Search results for: BEIR equations

Authors: Nurudeen Oluwasola Lasisi

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Newcastle disease is a highly contagious disease of birds caused by a para-myxo virus. In this paper, we presented Novel quarantine-adjusted incident and linear incident of Newcastle disease model equations. We considered the dynamics of transmission and control of Newcastle disease. The existence and uniqueness of the solutions were obtained. The existence of disease-free points was shown, and the model threshold parameter was examined using the next-generation operator method. The sensitivity analysis was carried out in order to identify the most sensitive parameters of the disease transmission. This revealed that as parameters β,ω, and ᴧ increase while keeping other parameters constant, the effective reproduction number R_ev increases. This implies that the parameters increase the endemicity of the infection of individuals. More so, when the parameters μ,ε,γ,δ_1, and α increase, while keeping other parameters constant, the effective reproduction number R_ev decreases. This implies the parameters decrease the endemicity of the infection as they have negative indices. Analytical results were numerically verified by the Differential Transformation Method (DTM) and quantitative views of the model equations were showcased. We established that as contact rate (β) increases, the effective reproduction number R_ev increases, as the effectiveness of drug usage increases, the R_ev decreases and as the quarantined individual decreases, the R_ev decreases. The results of the simulations showed that the infected individual increases when the susceptible person approaches zero, also the vaccination individual increases when the infected individual decreases and simultaneously increases the recovery individual.

Keywords: disease-free equilibrium, effective reproduction number, endemicity, Newcastle disease model, numerical, Sensitivity analysis

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Authors: Lei Zhang, Jean-Michel Ghidaglia, Anela Kumbaro

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This work focuses on numerical simulation of two-phase flows based on the bi-fluid six-equation model widely used in many industrial areas, such as nuclear power plant safety analysis. A pressure-based numerical method is adopted in our studies due to the fact that in two-phase flows, it is common to have a large range of Mach numbers because of the mixture of liquid and gas, and density-based solvers experience stiffness problems as well as a loss of accuracy when approaching the low Mach number limit. This work extends the semi-implicit pressure solver in the nuclear component CUPID code, where the governing equations are solved on unstructured grids with co-located variables to accommodate complicated geometries. A conservative version of the solver is developed in order to capture exactly the shock in one-phase flows, and is extended to two-phase situations. An inter-facial pressure term is added to the bi-fluid model to make the system hyperbolic and to establish a well-posed mathematical problem that will allow us to obtain convergent solutions with refined meshes. The ability of the numerical method to treat phase appearance and disappearance as well as the behavior of the scheme at low Mach numbers will be demonstrated through several numerical results. Finally, inter-facial mass and heat transfer models are included to deal with situations when mass and energy transfer between phases is important, and associated industrial numerical benchmarks with tabulated EOS (equations of state) for fluids are performed.

Keywords: two-phase flows, numerical simulation, bi-fluid model, unstructured grids, phase appearance and disappearance

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Authors: Guram Adamashvili

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Surface plasmon polariton is a surface optical wave which undergoes a strong enhancement and spatial confinement of its wave amplitude near an interface of two-dimensional layered structures. Phosphorene (single-layer black phosphorus) and other two-dimensional anisotropic phosphorene-like materials are recognized as promising materials for potential future applications of surface plasmon polariton. A theory of an optical breather of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene is developed. A theory of an optical soliton of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene have been investigated earlier Starting from the optical nonlinear wave equation for surface TM-modes interacting with a two-dimensional layer of atomic systems or semiconductor quantum dots and a phosphorene monolayer (or other two-dimensional anisotropic material), we have obtained the evolution equations for the electric field of the breather. In this case, one finds that the evolution of these pulses become described by the damped Bloch-Maxwell equations. For surface plasmon polariton fields, breathers are found to occur. Explicit relations of the dependence of breathers on the local media, phosphorene anisotropic conductivity, transition layer properties and transverse structures of the SPP, are obtained and will be given. It is shown that the phosphorene conductivity reduces exponentially the amplitude of the surface breather of SIT in the process of propagation. The direction of propagation corresponding to the maximum and minimum damping of the amplitude are assigned along the armchair and zigzag directions of black phosphorus nano-film, respectively. The most rapid damping of the intensity occurs when the polarization of breather is along the armchair direction.

Keywords: breathers, nonlinear waves, solitons, surface plasmon polaritons

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Authors: Hari Krishnan K. P., Anil Kumar M. V.

