Search results for: Boussinesq equations

Authors: Abraham Dayan

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Remediation of soil containing volatile contaminants is often conducted by vapor extraction (SVE) technique. The operation is based on injection of air at ambient temperatures with or without thermal soil warming. Thermal enhancements of soil vapor extraction (TESVE) processes are usually conducted by soil heating, sometimes assisted by added steam injections. The current study addresses a technique which has not received adequate attention and is based on using exclusively hot air as an alternative to the common TESVE practices. To demonstrate the merit of the hot air TESVE technique, a sandy soil containing contaminated water is studied. Numerical and analytical tools were used to evaluate the rate of decontamination processes for various geometries and operating conditions. The governing equations are based on the Darcy law and are applied to an expanding compressible flow within a sandy soil. The equations were solved to determine the minimal time required for complete soil remediation. An approximate closed form solution was developed based on the assumption of local thermodynamic equilibrium and on a linearized representation of temperature dependence of the vapor to air density ratio. The solution is general in nature and offers insight into the governing processes of the soil remediation operation, where self-similar temperature profiles under certain conditions may exist, and the noticeable role of the contaminants evaporation and recondensation processes in affecting the remediation time. Based on analyses of the hot air TESVE technique, it is shown that it is sufficient to heat the air during a certain period of the decontamination process without compromising its full advantage, and thereby, entailing a minimization of the air-heating-energy requirements. This in effect is achieved by regeneration, leaving the energy stored in the soil during the early period of the remediation process to heat the subsequently injected ambient air, which infiltrates through it for the decontamination of the remaining untreated soil zone. The characteristic time required to complete SVE operations are calculated as a function of, both, the injected air temperature and humidity. For a specific set of conditions, it is demonstrated that elevating the injected air temperature by 20oC, the hot air injection technique reduces the soil remediation time by 50%, while requiring 30% of additional energy consumption. Those evaluations clearly unveil the advantage of the hot air SVE process, which for insignificant cost of added air heating energy, the substantial cost expenditures for manpower and equipment utilization are reduced.

Keywords: Porous Media, Soil Decontamination, Hot Air, Vapor Extraction

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Authors: Awais Asif

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This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature.

Keywords: Chatterjea type F-contraction, F-cauchy sequence, F-convergent, multi valued mappings

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Authors: Xin-Yan Ji, Jing Wang, Chang Liu, Yan-Qiang Bi, Zhong-Xu Xu, Xi-Yuan Li

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Thermal tests of electronic units are critically important for the reliability validation and performance demonstration of the spacecraft hard-wares. The tailoring equation in MIL-STD-1540 is based on fatigue of solder date. In the present paper, a new test condition tailoring expression is proposed to fit different thermo-mechanical fatigue and different subsystems, by introducing an integrated evaluating method for the fatigue acceleration exponent. The validate test has been accomplished and the data has been analyzed and compared with that from the MIL-STD-1540 tailoring equations. The results are encouraging and reasonable.

Keywords: thermal cycling test, thermal fatigue, tailoring equation, test condition planning

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Authors: L. Belounar, K. Gerraiche, C. Rebiai, S. Benmebarek

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This paper presents the development of a new three dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending behavior. The developed element has the three essential external degrees of freedom (U, V and W) at each of the eight corner nodes. The displacements field of the developed element is based on assumed functions for the various strains satisfying the compatibility and the equilibrium equations. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element.

Keywords: brick element, strain approach, plate bending, civil engineering

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Authors: P. Mendes, H. Stel, R. E. M. Morales

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This article presents a numerical and experimental study of turbulent flow in corrugated pipes with helically “d-type" grooves, for Reynolds numbers between 7500 and 100,000. The ANSYS-CFX software is used to solve the RANS equations with the BSL two equation turbulence model, through the element-based finite-volume method approach. Different groove widths and helix angles are considered. Numerical results are validated with experimental pressure drop measurements for the friction factor. A correlation for the friction factor is also proposed considering the geometric parameters and Reynolds numbers evaluated.

