Search results for: semilinear parabolic equation

Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

Abstract:

For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Reza Mohammadi, Mahdieh Sahebi

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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

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Abdulrahman Abdulrahman

Abstract:

The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

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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 proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

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

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Avadhesh Yadav, Balram Manoj Kumar

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A solar powered air heating system using parabolic trough collector was experimentally investigated. In this experimental setup, the reflected solar radiations were focused on absorber tube which was placed at focal length of the parabolic trough. In this setup, air was used as working fluid which collects the heat from absorber tube. To enhance the performance of parabolic trough, collector with different type of reflectors were used. It was observed for aluminum sheet maximum temperature is 52.3ºC, which 24.22% more than steel sheet as reflector and 8.5% more than aluminum foil as reflector, also efficiency by using Aluminum sheet as reflector compared to steel sheet as reflector is 61.18% more. Efficiency by using aluminum sheet as reflector compared to aluminum foil as reflector is 18.98% more.

Keywords: parabolic trough collector, reflectors, air flow rates, solar power, aluminum sheet

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Authors: Hoang Van Ngoc, Nguyen Thu Huong, Nguyen Quang Bau

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Using the quantum kinetic equation for electrons interacting with acoustic phonon, the density of the constant current associated with the drag of charge carriers in cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field and a laser radiation field is calculated. The density of the constant current is studied as a function of the frequency of electromagnetic wave, as well as the frequency of laser field and the basic elements of quantum wire with a parabolic potential. The analytic expression of the constant current density is numerically evaluated and plotted for a specific quantum wires GaAs/AlGaAs to show the dependence of the constant current density on above parameters. All these results of quantum wire compared with bulk semiconductors and superlattices to show the difference.

Keywords: The photon-drag effect, the constant current density, quantum wire, parabolic potential

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Authors: R. Abd-Rahman, M. M. Isa, H. H. Goh

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A compound parabolic concentrator (CPC) is a well known non-imaging concentrator that will concentrate the solar radiation onto receiver (PV cell). One of disadvantage of CPC is has tall and narrow height compared to its diameter entry aperture area. Therefore, for economic reason, a truncation had been done by removed from the top of the full height CPC. This is also will lead to the decreases of concentration ratio but it will be negligible. In this paper, the flux distribution of untruncated and truncated 2-D hollow compound parabolic trough concentrator (hCPTC) design is presented. The untruncated design has initial height, H=193.4mm with concentration ratio, C_(2-D)=4. This paper presents the optical simulation of compound parabolic trough concentrator using ray-tracing software TracePro. Results showed that, after the truncation, the height of CPC reduced 45% from initial height with the geometrical concentration ratio only decrease 10%. Thus, the cost of reflector and material dielectric usage can be saved especially at manufacturing site.

Keywords: compound parabolic trough concentrator, optical modelling, ray-tracing analysis, improved performance

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Authors: Chuanzhi Chen, Wenjing Yu

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Parabolic cylindrical deployable antenna has the characteristics of wide cutting width, strong directivity, high gain, and easy automatic beam scanning. While, due to its large size, high flexibility, and strong coupling, the deployment process of parabolic cylindrical deployable antenna presents such problems as unsynchronized deployment speed, large local deformation and discontinuous switching of deployment state. A large deployable parabolic cylindrical antenna is taken as the research object, and the problem of unfolding process instability of cylindrical antenna is studied in the paper, which is caused by multiple factors such as multiple closed loops, elastic deformation, motion friction, and gap collision. Firstly, the multi-flexible system dynamics model of large-scale parabolic cylindrical antenna is established to study the influence of friction and elastic deformation on the stability of large multi-closed loop antenna. Secondly, the evaluation method of antenna expansion stability is studied, and the quantitative index of antenna configuration design is proposed to provide a theoretical basis for improving the overall performance of the antenna. Finally, through simulation analysis and experiment, the development dynamics and stability of large-scale parabolic cylindrical antennas are verified by in-depth analysis, and the principles for improving the stability of antenna deployment are summarized.

Keywords: multibody dynamics, expandable parabolic cylindrical antenna, stability, flexible deformation

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Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

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In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: Kobamelo Mashaba

Abstract:

The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Rohit Tripathi, Sumit Tiwari, G. N. Tiwari

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In present study, an approach is adopted where photovoltaic thermal flat plate collector is integrated with compound parabolic concentrator. Analytical expression of temperature dependent electrical efficiency of N number of partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) water collector connected in series has been derived with the help of basic thermal energy balance equations. Analysis has been carried for winter weather condition at Delhi location, India. Energy and exergy performance of N - partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) Water collector system has been compared for two cases: (i) 25% area of water collector covered by PV module, (ii) 75% area of water collector covered by PV module. It is observed that case (i) has been best suited for thermal performance and case (ii) for electrical energy as well as overall exergy.

