Search results for: mathematical equations

Authors: Anamika Paul, Sudipto Sarkar

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The flow behaviour of non-Newtonian fluid is quite complicated, although both the pseudoplastic (n < 1, n being the power index) and dilatant (n > 1) fluids under this category are used immensely in chemical and process industries. A limited research work is carried out for flow over a bluff body in non-Newtonian flow environment. In the present numerical simulation we control the vortices of a square cylinder by placing an upstream vertical splitter plate for pseudoplastic (n=0.8), Newtonian (n=1) and dilatant (n=1.2) fluids. The position of the upstream plate is also varied to calculate the critical distance between the plate and cylinder, below which the cylinder vortex shedding suppresses. Here the Reynolds number is considered as Re = 150 (Re = U∞a/ν, where U∞ is the free-stream velocity of the flow, a is the side of the cylinder and ν is the maximum value of kinematic viscosity of the fluid), which comes under laminar periodic vortex shedding regime. The vertical plate is having a dimension of 0.5a × 0.05a and it is placed at the cylinder centre-line. Gambit 2.2.30 is used to construct the flow domain and to impose the boundary conditions. In detail, we imposed velocity inlet (u = U∞), pressure outlet (Neumann condition), symmetry (free-slip boundary condition) at upper and lower domain. Wall boundary condition (u = v = 0) is considered both on the cylinder and the splitter plate surfaces. The unsteady 2-D Navier Stokes equations in fully conservative form are then discretized in second-order spatial and first-order temporal form. These discretized equations are then solved by Ansys Fluent 14.5 implementing SIMPLE algorithm written in finite volume method. Here, fine meshing is used surrounding the plate and cylinder. Away from the cylinder, the grids are slowly stretched out in all directions. To get an account of mesh quality, a total of 297 × 208 grid points are used for G/a = 3 (G being the gap between the plate and cylinder) in the streamwise and flow-normal directions respectively after a grid independent study. The computed mean flow quantities obtained from Newtonian flow are agreed well with the available literatures. The results are depicted with the help of instantaneous and time-averaged flow fields. Qualitative and quantitative noteworthy differences are obtained in the flow field with the changes in rheology of fluid. Also, aerodynamic forces and vortex shedding frequencies differ with the gap-ratio and power index of the fluid. We can conclude from the present simulation that fluent is capable to capture the vortex dynamics of unsteady laminar flow regime even in the non-Newtonian flow environment.

Keywords: CFD, critical gap-ratio, splitter plate, wake-wake interactions, dilatant, pseudoplastic

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Authors: Abdullah Al Faruque, Ram Balachandar

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Series of laboratory tests were carried out to study the extent of scour caused by a three-dimensional wall jets exiting from a square cross-section nozzle and into a non-cohesive sand beds. Previous observations have indicated that the effect of the tailwater depth was significant for densimetric Froude number greater than ten. However, the present results indicate that the cut off value could be lower depending on the value of grain size-to-nozzle width ratio. Numbers of equations are drawn out for a better scaling of numerous scour parameters. Also suggested the empirical prediction of scour to predict the scour centre line profile and plan view of scour profile at any particular time.

Keywords: densimetric froude number, jets, nozzle, sand, scour, tailwater, time

Procedia PDF Downloads 435

Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

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Heat transfer from flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube which is varied in range of 100 to 300. In these range of Reynolds number flow is considered to be laminar, unsteady, and incompressible. Equations are solved by using finite volume method. Results show that increasing l/D from 1 to 2 has insignificant effect on heat transfer and Nusselt number of flat tube is slightly lower than circular tube. However, thermal-hydraulic performance of flat tube is up to 2.7 times greater than circular tube.

Keywords: laminar flow, flat tube, convective heat transfer, heat exchanger

Procedia PDF Downloads 440

Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

Procedia PDF Downloads 255

Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

Procedia PDF Downloads 262

Authors: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

Procedia PDF Downloads 389

Authors: A. Bari

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Integer programming is a branch of mathematical programming techniques in operations research in which some or all of the variables are required to be integer valued. Various cuts have been used to solve these problems. We have also developed cuts known as NAZ cut & A-T cut to solve the integer programming problems. These cuts are used to reduce the feasible region and then reaching the optimal solution in minimum number of steps.

Keywords: Integer Programming, NAZ cut, A-T cut, Cutting plane method

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Authors: Sajeda Elbashabsheh, Kamel Al-Khaled

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This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations.