Keywords: turbulent flow, corrugated pipe, helical, numerical, experimental, friction factor, correlation

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Authors: Y. Sunita Rani, Y. Hari Krishna, M. V. Ramana Murthy, K. Sudhaker Reddy

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This article studied effects of radiation and chemical reaction on MHD casson fluoid flow past a Permeable Stretching Sheet in a Porous Medium. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like Runge- Kutta – Fehlberg shooting technique method. The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically.

Keywords: MHD, Casson fluid, porous medium, permeable stretching sheet

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Authors: Cagri Mollamahmutoglu, Aykut Levent, Ali Mercan

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Micro-beams are one of the most common components of Nano-Electromechanical Systems (NEMS) and Micro Electromechanical Systems (MEMS). For this reason, static bending, buckling, and free vibration analysis of micro-beams have been the subject of many studies. In addition, micro-beams restrained with elastic type foundations have been of particular interest. In the analysis of microstructures, closed-form solutions are proposed when available, but most of the time solutions are based on numerical methods due to the complex nature of the resulting differential equations. Thus, a robust and efficient solution method has great importance. In this study, a mixed finite element formulation is obtained for a functionally graded Timoshenko micro-beam resting on two-parameter elastic foundation. In the formulation modified couple stress theory is utilized for the micro-scale effects. The equation of motion and boundary conditions are derived according to Hamilton’s principle. A functional, derived through a scientific procedure based on Gateaux Differential, is proposed for the bending and buckling analysis which is equivalent to the governing equations and boundary conditions. Most important advantage of the formulation is that the mixed finite element formulation allows usage of C₀ type continuous shape functions. Thus shear-locking is avoided in a built-in manner. Also, element matrices are sparsely populated and can be easily calculated with closed-form integration. In this framework results concerning the effects of micro-scale length parameter, power-law parameter, aspect ratio and coefficients of partially or fully continuous elastic foundation over the static bending, buckling, and free vibration response of FG-micro-beam under various boundary conditions are presented and compared with existing literature. Performance characteristics of the presented formulation were evaluated concerning other numerical methods such as generalized differential quadrature method (GDQM). It is found that with less computational burden similar convergence characteristics were obtained. Moreover, formulation also includes a direct calculation of the micro-scale related contributions to the structural response as well.

Keywords: micro-beam, functionally graded materials, two-paramater elastic foundation, mixed finite element method

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Authors: Deva Kanta Phukan

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An attempt is made where an electrically conducting fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. A magnetic field is applied parallel to the axis of the cylindrical rod. The basic governing set of partial differential equations for conservation of mass and momentum are reduced to a set of non-linear ordinary differential equation by introducing similarity transformation, which are integrated numerically. A perturbation solution for the case of large magnetic parameter is derived for constant Reynolds number.

Keywords: annular axi-symmetric stagnation flow, conducting fluid, magnetic field, moving cylinder

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Authors: Manouchehr Amiri

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This article introduces a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary data matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principles are investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Beckenstein, and mass-energy equivalence are derived.

Keywords: physical theory of information, binary data matrix model, Shannon information theory, bit information principle

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Fikret Yalcinkaya, Hamza Unsal