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The Direct Strength Method (DSM) is used for the computation of the design strength of members whose behavior is governed by any form of buckling. DSM based semiempirical equations have been successfully used for cold-formed steel (CFS) members subjected to compression, bending, and shear. The DSM equations for the strength of a CFS member are based on the parameters accounting for strength [yield load (Py), yield moment (My), and shear yield load (Vy) for compression, bending, and shear respectively] and stability [buckling load (Pcr), buckling moment (Mcr), and shear buckling load (Vcr) for compression, bending and shear respectively]. The buckling of column and beam shall be governed by local, distortional, or global buckling modes and their interaction. Recently DSM-based methods are extended for the web crippling strength of CFS beams also. Numerous DSM-based expressions were reported in the literature, which is the function of loading case, cross-section shape, and boundary condition. Unlike members subjected to axial load, bending, or shear, no unified expression for the design web crippling strength irrespective of the loading case, cross-section shape, and end boundary conditions are available yet. This study, based on nonlinear finite element analysis results, shows that the slenderness of the web, which shall be represented either using web height to thickness ratio (h=t) or Pcr has negligible contribution to web crippling strength. Hence, the results in this paper question the suitability of DSM based approach for the web crippling strength of CFS beams.

Keywords: cold-formed steel, beams, DSM-based procedure, interior two flanged loading, web crippling

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Authors: Jae-Yeong Choi, Gyu-Mok Jeon, Jong-Chun Park, Yong-Jin Cho, Seok-Tae Yoon

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When air flow is injected into water, bubbles are formed in various types inside the water pool along with the air flow rate. The bubbles are floated in equilibrium with forces such as buoyancy, surface tension and shear force. Single bubble generated at low flow rate maintains shape, but bubbles with high flow rate break up to make mixing and turbulence. In addition to this phenomenon, as the hot air bubbles are injected into the water, heat affects the interface of phases. Therefore, the main scope of the present work reveals how to proceed heat transfer between water and hot air bubbles injected into water. In the present study, a series of CFD simulation for the heat transfer of hot bubbles injected through a nozzle near the bottom in a cylindrical water column are performed using a commercial CFD software, STAR-CCM+. The governing equations for incompressible and viscous flow are the continuous and the RaNS (Reynolds- averaged Navier-Stokes) equations and discretized by the FVM (Finite Volume Method) manner. For solving multi-phase flow, the Eulerian multiphase model is employed and the interface is defined by VOF (Volume-of-Fluid) technique. As a turbulence model, the SST k-w model considering the buoyancy effects is introduced. For spatial differencing the 3th-order MUSCL scheme is adopted and the 2nd-order implicit scheme for time integration. As the results, the dynamic behavior of the rising hot bubbles with the flow rate injected and regarding heat transfer mechanism are discussed based on the simulation results.

Keywords: heat transfer, hot bubble injection, eulerian multiphase model, flow rate, CFD (Computational Fluid Dynamics)

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Authors: Mohammadamin Esmaeilzadehazimi, Morteza Shayan Arani, Mohammad Toorani, Aouni Lakis

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This study uses a hybrid finite element method to predict the dynamic behavior of both fully and partially-filled truncated conical shells stiffened with ring stiffeners. The method combines classical shell theory and the finite element method, and employs displacement functions derived from exact solutions of Sanders' shell equilibrium equations for conical shells. The shell-fluid interface is analyzed by utilizing the velocity potential, Bernoulli's equation, and impermeability conditions to determine an explicit expression for fluid pressure. The equations of motion presented in this study apply to both conical and cylindrical shells. This study presents the first comparison of the method applied to ring-stiffened shells with other numerical and experimental findings. Vibration frequencies for conical shells with various boundary conditions and geometries in a vacuum and filled with water are compared with experimental and numerical investigations, achieving good agreement. The study thoroughly investigates the influence of geometric parameters, stiffener quantity, semi-vertex cone angle, level of water filled in the cone, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells, and draws some useful conclusions. The primary advantage of the current method is its use of a minimal number of finite elements while achieving highly accurate results.

