Ratios**

Authors: **Asel Beketaeva, Altynshash Naimanova**

Pages: **88-95**

Abstract: The vortex structures behind the transverse jet in a supersonic flow for moderate to high pressure ratios are studied. Numerical simulation is performed using the three-dimensional Favre-averaged Navier–Stokes equations coupled by the turbulence model which are solved by the algorithm based on the high-order non-oscillatory (ENO) scheme. The simulations correctly captured primary vortices: the well-known two counter-rotating vortices, the primary upstream vortex and the secondary upstream vortex, the horseshoe vortex, the pair of vortex in a separation region, and one pair of vortices appeared due to the interaction of the jet passing through the Mach disk, two pairs of vortices formed due to an overflow above the jet. The additional two vortices are found localized near the wall in the region behind the jet.

Title of the Paper: **The Study of the Mixing Layer Particles Distribution in Dependence on the Convective Mach Numbers**

Authors: **Altyn Makasheva, Altynshash Naimanova**

Pages: **79-87**

Abstract: The numerical studies of the quasi two-dimensional supersonic turbulent gas-particle mixing layer are performed using the 2D-DNS (Direct Numerical Simulations). The system of Navier-Stokes equations of a multi-species flow is solved using the ENO scheme of a third-order accuracy. The dispersion of the particles is simulated by the Lagrangian method following their trajectories in the mixing layer. The study focuses on the roles of the large-scale vortex structures in a particle dispersion dependence on the Stokes numbers and convective Mach numbers.

Title of the Paper: **Experimental Determination of Aeroelastic Derivatives for a Small-Scale Bridge Deck**

Authors: **M. Cassaro, E. Cestino, G. Frulla, P. Marzocca, M. Pertile**

Pages: **67-78**

Abstract: A heaving and pitching two degrees of freedom bridge-deck sectional model apparatus representative of a long-span bridge was designed, built, and tested in the wind tunnel to acquire measurement of aeroelastic derivatives. The main objective of this study was the experimental validation of the procedure to compute the aeroelastic derivatives based on the Iterative Least Square Method identification technique. A good correspondence was found between the flutter derivatives experimentally extracted from the model, and the corresponding reference values, which have been analytically derived from the Theodorsen’s theory. A simulation model in MATLAB/Simulink® environment, useful for future control laws applications, was also developed and validated by real experimental results.

Title of the Paper: **Frequency Analysis of Partially-Filled Rectangular Water Tank**

Authors: **K. Kotrasova, E. Kormanikova**

Pages: **59-66**

Abstract: This paper deals with experimental studies of sloshing of liquid in partially filled container subjected to external excitation horizontal harmonic motion. The theoretical background of fluid response on rectangular tank due to horizontal acceleration of tank bottom, impulsive and convective (sloshing) pressure and the fluid natural frequencies is presented in paper. The dynamic behavior of fluid filled rectangular container was monitored and was evaluated in realized experiment. The resulting peak slosh heights for various excitation frequencies and amplitudes in fluid filled rectangular tank are compared with the fluid natural frequencies.

Title of the Paper: **Complete Study for Solving Navier-Lame Equation with New Boundary Condition Using Mini Element Method**

Authors: **Ouadie Koubaiti, Jaouad El-Mekkaoui, Ahmed Elkhalfi**

Pages: **46-58**

Abstract: The objective of our article is to solve the Navier-Lame equation with a new boundary CA;B condition using the mixed finite elements method . We compare between minielement method and the ordinary finite element method by the other side. We compute the displacement and its divergence simultaneously by using an extra unknown. We prove the existence and uniqueness of the weak and discrete solution by proving the discrete inf-sup and coerciveness conditions. We expose two ways of comparison, that the first way we calculate the rate α called speed of convergence found by each of the two numerical methods, all this will be done by the use of the linear regression. An analytical example is used to validate the accuracy, convergence and robustness of the present mixed finite elements method for elasticity. In order to evaluate the performance of the method, and to confirm our method, the numerical results of mini element method are compared with others coming from commercial code like Abaqus system.

Title of the Paper: **Post-Newtonian Equations for Free-space Laser Communications between Space-based Systems**

Authors: **Jose M. Gambi, Maria L. Garcia del Pino, Jonathan Mosser, Ewa B. Weinmüller**

Pages: **38-45**

Abstract: The purpose of this paper is to show that the equations for relative motions derived from the two systems of post-Newtonian equations presented here, allow to increase the acquisition, pointing and tracking accuracy when compared to the Newtonian equations aimed to describe free-space laser communications between Low Earth Orbit (LEO) satellites, so as between LEO and Medium Earth Orbit (MEO), and Geostationary Earth Orbit (GEO) satellites. The equations discussed in this work are similar, but not equivalent to those proposed for space debris removal, i. e. in the context of spacebased systems to throw middle size LEO debris objects into the atmosphere via laser ablation. In fact, the present equations are computationally much more affordable because the aim is now less demanding, and so they result from subtractions within each post-Newtonian system here provided.