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To understand how neurons work, it is required to combine experimental studies on neural science with numerical simulations of neuron models in a computer environment. In this regard, the simplicity and applicability of spiking neuron modeling functions have been of great interest in computational neuron science and numerical neuroscience in recent years. Spiking neuron models can be classified by exhibiting various neuronal behaviors, such as spiking and bursting. These classifications are important for researchers working on theoretical neuroscience. In this paper, three different spiking neuron models; Izhikevich, Adaptive Exponential Integrate Fire (AEIF) and Hindmarsh Rose (HR), which are based on first order differential equations, are discussed and compared. First, the physical meanings, derivatives, and differential equations of each model are provided and simulated in the Matlab environment. Then, by selecting appropriate parameters, the models were visually examined in the Matlab environment and it was aimed to demonstrate which model can simulate well-known biological neuron behaviours such as Tonic Spiking, Tonic Bursting, Mixed Mode Firing, Spike Frequency Adaptation, Resonator and Integrator. As a result, the Izhikevich model has been shown to perform Regular Spiking, Continuous Explosion, Intrinsically Bursting, Thalmo Cortical, Low-Threshold Spiking and Resonator. The Adaptive Exponential Integrate Fire model has been able to produce firing patterns such as Regular Ignition, Adaptive Ignition, Initially Explosive Ignition, Regular Explosive Ignition, Delayed Ignition, Delayed Regular Explosive Ignition, Temporary Ignition and Irregular Ignition. The Hindmarsh Rose model showed three different dynamic neuron behaviours; Spike, Burst and Chaotic. From these results, the Izhikevich cell model may be preferred due to its ability to reflect the true behavior of the nerve cell, the ability to produce different types of spikes, and the suitability for use in larger scale brain models. The most important reason for choosing the Adaptive Exponential Integrate Fire model is that it can create rich ignition patterns with fewer parameters. The chaotic behaviours of the Hindmarsh Rose neuron model, like some chaotic systems, is thought to be used in many scientific and engineering applications such as physics, secure communication and signal processing.

Keywords: Izhikevich, adaptive exponential integrate fire, Hindmarsh Rose, biological neuron behaviours, spiking neuron models

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Authors: M. Yusefzad

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Law of energy conservation is one of the fundamental laws of physics. Energy is conserved, and the total amount of energy is constant. It can be transferred from one object to another and changed from one state to another. However, in the case of wave interference, this law faces important contradictions. Based on the presented mathematical relationship in this paper, it seems that validity of this law depends on the path of energy wave, like light, in which it is located. In this paper, by using some fundamental concepts in physics like the constancy of the electromagnetic wave speed in a specific media and wave theory of light, it will be shown that law of energy conservation is not valid in every condition and in some circumstances, it is possible to increase energy of a system with a determined amount of energy without any input.

Keywords: power, law of energy conservation, electromagnetic wave, interference, Maxwell’s equations

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Suleyman Ogul Ertugrul, Mustafa Turgut, Serkan Inandı, Mustafa Gorkem Coban, Mustafa Kıgılı, Ali Mert, Oguzhan Kesmez, Murat Ozancı, Caglar Uyulan

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In high-performance automotive engineering, the realistic simulation of suspension systems is crucial for enhancing vehicle dynamics and handling. This study focuses on the double wishbone suspension system, prevalent in racing vehicles due to its superior control and stability characteristics. Utilizing MATLAB and Adams Car simulation software, we conduct a comprehensive analysis of displacement behaviors and damper sizing under various dynamic conditions. The initial phase involves using MATLAB to simulate the entire suspension system, allowing for the preliminary determination of damper size based on the system's response under simulated conditions. Following this, manual calculations of wheel loads are performed to assess the forces acting on the front and rear suspensions during scenarios such as braking, cornering, maximum vertical loads, and acceleration. Further dynamic force analysis is carried out using MATLAB Simulink, focusing on the interactions between suspension components during key movements such as bumps and rebounds. This simulation helps in formulating precise force equations and in calculating the stiffness of the suspension springs. To enhance the accuracy of our findings, we focus on a detailed kinematic and dynamic analysis. This includes the creation of kinematic loops, derivation of relevant equations, and computation of Jacobian matrices to accurately determine damper travel and compression metrics. The calculated spring stiffness is crucial in selecting appropriate springs to ensure optimal suspension performance. To validate and refine our results, we replicate the analyses using the Adams Car software, renowned for its detailed handling of vehicular dynamics. The goal is to achieve a robust, reliable suspension setup that maximizes performance under the extreme conditions encountered in racing scenarios. This study exemplifies the integration of theoretical mechanics with advanced simulation tools to achieve a high-performance suspension setup that can significantly improve race car performance, providing a methodology that can be adapted for different types of racing vehicles.