Keywords: finite element method, fluid–structure interaction, conical shell, natural frequency, ring-stiffener

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Authors: Javad Jamali Khouei, Mohammadreza Khoshravan

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Considering that application of functionally graded material is increasing in most industries, it seems necessary to present a methodology for designing optimal profile of structures such as plate under mechanical loading which is highly consumed in industries. Therefore, volume fraction variation profile of functionally graded circular plate which has been considered two-directional is optimized so that stress of structure is minimized. For this purpose, equilibrium equations of two-directional functionally graded circular plate are solved by applying semi analytical-numerical method under mechanical loading and support conditions. By solving equilibrium equations, deflections and stresses are obtained in terms of control variables of volume fraction variation profile. As a result, the problem formula can be defined as an optimization problem by aiming at minimization of critical von-mises stress under constraints of deflections, stress and a physical constraint relating to structure of material. Then, the related problem can be solved with help of one of the metaheuristic algorithms such as genetic algorithm. Results of optimization for the applied model under constraints and loadings and boundary conditions show that functionally graded plate should be graded only in radial direction and there is no need for volume fraction variation of the constituent particles in thickness direction. For validating results, optimal values of the obtained design variables are graphically evaluated.

Keywords: two-directional functionally graded material, single objective optimization, semi analytical-numerical solution, genetic algorithm, graphical solution with contour

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Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence.

Keywords: basins of attraction, convergence, multiple-root, nonlinear equation

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Authors: Salvatore Brischetto, Domenico Cesare

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Major improvements in future aircraft and spacecraft could be those dependent on an increasing use of conventional and unconventional multilayered structures embedding composite materials, functionally graded materials, piezoelectric or piezomagnetic materials, and soft foam or honeycomb cores. Layers made of such materials can be combined in different ways to obtain structures that are able to fulfill several structural requirements. The next generation of aircraft and spacecraft will be manufactured as multilayered structures under the action of a combination of two or more physical fields. In multifield problems for multilayered structures, several physical fields (thermal, hygroscopic, electric and magnetic ones) interact each other with different levels of influence and importance. An exact 3D shell model is here proposed for these types of analyses. This model is based on a coupled system including 3D equilibrium equations, 3D Fourier heat conduction equation, 3D Fick diffusion equation and electric and magnetic divergence equations. The set of partial differential equations of second order in z is written using a mixed curvilinear orthogonal reference system valid for spherical and cylindrical shell panels, cylinders and plates. The order of partial differential equations is reduced to the first one thanks to the redoubling of the number of variables. The solution in the thickness z direction is obtained by means of the exponential matrix method and the correct imposition of interlaminar continuity conditions in terms of displacements, transverse stresses, electric and magnetic potentials, temperature, moisture content and transverse normal multifield fluxes. The investigated structures have simply supported sides in order to obtain a closed form solution in the in-plane directions. Moreover, a layerwise approach is proposed which allows a 3D correct description of multilayered anisotropic structures subjected to field loads. Several results will be proposed in tabular and graphical formto evaluate displacements, stresses and strains when mechanical loads, temperature gradients, moisture content gradients, electric potentials and magnetic potentials are applied at the external surfaces of the structures in steady-state conditions. In the case of inclusions of piezoelectric and piezomagnetic layers in the multilayered structures, so called smart structures are obtained. In this case, a free vibration analysis in open and closed circuit configurations and a static analysis for sensor and actuator applications will be proposed. The proposed results will be useful to better understand the physical and structural behaviour of multilayered advanced composite structures in the case of multifield interactions. Moreover, these analytical results could be used as reference solutions for those scientists interested in the development of 3D and 2D numerical shell/plate models based, for example, on the finite element approach or on the differential quadrature methodology. The correct impositions of boundary geometrical and load conditions, interlaminar continuity conditions and the zigzag behaviour description due to transverse anisotropy will be also discussed and verified.

Keywords: composite structures, 3D shell model, stress analysis, multifield loads, exponential matrix method, layer wise approach

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Authors: Malorzata Kmiotek, Anna Kucaba-Pietal, Robert Smusz

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Due to the miniaturisation process, in many technical devices, microchannels are used in cooling systems. Because of the small size of microchannels, the flow inside is laminar, which caused a slow heat exchange. In order to intensify the heat exchange, the flow must be disturbed, for example, by introducing obstacles. We present results on the influence of a thin obstacle, placed on microchannel wall, on the fluid and heat flow in the aspect of their use by constructors of heat exchangers. The obstacle is called 'thin' when its geometrical parameter (o=w/h, w- width, h - height of the obstacle) satisfies inequality: o < 0.5. In this work, we report numerical results on heat and mass transfer in the microchannels of 400 micrometer height (H - height of the microchannel), where thin obstacles are immersed on the walls, to disturb the flow. The Reynolds number of the flow in microchannel varies between 20 and 200 and is typical for the flow in micro heat exchangers. The equations describing the fluid and heat flows in microchannels were solved numerically by using the finite element method with an application of CFD&FSI package of ADINA R&D, Inc. 9.4 solver. In the case of flows in the microchannels with sequences of thin rectangular obstacles placed on the bottom and the top wall of a microchannel, the influence of distances s (s is the distance between two thin obstacles) and heights of obstacles on the fluid and heat transfer was investigated. Thermal and flow conditions of the application area of microchannels in electronic cooling systems, i.e., wall temperature of 60 °C, the fluid temperature of 20°C were used to solve equations. Additionally, the distance s between the thin obstacles in microchannels as a multiple of the amount of the channel height was determined. Results show that placing thin obstacles on microchannel walls increase the length of recirculation zones of the flow and improves the heat transfer.