Keywords: approximate solutions, Jaulent-Miodek system, Adomian decomposition method, solitons

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Sahithi Yarlagadda

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The design of antenna is constrained by mathematical and geometrical parameters. Though there are diverse antenna structures with wide range of feeds yet, there are many geometries to be tried, which cannot be customized into predefined computational methods. The antenna design and optimization qualify to apply evolutionary algorithmic approach since the antenna parameters weights dependent on geometric characteristics directly. The evolutionary algorithm can be explained simply for a given quality function to be maximized. We can randomly create a set of candidate solutions, elements of the function's domain, and apply the quality function as an abstract fitness measure. Based on this fitness, some of the better candidates are chosen to seed the next generation by applying recombination and permutation to them. In conventional approach, the quality function is unaltered for any iteration. But the antenna parameters and geometries are wide to fit into single function. So, the weight coefficients are obtained for all possible antenna electrical parameters and geometries; the variation is learnt by mining the data obtained for an optimized algorithm. The weight and covariant coefficients of corresponding parameters are logged for learning and future use as datasets. This paper drafts an approach to obtain the requirements to study and methodize the evolutionary approach to automated antenna design for our past work on Vivaldi antenna as test candidate. The antenna parameters like gain, directivity, etc. are directly caged by geometries, materials, and dimensions. The design equations are to be noted here and valuated for all possible conditions to get maxima and minima for given frequency band. The boundary conditions are thus obtained prior to implementation, easing the optimization. The implementation mainly aimed to study the practical computational, processing, and design complexities that incur while simulations. HFSS is chosen for simulations and results. MATLAB is used to generate the computations, combinations, and data logging. MATLAB is also used to apply machine learning algorithms and plotting the data to design the algorithm. The number of combinations is to be tested manually, so HFSS API is used to call HFSS functions from MATLAB itself. MATLAB parallel processing tool box is used to run multiple simulations in parallel. The aim is to develop an add-in to antenna design software like HFSS, CSTor, a standalone application to optimize pre-identified common parameters of wide range of antennas available. In this paper, we have used MATLAB to calculate Vivaldi antenna parameters like slot line characteristic impedance, impedance of stripline, slot line width, flare aperture size, dielectric and K means, and Hamming window are applied to obtain the best test parameters. HFSS API is used to calculate the radiation, bandwidth, directivity, and efficiency, and data is logged for applying the Evolutionary genetic algorithm in MATLAB. The paper demonstrates the computational weights and Machine Learning approach for automated antenna optimizing for Vivaldi antenna.

Keywords: machine learning, Vivaldi, evolutionary algorithm, genetic algorithm

Procedia PDF Downloads 110

Authors: Qaisar Ali, Waqar A. Khan, Shafiq R. Qureshi

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Heat transfer in Power Law Fluids across cylindrical surfaces has copious engineering applications. These applications comprises of areas such as underwater pollution, bio medical engineering, filtration systems, chemical, petroleum, polymer, food processing, recovery of geothermal energy, crude oil extraction, pharmaceutical and thermal energy storage. The quantum of research work with diversified conditions to study the effects of combined heat transfer and fluid flow across porous media has increased considerably over last few decades. The most non-Newtonian fluids of practical interest are highly viscous and therefore are often processed in the laminar flow regime. Several studies have been performed to investigate the effects of free and mixed convection in Newtonian fluids along vertical and horizontal cylinder embedded in a saturated porous medium, whereas very few analysis have been performed on Power law fluids along wedge. In this study, boundary layer analysis under the effects of radiation-mixed convection in power law fluids along vertical wedge in porous medium have been investigated using an implicit finite difference method (Keller box method). Steady, 2-D laminar flow has been considered under prescribed surface heat flux condition. Darcy, Boussinesq and Roseland approximations are assumed to be valid. Neglecting viscous dissipation effects and the radiate heat flux in the flow direction, the boundary layer equations governing mixed convection flow over a vertical wedge are transformed into dimensionless form. The single mathematical model represents the case for vertical wedge, cone and plate by introducing the geometry parameter. Both similar and Non- similar solutions have been obtained and results for Non similar case have been presented/ plotted. Effects of radiation parameter, variable heat flux parameter, wedge angle parameter ‘m’ and mixed convection parameter have been studied for both Newtonian and Non-Newtonian fluids. The results are also compared with the available data for the analysis of heat transfer in the prescribed range of parameters and found in good agreement. Results for the details of dimensionless local Nusselt number, temperature and velocity fields have also been presented for both Newtonian and Non-Newtonian fluids. Analysis of data revealed that as the radiation parameter or wedge angle is increased, the Nusselt number decreases whereas it increases with increase in the value of heat flux parameter at a given value of mixed convection parameter. Also, it is observed that as viscosity increases, the skin friction co-efficient increases which tends to reduce the velocity. Moreover, pseudo plastic fluids are more heat conductive than Newtonian and dilatant fluids respectively. All fluids behave identically in pure forced convection domain.