Keywords: FSAE, suspension system, Adams Car, kinematic

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Authors: I. Ait El Harch, K. Outaaoui, Y. El Foutayeni

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This study aims to deepen the understanding and optimize fishing activity in Morocco by holistically integrating biological and economic aspects. We develop a biological equilibrium model in which these competing species present their natural growth by logistic equations, taking into account density and competition between them. The integration of human intervention adds a realistic dimension to our model. A company specifically targets the three species, thus influencing population dynamics according to their fishing activities. The aim of this work is to determine the fishing effort that maximizes the company’s profit, taking into account the constraints associated with conserving ecosystem equilibrium.

Keywords: bioeconomical modeling, optimization techniques, linear complementarity problem LCP, biological equilibrium, maximizing profits

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Authors: L. Joseph, B. Farid, F. Ravelet

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Fundamental studies were performed on bifurcation, instabilities and turbulence in Taylor-Couette flow and applied to many engineering applications like astrophysics models in the accretion disks, shrouded fans, and electric motors. Such rotating machinery performances need to have a better understanding of the fluid flow distribution to quantify the power losses and the heat transfer distribution. The present investigation is focused on high gap ratio of Taylor-Couette flow with high rotational speeds, for smooth and grooved surfaces. So far, few works has been done in a very narrow gap and with very high rotation rates and, to the best of our knowledge, not with this combination with grooved surface. We study numerically the turbulent flow between two coaxial cylinders where R1 and R2 are the inner and outer radii respectively, where only the inner is rotating. The gap between the rotor and the stator varies between 0.5 and 2 mm, which corresponds to a radius ratio η = R1/R2 between 0.96 and 0.99 and an aspect ratio Γ= L/d between 50 and 200, where L is the length of the rotor and d being the gap between the two cylinders. The scaling of the torque with the Reynolds number is determined at different gaps for different smooth and grooved surfaces (and also with different number of grooves). The fluid in the gap is air. Re varies between 8000 and 30000. Another dimensionless parameter that plays an important role in the distinction of the regime of the flow is the Taylor number that corresponds to the ratio between the centrifugal forces and the viscous forces (from 6.7 X 105 to 4.2 X 107). The torque will be first evaluated with RANS and U-RANS models, and compared to empirical models and experimental results. A mesh convergence study has been done for each rotor-stator combination. The results of the torque are compared to different meshes in 2D dimensions. For the smooth surfaces, the models used overestimate the torque compared to the empirical equations that exist in the bibliography. The closest models to the empirical models are those solving the equations near to the wall. The greatest torque achieved with grooved surface. The tangential velocity in the gap was always higher in between the rotor and the stator and not on the wall of rotor. Also the greater one was in the groove in the recirculation zones. In order to avoid endwall effects, long cylinders are used in our setup (100 mm), torque is measured by a co-rotating torquemeter. The rotor is driven by an air turbine of an automotive turbo-compressor for high angular velocities. The results of the experimental measurements are at rotational speed of up to 50 000 rpm. The first experimental results are in agreement with numerical ones. Currently, quantitative study is performed on grooved surface, to determine the effect of number of grooves on the torque, experimentally and numerically.

Keywords: Taylor-Couette flow, high gap ratio, grooved surface, high speed

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: J. Fernandez de Canete, P. Del Saz Orozco, I. Garcia-Moral, A. Akhrymenka

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Object-oriented modeling is spreading in current simulation of wastewater treatments plants through the use of the individual components of the process and its relations to define the underlying dynamic equations. In this paper, we describe the use of the free-software OpenModelica simulation environment for the object-oriented modeling of an activated sludge process under feedback control. The performance of the controlled system was analyzed both under normal conditions and in the presence of disturbances. The object-oriented described approach represents a valuable tool in teaching provides a practical insight in wastewater process control field.