Keywords: Finite Element Method, heat transfer, mechanical engineering, microchannel

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Jinghua Zhang

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Shaft-tunnel junction is a typical case of the structural nonuniformity in underground structures. The shaft and the tunnel possess greatly different structural features. Even under uniform excitations, they tend to behave discrepantly. Studies on shaft-tunnel junctions are mainly performed numerically. Shaking table tests are also conducted. Although many numerical and experimental data are obtained, an analytical solution still has great merits of gaining more insights into the shaft-tunnel problem. This paper will try to remedy the situation. Since the seismic responses of shaft-tunnel junctions are very related to directions of the excitations, they are studied in two scenarios: the longitudinal-excitation scenario and the transverse-excitation scenario. The former scenario will be addressed in this paper. Given that responses of the tunnel are highly dependent on the shaft, the analytical solutions would be developed firstly for the vertical shaft. Then, the seismic responses of the tunnel would be discussed. Since vertical shafts bear a resemblance to rigid caissons, the solution proposed in this paper is derived by introducing terms of shaft-tunnel and soil-tunnel interactions into equations originally developed for rigid caissons. The validity of the solution is examined by a validation model computed by finite element method. The mutual influence between the shaft and the tunnel is introduced. The soil-structure interactions are discussed parametrically based on the proposed equations. The shaft-tunnel relative displacement and the soil-tunnel relative stiffness are found to be the most important parameters affecting the magnitudes and distributions of the internal forces of the tunnel. A hinge-joint at the shaft-tunnel junction could significantly reduce the degree of stress concentration compared with a rigid joint.

Keywords: analytical solution, longitudinal excitation, numerical validation , shaft-tunnel junction

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Authors: Azadeh Jafari, Robert G. Owens

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In this study, a geometrical multiscale approach which means coupling together the 2-D Navier-Stokes equations, constitutive equations and 0-D lumped parameter models is investigated. A multiscale approach, suggest a natural way of coupling detailed local models (in the flow domain) with coarser models able to describe the dynamics over a large part or even the whole cardiovascular system at acceptable computational cost. In this study we introduce a new velocity correction scheme to decouple the velocity computation from the pressure one. To evaluate the capability of our new scheme, a comparison between the results obtained with Neumann outflow boundary conditions on the velocity and Dirichlet outflow boundary conditions on the pressure and those obtained using coupling with the lumped parameter model has been performed. Comprehensive studies have been done based on the sensitivity of numerical scheme to the initial conditions, elasticity and number of spectral modes. Improvement of the computational algorithm with stable convergence has been demonstrated for at least moderate Weissenberg number. We comment on mathematical properties of the reduced model, its limitations in yielding realistic and accurate numerical simulations, and its contribution to a better understanding of microvascular blood flow. We discuss the sophistication and reliability of multiscale models for computing correct boundary conditions at the outflow boundaries of a section of the cardiovascular system of interest. In this respect the geometrical multiscale approach can be regarded as a new method for solving a class of biofluids problems, whose application goes significantly beyond the one addressed in this work.

Keywords: geometrical multiscale models, haemorheology model, coupled 2-D navier-stokes 0-D lumped parameter modeling, computational fluid dynamics

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Authors: D. S. Gomes, A. T. Silva