Keywords: porous medium, power law fluids, surface heat flux, vertical wedge

Procedia PDF Downloads 312

Authors: Abdelghafour Galadi

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In this paper, accurate power MOSFET models including quasi-saturation effect are presented. These models have no internal node voltages determined by the circuit simulator and use one JFET or one depletion mode MOSFET transistors controlled by an “effective” gate voltage taking into account the quasi-saturation effect. The proposed models achieve accurate simulation results with an average error percentage less than 9%, which is an improvement of 21 percentage points compared to the commonly used standard power MOSFET model. In addition, the models can be integrated in any available commercial circuit simulators by using their analytical equations. A description of the models will be provided along with the parameter extraction procedure.

Keywords: power MOSFET, drift layer, quasi-saturation effect, SPICE model

Procedia PDF Downloads 194

Authors: Fatma Khaled, Khaoula Hidouri, Bechir Chaouachi

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Desalination using solar energy coupled with membrane techniques such as vacuum membrane distillation (VMD) is considered as an interesting alternative for the production of pure water. During this work, a developed model of a polytetrafluoroethylene (PTFE) hollow fiber membrane module of a VMD unit of seawater was carried out. This simulation leads to establishing a comparison between the effects of two different equations of the vaporization latent heat on the membrane surface temperature and on the unit productivity. Besides, in order to study the effect of putting membrane modules in series on the outlet fluid temperature and on the productivity of the process, a simulation was executed.

Keywords: vacuum membrane distillation, membrane module, membrane temperature, productivity

Procedia PDF Downloads 191

Authors: N. Targui, H. Kahalerras

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The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy-Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: double pipe heat exchanger, nanofluids, nanoparticles, porous baffles

Procedia PDF Downloads 243

Authors: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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Authors: Brahim Mahfoud, Ali 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

Procedia PDF Downloads 368

Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

Procedia PDF Downloads 206

Authors: Sanjeet Patra, Soham Roychowdhury

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In recent times, functionally graded dielectric elastomer (FGDE) has gained significant attention within the realm of soft actuation due to its dual capacity to exert highly localized stresses while maintaining its compliant characteristics on application of electro-mechanical loading. Nevertheless, the full potential of dielectric elastomer (DE) has not been fully explored due to their susceptibility to instabilities when subjected to electro-mechanical loads. As a result, study and analysis of such instabilities becomes crucial for the design and realization of dielectric actuators. Prismatic bifurcation is a type of instability that has been recognized in a DE tube. Though several studies have reported on the analysis for prismatic bifurcation in an isotropic DE tube, there is an insufficiency in studies related to prismatic bifurcation of FGDE tubes. Therefore, this paper aims to determine the onset of prismatic bifurcations on an incompressible FGDE tube when subjected to electrical loading across the thickness of the tube and internal pressurization. The analysis has been conducted by imposing two axial boundary conditions on the tube, specifically axially free ends and axially clamped ends. Additionally, the rigidity modulus of the tube has been linearly graded in the direction of thickness where the inner surface of the tube has a lower stiffness than the outer surface. The static equilibrium equations for deformation of the axisymmetric tube are derived and solved using numerical technique. The condition for prismatic bifurcation of the axisymmetric static equilibrium solutions has been obtained by using the linearized incremental constitutive equations. Two modes of bifurcations, corresponding to two different non-circular cross-sectional geometries, have been explored in this study. The outcomes reveal that the FGDE tubes experiences prismatic bifurcation before the Hessian criterion of failure is satisfied. It is observed that the lower mode of bifurcation can be triggered at a lower critical voltage as compared to the higher mode of bifurcation. Furthermore, the tubes with larger stiffness gradient require higher critical voltages for triggering the bifurcation. Moreover, with the increase in stiffness gradient, a linear variation of the critical voltage is observed with the thickness of the tube. It has been found that on applying internal pressure to a tube with low thickness, the tube becomes less susceptible to bifurcations. A thicker tube with axially free end is found to be more stable than the axially clamped end tube at higher mode of bifurcation.