Keywords: object-oriented programming, activated sludge process, OpenModelica, feedback control

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Authors: Ali Dinarveis

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This paper compares the energy and exergy efficiency of a vapour compression refrigeration system using refrigerants of different groups. In this study, five different refrigerants including R507A, R134a, R114, R22 and R717 have been studied. EES Program is used to solve the thermodynamic equations. The results of this analysis are shown graphically. Based on the results, energy and exergy efficiencies for R717 are higher than the other refrigerants. Also, the energy and exergy efficiencies will be decreased with increasing the condensing temperature and decreasing the evaporating temperature.

Keywords: Energy, Exergy, Refrigeration, thermodynamic, vapour

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Authors: Thanutch Sukwimolseree, Preeyaphorn Kosa

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Many problems are occurred in watershed due to human activity and economic development. The purpose is to determine the effects of the land use change on surface runoff using land use map on 1980, 2001 and 2008 and daily weather data during January 1, 1979 to September 30, 2010 applied to SWAT. The results can be presented that the polynomial equation is suitable to display that relationship. These equations for land use in 1980, 2001 and 2008 are consisted of y = -0.0076x5 + 0.1914x4–1.6386x3 + 6.6324x2–8.736x + 7.8023(R2 = 0.9255), y = -0.0298x5 + 0.8794x4 - 9.8056x3 + 51.99x2 - 117.04x + 96.797; (R2 = 0.9186) and y = -0.0277x5 + 0.8132x4 - 8.9598x3 + 46.498x2–101.83x +81.108 (R2 = 0.9006), respectively. Moreover, if the agricultural area is the largest area, it is a sensitive parameter to concern surface runoff.

Keywords: land use, runoff, SWAT, upper Mun River basin

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Authors: Engin Metin Kaplan, Kemal Yaman

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In this study, the crash of a medium heavy vehicle onto a designed Road blocker (vehicle barrier) is studied numerically. Structural integrity of the Road blocker is studied by nonlinear dynamic methods under the loading conditions which are defined in the standards. NASTRAN® and LS-DYNA® which are commercial software are used to solve the problem. Outer geometry determination, alignment of the inner part and material properties of the road blocker are studied linearly to yield design parameters. Best design parameters are determined to achieve the most structurally optimized road blocker. Strain and stress values of the vehicle barrier are obtained by solving the partial differential equations.

Keywords: vehicle barrier, truck collision, road blocker, crash analysis

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Authors: B. Mahfoud, A. Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Y. Yongli, M. H. Aissa

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The purpose of this paper aims for a geotechnical analysis based on experimental physical and mechanical characteristics of Miocene marl situated at Medea region in Algeria. More than 150 soil samples were taken in the investigation part of the North-South Highway which extends over than 53 km from Chiffa in the North to Berrouaghia in the South of Algeria. The analysis of data in terms of Atterberg limits, plasticity index, and clay content reflects an acceptable correlation justified by a high coefficient of regression which was compared with the previous works in the region. Finally, approximated equations that serve as a guideline for geotechnical design locally have been suggested.

Keywords: correlation, geotechnical properties, miocene marl, north-south highway

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Authors: Muhammad Hassan Khalil, Xu Jiadong

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Early detection through screening is the best tool short of a perfect treatment against the malignant tumor inside the breast of a woman. By detecting cancer in its early stages, it can be recognized and treated before it has the opportunity to spread and change into potentially dangerous. Microwave tomography is a new imaging method based on contrast in dielectric properties of materials. The mathematical theory of microwave tomography involves solving an inverse problem for Maxwell’s equations. In this paper, we present designed antenna for breast cancer detection, which will use in microwave tomography configuration.