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Analysis of the uncertainty quantification related to nuclear safety margins applied to the nuclear reactor is an important concept to prevent future radioactive accidents. The nuclear fuel performance code may involve the tolerance level determined by traditional deterministic models producing acceptable results at burn cycles under 62 GWd/MTU. The behavior of nuclear fuel can simulate applying a series of material properties under irradiation and physics models to calculate the safety limits. In this study, theoretical predictions of nuclear fuel failure under transient conditions investigate extended radiation cycles at 75 GWd/MTU, considering the behavior of fuel rods in light-water reactors under reactivity accident conditions. The fuel pellet can melt due to the quick increase of reactivity during a transient. Large power excursions in the reactor are the subject of interest bringing to a treatment that is known as the Fuchs-Hansen model. The point kinetic neutron equations show similar characteristics of non-linear differential equations. In this investigation, the multivariate logistic regression is employed to a probabilistic forecast of fuel failure. A comparison of computational simulation and experimental results was acceptable. The experiments carried out use the pre-irradiated fuels rods subjected to a rapid energy pulse which exhibits the same behavior during a nuclear accident. The propagation of uncertainty utilizes the Wilk's formulation. The variables chosen as essential to failure prediction were the fuel burnup, the applied peak power, the pulse width, the oxidation layer thickness, and the cladding type.

Keywords: logistic regression, reactivity-initiated accident, safety margins, uncertainty propagation

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Authors: Temur Chilachava

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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.

Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population

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Authors: Alhaji M. H. Conteh, Xiangbin Yan, Issa Fofana, Brima Gegbe, Tamba I. Isaac

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Rice grain is Sierra Leone’s staple food and the nation imports over 120,000 metric tons annually due to a shortfall in its cultivation. Thus, the insufficient level of the crop's cultivation in Sierra Leone is caused by many problems and this led to the endlessly widening supply and demand for the crop within the country. Consequently, this has instigated the government to spend huge money on the importation of this grain that would have been otherwise cultivated domestically at a cheaper cost. Hence, this research attempts to explore the response of rice supply with respect to its demand in Sierra Leone within the period 1980-2010. The Nerlovian adjustment model to the Sierra Leone rice data set within the period 1980-2010 was used. The estimated trend equations revealed that time had significant effect on output, productivity (yield) and area (acreage) of rice grain within the period 1980-2010 and this occurred generally at the 1% level of significance. The results showed that, almost the entire growth in output had the tendency to increase in the area cultivated to the crop. The time trend variable that was included for government policy intervention showed an insignificant effect on all the variables considered in this research. Therefore, both the short-run and long-run price response was inelastic since all their values were less than one. From the findings above, immediate actions that will lead to productivity growth in rice cultivation are required. To achieve the above, the responsible agencies should provide extension service schemes to farmers as well as motivating them on the adoption of modern rice varieties and technology in their rice cultivation ventures.

Keywords: Nerlovian adjustment model, price elasticities, Sierra Leone, trend equations

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Authors: Zineddine Bouyahiaoui, Rabah Haoui

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The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.

Keywords: blunt body, finite volume, hypersonic flow, viscous flow

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Authors: Fatma Abidi, Taoufik Harizi, Slah Msahli, Faouzi Sakli

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Nine different Tunisian handmade carpets were used for the investigation. The raw material of the carpet pile yarns was wool. The influence of the different structure parameters (linear density and pile height) on the carpet compression was investigated. Carpets were tested under dynamic loading in order to evaluate and observe the thickness loss and carpet behavior under dynamic loads. To determine the loss of pile height under dynamic loading, the pile height carpets were measured. The test method was treated according to the Tunisian standard NT 12.165 (corresponds to the standard ISO 2094). The pile height measurements are taken and recorded at intervals up to 1000 impacts (measures of this study were made after 50, 100, 200, 500, and 1000 impacts). The loss of pile height is calculated using the variation between the initial height and those measured after the number of reported impacts. The experimental results were statistically evaluated using Design Expert Analysis of Variance (ANOVA) software. As regards the deformation, results showed that both of the structure parameters of the pile yarn and the pile height have an influence. The carpet with the higher pile and the less linear density of pile yarn showed the worst performance. Results of a polynomial regression analysis are highlighted. There is a good correlation between the loss of pile height and the impacts number of dynamic loads. These equations are in good agreement with measured data. Because the prediction is reasonably accurate for all samples, these equations can also be taken into account when calculating the theoretical loss of pile height for the considered carpet samples. Statistical evaluations of the experimen¬tal data showed that the pile material and number of impacts have a significant effect on mean thickness and thickness loss variations.