Keywords: critical voltage, functionally graded dielectric elastomer, linearized incremental approach, modulus of rigidity, prismatic bifurcation

Procedia PDF Downloads 77

Authors: V. Benedico, C. Anacleto, A. Bearzi, L. Brice, V. Delahaye

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The aim in present paper is to construct an affordable and reliable commodity prices based on a recalculation of its cost through time which allows visualize the potential risks and thus, take more appropriate decisions regarding forecasts. Here attention has been focused on Levy model, more reliable and realistic than classical random Gaussian one as it takes into consideration observed abrupt jumps in case of sudden price variation. In application to Energy Trading sector where it has never been used before, equations corresponding to Levy model have been written for electricity pricing in European market. Parameters have been set in order to predict and simulate the price and its evolution through time to remarkable accuracy. As predicted by Levy model, the results show significant spikes which reach unconventional levels contrary to currently used Brownian model.

Keywords: commodity pricing, Lévy Model, price spikes, electricity market

Procedia PDF Downloads 429

Authors: Pablo Oteiza, Ricardo Alvarez, Mehrdad Pirnia, Fuat Can

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To effectively combat climate change, many countries around the world have committed to a decarbonisation of their electricity, along with promoting a large-scale integration of renewable energy sources (RES). While this trend represents a unique opportunity to effectively combat climate change, achieving a sound and cost-efficient energy transition towards low-carbon power systems poses significant challenges for the multi-year Transmission Network Expansion Planning (TNEP) problem. The objective of the multi-year TNEP is to determine the necessary network infrastructure to supply the projected demand in a cost-efficient way, considering the evolution of the new generation mix, including the integration of RES. The rapid integration of large-scale RES increases the variability and uncertainty in the power system operation, which in turn increases short-term flexibility requirements. To meet these requirements, flexible generating technologies such as energy storage systems must be considered within the TNEP as well, along with proper models for capturing the operational challenges of future power systems. As a consequence, TNEP formulations are becoming more complex and difficult to solve, especially for its application in realistic-sized power system models. To meet these challenges, there is an increasing need for developing efficient algorithms capable of solving the TNEP problem with reasonable computational time and resources. In this regard, a promising research area is the use of artificial intelligence (AI) techniques for solving large-scale mixed-integer optimization problems, such as the TNEP. In particular, the use of AI along with mathematical optimization strategies based on decomposition has shown great potential. In this context, this paper presents an efficient algorithm for solving the multi-year TNEP problem. The algorithm combines AI techniques with Column Generation, a traditional decomposition-based mathematical optimization method. One of the challenges of using Column Generation for solving the TNEP problem is that the subproblems are of mixed-integer nature, and therefore solving them requires significant amounts of time and resources. Hence, in this proposal we solve a linearly relaxed version of the subproblems, and trained a binary classifier that determines the value of the binary variables, based on the results obtained from the linearized version. A key feature of the proposal is that we integrate the binary classifier into the optimization algorithm in such a way that the optimality of the solution can be guaranteed. The results of a study case based on the HRP 38-bus test system shows that the binary classifier has an accuracy above 97% for estimating the value of the binary variables. Since the linearly relaxed version of the subproblems can be solved with significantly less time than the integer programming counterpart, the integration of the binary classifier into the Column Generation algorithm allowed us to reduce the computational time required for solving the problem by 50%. The final version of this paper will contain a detailed description of the proposed algorithm, the AI-based binary classifier technique and its integration into the CG algorithm. To demonstrate the capabilities of the proposal, we evaluate the algorithm in case studies with different scenarios, as well as in other power system models.