Keywords: microwave imaging, inverse scattering, breast cancer, malignant tumor detection

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Authors: S. Vivek, Sharad Sharan, R. Arvind, D. V. Praveen, J. Vigneshwar, S. Ajith, V. R. Sanal Kumar

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In this paper numerical studies have been carried out to examine the starting transient flow features of high-performance solid propellant rocket motors with different port geometries but with same propellant loading density. Numerical computations have been carried out using a 3D SST k-ω turbulence model. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second order implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier-Stokes equations are employed. We have observed from the numerical results that in solid rocket motors with highly loaded propellants having divergent port geometry the hot igniter gases can create pre-ignition thrust oscillations due to flow unsteadiness and recirculation. Under these conditions the convective flux to the surface of the propellant will be enhanced, which will create reattachment point far downstream of the transition region and it will create a situation for secondary ignition and formation of multiple-flame fronts. As a result the effective time required for the complete burning surface area to be ignited comes down drastically giving rise to a high pressurization rate (dp/dt) in the second phase of starting transient. This in effect could lead to starting thrust oscillations and eventually a hard start of the solid rocket motor. We have also observed that the igniter temperature fluctuations will be diminished rapidly and will reach the steady state value faster in the case of solid propellant rocket motors with convergent port than the divergent port irrespective of the igniter total pressure. We have concluded that the thrust oscillations and unexpected thrust spike often observed in solid rockets with non-uniform ports are presumably contributed due to the joint effects of the geometry dependent driving forces, transient burning and the chamber gas dynamics forces. We also concluded that the prudent selection of the port geometry, without altering the propellant loading density, for damping the total temperature fluctuations within the motor is a meaningful objective for the suppression and control of instability and/or pressure/thrust oscillations often observed in solid propellant rocket motors with non-uniform port geometry.

Keywords: ignition transient, solid rockets, starting transient, thrust transient

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Authors: J.R.S.S. Kumara, M.A.R.M. Fernando, S.Venkatesh, D.K. Jayaratne

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Protection of heritage monuments against lightning has become extremely important as far as their historical values are concerned. When such structures are large and tall, the risk of lightning initiated from both cloud and ground can be high. This paper presents a lightning risk analysis of three giant stupas in Anuradhapura era (fourth century BC onwards) in Sri Lanka. The three stupas are Jethawaaramaya (269-296 AD), Abayagiriya (88-76 BC) and Ruwanweliseya (161-137 BC), the third, fifth and seventh largest ancient structures in the world. These stupas are solid brick structures consisting of a base, a near hemispherical dome and a conical spire on the top. The ancient stupas constructed with a dielectric crystal on the top and connected to the ground through a conducting material, was considered as the hypothesis for their original lightning protection technique. However, at present, all three stupas are protected with Franklin rod type air termination systems located on top of the spire. First, a risk analysis was carried out according to IEC 62305 by considering the isokeraunic level of the area and the height of the stupas. Then the standard protective angle method and rolling sphere method were used to locate the possible touching points on the surface of the stupas. The study was extended to estimate the critical current which could strike on the unprotected areas of the stupas. The equations proposed by (Uman 2001) and (Cooray2007) were used to find the striking distances. A modified version of rolling sphere method was also applied to see the effects of upward leaders. All these studies were carried out for two scenarios: with original (i.e. ancient) lightning protection system and with present (i.e. new) air termination system. The field distribution on the surface of the stupa in the presence of a downward leader was obtained using finite element based commercial software COMSOL Multiphysics for further investigations of lightning risks. The obtained results were analyzed and compared each other to evaluate the performance of ancient and new lightning protection methods and identify suitable methods to design lightning protection systems for stupas. According to IEC standards, all three stupas with new and ancient lightning protection system has Level IV protection as per protection angle method. However according to rolling sphere method applied with Uman’s equation protection level is III. The same method applied with Cooray’s equation always shows a high risk with respect to Uman’s equation. It was found that there is a risk of lightning strikes on the dome and square chamber of the stupa, and the corresponding critical current values were different with respect to the equations used in the rolling sphere method and modified rolling sphere method.

Keywords: Stupa, heritage, lightning protection, rolling sphere method, protection level

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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