Keywords: Tunisian handmade carpet, loss of pile height, dynamic loads, performance

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Magu Raam Prasaad R., Venkatramani Jagadish

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Recent studies in the literature have shown that randomly fluctuating wind flows can give rise to a distinct regime of pre-flutter oscillations called intermittency. Intermittency is characterized by the presence of sporadic bursts of high amplitude oscillations interspersed amidst low-amplitude aperiodic fluctuations. The focus of this study is on investigating the energy harvesting potential of these intermittent oscillations. Available literature has by and large devoted its attention on extracting energy from flutter oscillations. The possibility of harvesting energy from pre-flutter regimes have remained largely unexplored. However, extracting energy from violent flutter oscillations can be severely detrimental to the structural integrity of airfoil structures. Consequently, investigating the relatively stable pre-flutter responses for energy extraction applications is of practical importance. The present study is devoted towards addressing these concerns. A pitch-plunge airfoil with cubic hardening nonlinearity in the plunge and pitch degree of freedom is considered. The input flow fluctuations are modelled using a sinusoidal term with randomly perturbed frequencies. An electromagnetic coupling is provided to the pitch-plunge equations, such that, energy from the wind induced vibrations of the structural response are extracted. With the mean flow speed as the bifurcation parameter, a fourth order Runge-Kutta based time marching algorithm is used to solve the governing aeroelastic equations with electro-magnetic coupling. The harnessed energy from the intermittency regime is presented and the results are discussed in comparison to that obtained from the flutter regime. The insights from this study could be useful in health monitoring of aeroelastic structures.

Keywords: aeroelasticity, energy harvesting, intermittency, randomly fluctuating flows

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Authors: Samsher Gautam, Apoorva Roy, Bhuvan Aggarwal

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Vapor absorption refrigeration systems can replace vapor compression systems in many applications as they can operate on a low-grade heat source and are environment-friendly. Widely used refrigerants such as CFCs and HFCs cause significant global warming. Natural refrigerants can be an alternative to them, among which carbon dioxide is promising for use in automotive air conditioning systems. Its inherent safety, ability to withstand high pressure and high heat transfer coefficient coupled with easy availability make it a likely choice for refrigerant. Various properties of the ionic liquid [bmim][PF₆], such as non-toxicity, stability over a wide temperature range and ability to dissolve gases like carbon dioxide, make it a suitable absorbent for a vapor absorption refrigeration system. In this paper, an absorption chiller consisting of a generator, condenser, evaporator and absorber was studied at an operating temperature of 70⁰C. A thermodynamic model was set up using the Peng-Robinson equations of state to predict the behavior of the refrigerant and absorbent pair at different points in the system. A MATLAB code was used to obtain the values of enthalpy and entropy at selected points in the system. The exergy destruction in each component and exergetic coefficient of performance (ECOP) of the system were calculated by performing an exergy analysis based on the second law of thermodynamics. Graphs were plotted between varying operating conditions and the ECOP obtained in each case. The effect of every component on the ECOP was examined. The exergetic coefficient of performance was found to be lesser than the coefficient of performance based on the first law of thermodynamics.

Keywords: [bmim][PF₆] as absorbent, carbon dioxide as refrigerant, exergy analysis, Peng-Robinson equations of state, vapor absorption refrigeration

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Authors: Ahmet Koyuncu, Abdullah Berkan Erdogmus, Orkun Dogu, Sinan Uygur

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Thermoelectric modules are integrated to electronic components to keep their temperature in specific values in electronic cooling applications. They can be used in different ambient temperatures. The cold side temperatures of thermoelectric modules depend on their hot side temperatures, operation currents, and heat loads. Performance curves of thermoelectric modules are given at most two different hot surface temperatures in product catalogs. Characteristic properties are required to select appropriate thermoelectric modules in thermal design phase of projects. Generally, manufacturers do not provide characteristic material property values of thermoelectric modules to customers for confidentiality. Common commercial software applied like ANSYS ICEPAK, FloEFD, etc., include thermoelectric modules in their libraries. Therefore, they can be easily used to predict the effect of thermoelectric usage in thermal design. Some software requires only the performance values in different temperatures. However, others like ICEPAK require three temperature-dependent equations for material properties (Seebeck coefficient (α), electrical resistivity (β), and thermal conductivity (γ)). Since the number and the variety of thermoelectric modules are limited in this software, definitions of characteristic material properties of thermoelectric modules could be required. In this manuscript, the method of derivation of characteristic material properties from the datasheet of thermoelectric modules is presented. Material characteristics were estimated from two different performance curves by experimentally and numerically in this study. Numerical calculations are accomplished in ICEPAK by using a thermoelectric module exists in the ICEPAK library. A new experimental setup was established to perform experimental study. Because of similar results of numerical and experimental studies, it can be said that proposed equations are approved. This approximation can be suggested for the analysis includes different type or brand of TEC modules.