Keywords: integer optimization, machine learning, mathematical decomposition, transmission planning

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

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The analytical bright two soliton solution of the 3-coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: optical soliton, soliton interaction, soliton switching, WDM

Procedia PDF Downloads 505

Authors: Haseen Siddiqui, Sanjay M. Mahajani

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Various important reactions in chemical and metallurgical industries fall in the category of gas-solid reactions. These reactions can be categorized as catalytic and non-catalytic gas-solid reactions. In gas-solid reaction systems, heat and mass transfer limitations put an appreciable influence on the rate of the reaction. The consequences can be unavoidable for overlooking such effects while collecting the reaction rate data for the design of the reactor. Pyrolysis reaction comes in this category that involves the production of gases due to the interaction of heat and solid substance. Pyrolysis is also an important step in the gasification process and therefore, the gasification reactivity majorly influenced by the pyrolysis process that produces the char, as a feed for the gasification process. Therefore, in the present study, a non-isothermal transient 1-D model is developed for a single biomass pellet to investigate the effect of heat and mass transfer limitations on the rate of pyrolysis reaction. The obtained set of partial differential equations are firstly discretized using the concept of ‘method of lines’ to obtain a set of ordinary differential equation with respect to time. These equations are solved, then, using MATLAB ode solver ode15s. The model is capable of incorporating structural changes, porosity variation, variation in various thermal properties and various pellet shapes. The model is used to analyze the effectiveness factor for different values of Lewis number and heat of reaction (G factor). Lewis number includes the effect of thermal conductivity of the solid pellet. Higher the Lewis number, the higher will be the thermal conductivity of the solid. The effectiveness factor was found to be decreasing with decreasing Lewis number due to the fact that smaller Lewis numbers retard the rate of heat transfer inside the pellet owing to a lower rate of pyrolysis reaction. G factor includes the effect of the heat of reaction. Since the pyrolysis reaction is endothermic in nature, the G factor takes negative values. The more the negative value higher will be endothermic nature of the pyrolysis reaction. The effectiveness factor was found to be decreasing with more negative values of the G factor. This behavior can be attributed to the fact that more negative value of G factor would result in more energy consumption by the reaction owing to a larger temperature gradient inside the pellet. Further, the analytical expressions are also derived for gas and solid concentrations and effectiveness factor for two limiting cases of the general model developed. The two limiting cases of the model are categorized as the homogeneous model and unreacted shrinking core model.

Keywords: effectiveness factor, G-factor, homogeneous model, lewis number, non-catalytic, shrinking core model

Procedia PDF Downloads 138

Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi

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This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

Procedia PDF Downloads 482

Authors: Ekaterina Artiukhina, Panagiotis Grammelis

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Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion and co-firing applications. In the course of torrefaction the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The non-stationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: torrefaction, biomass pellets, model, heat, mass transfer

Procedia PDF Downloads 480

Authors: Utsav Bhardwaj, Shyama Prasad Das

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To meet the extensive requirements of thermal management of the circuit card assemblies (CCAs), satellites, PCBs, microprocessors, any other electronic circuitry, pulsating heat pipes (PHPs) have emerged in the recent past as one of the best solutions technically. But industrial application of PHPs is still unexplored up to a large extent due to their poor reliability. There are several systems as well as operational parameters which not only affect the performance of an operating PHP, but also decide whether the PHP can operate sustainably or not. Functioning may completely be halted for some particular combinations of the values of system and operational parameters. Among the system parameters, adiabatic length is one of the important ones. In the present work, a simplest single branch PHP system with an adiabatic section has been considered. It is assumed to have only one vapour bubble and one liquid plug. First, the system has been mathematically modeled using film evaporation/condensation model, followed by the steps of recognition of equilibrium zone, non-dimensionalization and linearization. Then proceeding with a periodical solution of the linearized and reduced differential equations, stability analysis has been performed. Slow and fast variables have been identified, and averaging approach has been used for the slow ones. Ultimately, temporal evolution of the PHP is predicted by numerically solving the averaged equations, to know whether the oscillations are likely to sustain/decay temporally. Stability threshold has also been determined in terms of some non-dimensional numbers formed by different groupings of system and operational parameters. A combined analytical and numerical approach has been used, and it has been found that for each combination of all other parameters, there exists a maximum length of the adiabatic section beyond which the PHP cannot function at all. This length has been called as “Critical Adiabatic Length (L_ac)”. For adiabatic lengths greater than “L_ac”, oscillations are found to be always decaying sooner or later. Dependence of “L_ac” on some other parameters has also been checked and correlated at certain evaporator & condenser section temperatures. “L_ac” has been found to be linearly increasing with increase in evaporator section length (L_e), whereas the condenser section length (L_c) has been found to have almost no effect on it upto a certain limit. But at considerably large condenser section lengths, “L_ac” is expected to decrease with increase in “L_c” due to increased wall friction. Rise in static pressure (p_r) exerted by the working fluid reservoir makes “L_ac” rise exponentially whereas it increases cubically with increase in the inner diameter (d) of PHP. Physics of all such variations has been given a good insight too. Thus, a methodology for quantification of the critical adiabatic length for any possible set of all other parameters of PHP has been established.