Title of the Paper: **Estimation of Dynamic Behavior and Energy Efficiency of Thrust Hybrid Bearings with Active Control**

Authors: **Alexander Babin, Sergey Majorov, Leonid Savin**

Pages: **32-37**

Abstract: The present paper considers analysis of world tendencies of application of bearings with feedback control systems in various types of rotor machines. A possibility of qualitative improvement of operational characteristics has been highlighted for bearings with integrated additional functions of automated diagnostics and active control of geometric, rheological and force parameters. The present paper features a mathematical model, its implementation in a form of an algorithm, and numerical results including pressure and temperature distribution in a bearing in question, load capacity and rotor’s axial trajectories. A quality index has been formulated for thrust tapered land hybrid bearings with a central feeding chamber that is based on a combination of minimum power loss due to friction and stability of motion of a rotor. Various combinations of roughness and axial gaps have been taken into account.

Title of the Paper: **Influence of Non-Linear Behavior on Seismic Response Parameters**

Authors: **Rita Greco, Alessandra Fiore, Ivo Vanzi**

Pages: **19-31**

Abstract: This paper deals with the effects of post-yielding stiffness on the response of non-linear structural systems under seismic actions. In detail, two hysteretic models are considered: a bilinear plastic model, representing structures that exhibit strain hardening characteristics, and an elastic-perfectly-plastic model, widely adopted in design codes. For these models, a parametrical study is carried out to assess the influence of post-yielding stiffness ratio on some non-linear response quantities, such as the response modification factor, the ductility demand and the damage index. The analysis is developed on a SDOF system subject to El Centro earthquake and demonstrates that the elastic-plastic constitutive law is excessively conservative to evaluate structural deformations. Finally the study provides useful information also from an energetic point of view.

Title of the Paper: **Axisymmetric Deformation Analysis of Thick-Walled Cylinders and Rotating-Disks Using an Improved Adomian Decomposition Method**

Authors: **Safa Bozkurt Coşkun, Zuhal Elif Kara**

Pages: **14-18**

Abstract: In this study, a problem arising in advanced engineering mechanics governed by a singular differential equation is solved using an improved Adomian decomposition method. The technique was previously used in literature for the solution of two-point singular boundary value problems in applied mathematics. Authors extend the use of the mathematical technique to presented problem and the results show that improved Adomian decomposition method can be successfully used in the axisymmetric deformation and stress analysis of thick-walled cylinders and rotating disks.

Title of the Paper: **Model of Pressure Losses in Pipes During the Transport of Heavy Oil with 11 API Gravity**

Authors: **Manuel A. Falconi, Enrique T. Tamayo, Héctor L. Laurencio, Jorge P. Vega, Elvis P. Gualotuña, Edwin R. Grijalva, Luís Grijalva Campana**

Pages: **8-13**

Abstract: During the transport of heavy oils by pipes, there are difficulties related to their high viscosity with non-Newtonian behavior, directly affecting the performance of the transport facilities, because of the inaccuracies of the calculation methodologies. In the present work it obtain a mathematical model that describes the pressure variations for non-Newtonian oil flow in pipes; obtained from the limitations of methodologies and correlations, that allows the evaluation of the simultaneous effects of the viscous force and of mixing in the laminar and turbulent regime during the transport of heavy oils by pipes. Equation 15 is the generalized theoretical model for the calculation of pressure variations in the transport of heavy crude oil by pipeline. It takes into account the variation of temperature during transport, the effects of viscous friction, and the effects of mixing between flow layers. The values of the flow index for the transport of heavy oil of 11ºAPI by pipes oscillates between 0,917 and 0,929 in function of the temperature values that vary between 29 oC and 69.8 oC. The consistency index varies between 13.55 Pa.s and 1.46 Pa.s for the same temperature range.

Title of the Paper: **Numerical Study of Disperse Materials Process in a Continuous-Flow Plasma Reactor**

Authors: **Issakhov A. A., Urmashev B. A.**

Pages: **1-7**

Abstract: The paper presents a numerical study of the temperature propagation in the direct-flow plasma reactor, which is solved by the compressible Navier - Stokes equations that is approximated by finite volume method, the numerical algorithm based on the SIMPLE method. In the numerical algorithm of the equation system can be divided into four stages. The first stage is that the transfer of momentum carried out only by convection and diffusion. The intermediate velocity field is solved by the solution of the differential velocity gradient equation with the Green-Gauss Cell Based scheme. For the pressure field is applied PRESTO numerical scheme. In a third step it is assumed that the transfer is carried out only by the pressure gradient. The fourth step of the equation is solved for the energy transport equation as well as the momentum equations by the Green-Gauss Cell Based scheme. The algorithm is parallelized on high-performance systems. With this numerical algorithm was obtained numerical results of temperature distribution in a continuousflow plasma reactor. Numerical modelling allows us to give a more precise description of the processes that have been identified and studied theoretically and can reveal new physical phenomena processes that are not yet available, seen in experimental studies. Simulation results show that the constructed numerical model provides the necessary accuracy and stability, which should accurately describe the process during the time interval.