Keywords: electrical resistivity, material characteristics, thermal conductivity, thermoelectric coolers, seebeck coefficient

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Authors: Binyam Teferi

Abstract:

Numerical and theoretical analysis of mixed convection flow of magneto- hydrodynamics micropolar fluid with stretching capillary in the presence of thermal radiation, chemical reaction, viscous dissipation, and heat generation/ absorption have been studied. The non-linear partial differential equations of momentum, angular velocity, energy, and concentration are converted into ordinary differential equations using similarity transformations which can be solved numerically. The dimensionless governing equations are solved by using Runge Kutta fourth and fifth order along with the shooting method. The effect of physical parameters viz., micropolar parameter, unsteadiness parameter, thermal buoyancy parameter, concentration buoyancy parameter, Hartmann number, spin gradient viscosity parameter, microinertial density parameter, thermal radiation parameter, Prandtl number, Eckert number, heat generation or absorption parameter, Schmidt number and chemical reaction parameter on flow variables viz., the velocity of the micropolar fluid, microrotation, temperature, and concentration has been analyzed and discussed graphically. MATLAB code is used to analyze numerical and theoretical facts. From the simulation study, it can be concluded that an increment of micropolar parameter, Hartmann number, unsteadiness parameter, thermal and concentration buoyancy parameter results in decrement of velocity flow of micropolar fluid; microrotation of micropolar fluid decreases with an increment of micropolar parameter, unsteadiness parameter, microinertial density parameter, and spin gradient viscosity parameter; temperature profile of micropolar fluid decreases with an increment of thermal radiation parameter, Prandtl number, micropolar parameter, unsteadiness parameter, heat absorption, and viscous dissipation parameter; concentration of micropolar fluid decreases as unsteadiness parameter, Schmidt number and chemical reaction parameter increases. Furthermore, computational values of local skin friction coefficient, local wall coupled coefficient, local Nusselt number, and local Sherwood number for different values of parameters have been investigated. In this paper, the following important results are obtained; An increment of micropolar parameter and Hartmann number results in a decrement of velocity flow of micropolar fluid. Microrotation decreases with an increment of the microinertial density parameter. Temperature decreases with an increasing value of the thermal radiation parameter and viscous dissipation parameter. Concentration decreases as the values of Schmidt number and chemical reaction parameter increases. The coefficient of local skin friction is enhanced with an increase in values of both the unsteadiness parameter and micropolar parameter. Increasing values of unsteadiness parameter and micropolar parameter results in an increment of the local couple stress. An increment of values of unsteadiness parameter and thermal radiation parameter results in an increment of the rate of heat transfer. As the values of Schmidt number and unsteadiness parameter increases, Sherwood number decreases.

Keywords: thermal radiation, chemical reaction, viscous dissipation, heat absorption/ generation, similarity transformation

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Authors: Y. Hamaizi, H. Triki, A. El-Akrmi

Abstract:

In this paper, the reflection spectra, group delay and dispersion of a uniform fiber Bragg grating (FBG) are obtained. FBGs with two types of apodized variations of the refractive index were modeled to show how the side-lobes can be suppressed. Apodization techniques are used to get optimized reflection spectra. The simulation is based on solving coupled mode equations together with the transfer matrix method.

Keywords: fiber bragg gratings, coupled-mode theory, reflectivity, apodization

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Authors: A. Abdul-Ameer

Abstract:

The equations governing the distance, pressure- volume flow relationships for the pipeline transportation of gaseous mixtures, are considered. A derivation based on differential calculus, for an element of this system model, is addressed. Solutions, yielding the input- output response following pressure changes, are reviewed. The technical problems associated with these analytical results are identified. Procedures resolving these difficulties providing thereby an attractive, simple, analysis route are outlined. Computed responses, validating thereby calculated predictions, are presented.

Keywords: pressure, distance, flow, dissipation, models

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Authors: H. Shokouhmand, M. Tajerian

Abstract:

A numerical investigation of laminar forced convection flows through a square cross section micro heat pipe by applying electrohydrodynamic (EHD) field has been studied. In the present study, pentane is selected as working fluid. Temperature and velocity profiles and heat transfer enhancement in the micro heat pipe by using EHD field at the two-dimensional and single phase fluid flow in steady state regime have been numerically calculated. At this model, only Coulomb force is considered. The study has been carried out for the Reynolds number 10 to 100 and EHD force field up to 8 KV. Coupled, non-linear equations governed on the model (continuity, momentum, and energy equations) have been solved simultaneously by CFD numerical methods. Steady state behavior of affecting parameters, e.g. friction factor, average temperature, Nusselt number and heat transfer enhancement criteria, have been evaluated. It has been observed that by increasing Reynolds number, the effect of EHD force became more significant and for smaller Reynolds numbers the rate of heat transfer enhancement criteria is increased. By obtaining and plotting the mentioned parameters, it has been shown that the EHD field enhances the heat transfer process. The numerical results show that by increasing EHD force field the absolute value of Nusselt number and friction factor increases and average temperature of fluid flow decreases. But the increasing rate of Nusselt number is greater than increasing value of friction factor, which makes applying EHD force field for heat transfer enhancement in micro heat pipes acceptable and applicable. The numerical results of model are in good agreement with the experimental results available in the literature.

Keywords: micro heat pipe, electrohydrodynamic force, Nusselt number, average temperature, friction factor

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Authors: Abderrahim Elmoataz

Abstract:

More and more contemporary applications involve data in the form of functions defined on irregular and topologically complicated domains (images, meshs, points clouds, networks, etc). Such data are not organized as familiar digital signals and images sampled on regular lattices. However, they can be conveniently represented as graphs where each vertex represents measured data and each edge represents a relationship (connectivity or certain affinities or interaction) between two vertices. Processing and analyzing these types of data is a major challenge for both image and machine learning communities. Hence, it is very important to transfer to graphs and networks many of the mathematical tools which were initially developed on usual Euclidean spaces and proven to be efficient for many inverse problems and applications dealing with usual image and signal domains. Historically, the main tools for the study of graphs or networks come from combinatorial and graph theory. In recent years there has been an increasing interest in the investigation of one of the major mathematical tools for signal and image analysis, which are Partial Differential Equations (PDEs) variational methods on graphs. The normalized p-laplacian operator has been recently introduced to model a stochastic game called tug-of-war-game with noise. Part interest of this class of operators arises from the fact that it includes, as particular case, the infinity Laplacian, the mean curvature operator and the traditionnal Laplacian operators which was extensiveley used to models and to solve problems in image processing. The purpose of this paper is to introduce and to study a new class of normalized p-Laplacian on graphs. The introduction is based on the extension of p-harmonious function introduced in as discrete approximation for both infinity Laplacian and p-Laplacian equations. Finally, we propose to use these operators as a framework for solving many inverse problems in image processing.

Keywords: normalized p-laplacian, image processing, stochastic game, inverse problems

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Authors: Akhilesh Kumar, Sathyanarayan G., Nirmala S.

Abstract:

An unusual approach is developed to determine the orbit of satellites/space objects. The determination of orbits is considered a boundary value problem and has been solved using the finite difference method (FDM). Only positions of the satellites/space objects are known at two end times taken as boundary conditions. The technique of finite difference has been used to calculate the orbit between end times. In this approach, the governing equation is defined as the satellite's equation of motion with a perturbed acceleration. Using the finite difference method, the governing equations and boundary conditions are discretized. The resulting system of algebraic equations is solved using Tri Diagonal Matrix Algorithm (TDMA) until convergence is achieved. This methodology test and evaluation has been done using all GPS satellite orbits from National Geospatial-Intelligence Agency (NGA) precise product for Doy 125, 2023. Towards this, two hours of twelve sets have been taken into consideration. Only positions at the end times of each twelve sets are considered boundary conditions. This algorithm is applied to all GPS satellites. Results achieved using FDM compared with the results of NGA precise orbits. The maximum RSS error for the position is 0.48 [m] and the velocity is 0.43 [mm/sec]. Also, the present algorithm is applied on the IRNSS satellites for Doy 220, 2023. The maximum RSS error for the position is 0.49 [m], and for velocity is 0.28 [mm/sec]. Next, a simulation has been done for a Highly Elliptical orbit for DOY 63, 2023, for the duration of 6 hours. The RSS of difference in position is 0.92 [m] and velocity is 1.58 [mm/sec] for the orbital speed of more than 5km/sec. Whereas the RSS of difference in position is 0.13 [m] and velocity is 0.12 [mm/sec] for the orbital speed less than 5km/sec. Results show that the newly created method is reliable and accurate. Further applications of the developed methodology include missile and spacecraft targeting, orbit design (mission planning), space rendezvous and interception, space debris correlation, and navigation solutions.

Keywords: finite difference method, grid generation, NavIC system, orbit perturbation

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, heteroclinic orbits, steady state, traveling wave

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