Keywords: critical adiabatic length, evaporation/condensation, pulsating heat pipe (PHP), thermal management

Procedia PDF Downloads 226

Authors: Ridhish Kumar, Sudeep Nadukkandy, Anirban Roy

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The development of reverse osmosis happened in 1960. Along the years this technique has been widely accepted all over the world for varied applications ranging from seawater desalination to municipal water treatment. Forward osmosis (FO) is one of the foremost technologies for low energy consuming solutions for water purification. In this study, we have carried out a detailed analysis on selection, design, and pricing for a prototype of potable water system for purifying water in emergency situations. The portable and light purification system is envisaged to be driven by FO. This pouch will help to serve as an emergency water filtration device. The current effort employs a model to understand the interplay of permeability and area on the rate of purification of water from any impure source/brackish water. The draw solution for the FO pouch is considered to be a combination of salt and sugar such that dilution of the same would result in an oral rehydration solution (ORS) which is a boon for dehydrated patients. However, the effort takes an extra step to actually estimate the cost and pricing of designing such a prototype. While the mathematical model yields the best membrane (compositions are taken from literature) combination in terms of permeability and area, the pricing takes into account the feasibility of such a solution to be made available as a retail item. The product is envisaged to be a market competitor for packaged drinking water and ORS combination (costing around $0.5 combined) and thus, to be feasible has to be priced around the same range with greater margins in order to have a better distribution. Thus a proper business plan and production of the same has been formulated in order to be a feasible solution for unprecedented calamities and emergency situations.

Keywords: forward osmosis, water treatment, oral rehydration solution, prototype

Procedia PDF Downloads 184

Authors: Saima Q. Memon, Mazhar I. Khaskheli

Abstract:

The aim of present study was to investigate the efficiency of mulberry leaves for the removal of both arsenic (III) and arsenic (V) from aqueous medium. Batch equilibrium studies were carried out to optimize various parameters such as pH of metal ion solution, volume of sorbate, sorbent doze, and agitation speed and agitation time. Maximum sorption efficiency of mulberry leaves for As (III) and As (V) at optimum conditions were 2818 μg.g-1 and 4930 μg.g-1, respectively. The experimental data was a good fit to Freundlich and D-R adsorption isotherm. Energy of adsorption was found to be in the range of 3-6 KJ/mole suggesting the physical nature of process. Kinetic data followed the first order rate, Morris-Weber equations. Developed method was applied to remove arsenic from real water samples.

Keywords: arsenic removal, mulberry, adsorption isotherms, kinetics of adsorption

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Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wave beam both in elevation and azimuth. In this paper, a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: beamforming, transducer array, BIS-expansion, piezoelectric layer

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Authors: Abolghasem Yousefi-Babadi, Ali Bozorgi-Amiri, Aida Kazempour, Reza Tavakkoli-Moghaddam, Maryam Irani

Abstract:

All over the world, natural disasters (e.g., earthquakes, floods, volcanoes and hurricanes) causes a lot of deaths. Earthquakes are introduced as catastrophic events, which is accident by unusual phenomena leading to much loss around the world. Such could be replaced by disasters or any other synonyms strongly demand great long-term help and relief, which can be hard to be managed. Supplies and facilities are very important challenges after any earthquake which should be prepared for the disaster regions to satisfy the people's demands who are suffering from earthquake. This paper proposed disaster response facility allocation problem for disaster relief operations as a mathematical programming model. Not only damaged people in the earthquake victims, need the consumable commodities (e.g., food and water), but also they need non-consumable commodities (e.g., clothes) to protect themselves. Therefore, it is concluded that paying attention to disaster points and people's demands are very necessary. To deal with this objective, both commodities including consumable and need non-consumable commodities are considered in the presented model. This paper presented the multi-objective multi-period mathematical programming model regarding the minimizing the average of the weighted response times and minimizing the total operational cost and penalty costs of unmet demand and unused commodities simultaneously. Furthermore, a Chebycheff multi-objective solution procedure as a powerful solution algorithm is applied to solve the proposed model. Finally, to illustrate the model applicability, a case study of the Tehran earthquake is studied, also to show model validation a sensitivity analysis is carried out.

Keywords: facility location, multi-objective model, disaster response, commodity

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

Procedia PDF Downloads 352