Keywords: compound parabolic concentrator, energy, photovoltaic thermal, temperature dependent electrical efficiency

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Authors: Alibakhsh Kasaeian, Mohammad Sameti, Zahra Noori, Mona Rastgoo Bahambari

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Nowadays, the parabolic trough solar collector technology has become the most promising large-scale technology among various solar thermal generations. In this paper, a detailed numerical heat transfer model for a parabolic trough collector with nanofluid is presented based on the finite difference approach for which a MATLAB code was developed. The model was used to simulate the performance of a parabolic trough solar collector’s linear receiver, called a heat collector element (HCE). In this model, the heat collector element of the receiver was discretized into several segments in axial directions and energy balances were used for each control volume. All the heat transfer correlations, the thermodynamic equations and the optical properties were considered in details and the set of algebraic equations were solved simultaneously using iterative numerical solutions. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.

Keywords: heat transfer, nanofluid, numerical analysis, trough

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Authors: Clarinda V. Nhangumbe, Ercília Sousa

Abstract:

Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.

Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives

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Authors: I. A. Simsek, S. N. Dogan, A. S. Kipcak, E. Morodor Derun, N. Tugrul

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In this study, the drying characteristics of shrimp are studied by using the traditional drying method of oven. Drying temperatures are selected between 60-80°C. Obtained experimental drying results are applied to eleven mathematical models of Alibas, Aghbashlo et al., Henderson and Pabis, Jena and Das, Lewis, Logaritmic, Midilli and Kucuk, Page, Parabolic, Wang and Singh and Weibull. The best model was selected as parabolic based on the highest coefficient of determination (R²) (0.999990 at 80°C) and the lowest χ² (0.000002 at 80°C), and the lowest root mean square error (RMSE) (0.000976 at 80°C) values are compared to other models. The effective moisture diffusivity (Deff) values were calculated using the Fick’s second law’s cylindrical coordinate approximation and are found between 6.61×10⁻⁸ and 6.66×10⁻⁷ m²/s. The activation energy (Ea) was calculated using modified form of Arrhenius equation and is found as 18.315 kW/kg.

Keywords: activation energy, drying, effective moisture diffusivity, modelling, oven, shrimp

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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

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

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Authors: M. Bidi, H. Akhbari, S. Eslami, A. Bakhtiari

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Due to the high potential of solar energy utilization in Iran, development of related technologies is of great necessity. Linear parabolic collectors are among the most common and most efficient means to harness the solar energy. The main goal of this paper is design and construction of a parabolic trough collector to produce hot water and steam in Tehran. To provide precise and practical plans, 3D models of the collector under consideration were developed using Solidworks software. This collector was designed in a way that the tilt angle can be adjusted manually. To increase concentraion ratio, a small diameter absorber tube is selected and to enhance solar absorbtion, a shape of U-tube is used. One of the outstanding properties of this collector is its simple design and use of low cost metal and plastic materials in its manufacturing procedure. The collector under consideration was installed in Shahid Beheshti University of Tehran and the values of solar irradiation, ambient temperature, wind speed and collector steam production rate were measured in different days and hours of July. Results revealed that a 1×2 m parabolic trough collector located in Tehran is able to produce steam by the rate of 300ml/s under the condition of atmospheric pressure and without using a vacuum cover over the absorber tube.

Keywords: desalination, parabolic trough collector, direct steam production, solar water heater, design and construction

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Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Chen Chuanzhi, Guo Yunyun

Abstract:

The large linear array feeding parabolic cylindrical antenna of the satellite has the ability of large-area line focusing, multi-directional beam clusters simultaneously in a certain azimuth plane and elevation plane, corresponding quickly to different orientations and different directions in a wide frequency range, dual aiming of frequency and direction, and combining space power. Therefore, the large-diameter parabolic cylindrical antenna has become one of the new development directions of spaceborne antennas. Limited by the size of the rocked fairing, the large-diameter spaceborne antenna is required to be small mass and have a deployment function. After being orbited, the antenna can be deployed by expanding and be stabilized. However, few types of structures can be used to construct large cylindrical shell structures in existing structures, which greatly limits the development and application of such antennas. Aiming at high structural efficiency, the geometrical characteristics of parabolic cylinders and mechanism topological mapping law to the expandable truss are studied, and the basic configuration of deployable truss with cylindrical shell is structured. Then a modular truss parabolic cylindrical antenna is designed in this paper. The antenna has the characteristics of stable structure, high precision of reflecting surface formation, controllable motion process, high storage rate, and lightweight, etc. On the basis of the overall configuration comprehensive theory and optimization method, the structural stiffness of the modular truss parabolic cylindrical antenna is improved. And the bearing density and impact resistance of support structure are improved based on the internal tension optimal distribution method of reflector forming. Finally, a truss-type cylindrical deployable support structure with high constriction-deployment ratio, high stiffness, controllable deployment, and low mass is successfully developed, laying the foundation for the application of large-diameter parabolic cylindrical antennas in satellite antennas.

Keywords: linear array feed antenna, truss type, parabolic cylindrical antenna, spaceborne antenna

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Authors: Defne Akay, Bekir S. Kandemir

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In this paper, we investigate the low-lying energy levels of the two-dimensional parabolic graphene quantum dots (GQDs) in the presence of topological defects with long range Coulomb impurity and subjected to an external uniform magnetic field. The low-lying energy levels of the system are obtained within the framework of the perturbation theory. We theoretically demonstrate that a valley splitting can be controlled by geometrical parameters of the graphene quantum dots and/or by tuning a uniform magnetic field, as well as topological defects. It is found that, for parabolic graphene dots, the valley splitting occurs due to the introduction of spatial confinement. The corresponding splitting is enhanced by the introduction of a uniform magnetic field and it increases by increasing the angle of the cone in subcritical regime.

Keywords: coulomb impurity, graphene cones, graphene quantum dots, topological defects

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: A. A. A. Aboalnour, Ahmed M. Amasaib, Mohammed-Almujtaba A. Mohammed-Farah, Abdelhakam, A. Noreldien

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This paper presents a design and study of Parabolic Trough Solar Collector (PTC). Mathematical models were used in this work to find the direct and reflected solar radiation from the air layer on the surface of the earth per hour based on the total daily solar radiation on a horizontal surface. Also mathematical models had been used to calculate the radiation of the tilted surfaces. Most of the ingredients used in this project as previews data required on several solar energy applications, thermal simulation, and solar power systems. In addition, mathematical models had been used to study the flow of the fluid inside the tube (receiver), and study the effect of direct and reflected solar radiation on the pressure, temperature, speed, kinetic energy and forces of fluid inside the tube. Finally, the mathematical models had been used to study the (PTC) performances and estimate its thermal efficiency.

Keywords: CFD, experimental, mathematical models, parabolic trough, radiation

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Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Jian-Jun Shu

Abstract:

It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Atwari Rawani, Hari Narayan Singh, K. D. P. Singh

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In this paper, an analytical investigation of the enhancement of thermal performance of parabolic trough collector (PTC) with twisted tape inserts in the absorber tube is being reported. A comparative study between the absorber with various types of twisted tape inserts and plain tube collector has been performed in turbulent flows conditions. The parametric studies were conducted to investigate the effects of system and operating parameters on the performance of the collector. The parameters such as heat gain, overall heat loss coefficient, air rise temperature and efficiency are used to analyze the relative performance of PTC. The results show that parabolic through collector with serrated twisted tape insert shows the best performance under same set of conditions under range of parameters investigated. Results reveal that for serrated twisted tape with x=1, Nusselt number/heat transfer coefficient is found to be 4.38 and 3.51 times over plain absorber of PTC at mass flow rate of 0.06 kg/s and 0.16 kg/s respectively; while corresponding enhancement in thermal efficiency is 15.7% and 5.41% respectively.

Keywords: efficiency, heat transfer, twisted tape ratio, turbulent flow

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Authors: Olukunle C. Olawole, Dilip K. De, Moses Emetere, Omoje Maxwell

Abstract:

Graphene can stand very high temperature up to 4500 K in vacuum and has potential for application in thermionic energy converter. In this paper, we discuss the application of energy dynamics principles and the modified Richardson-Dushman Equation, to estimate the efficiency of solar power conversion to electrical power by a solar thermionic energy converter (STEC) containing emitter made of graphene. We present detailed simulation of power output for different solar insolation, diameter of parabolic concentrator, area of the graphene emitter (same as that of the collector), temperature of the collector, physical dimensions of the emitter-collector etc. After discussing possible methods of reduction or elimination of space charge problem using magnetic field and gate, we finally discuss relative advantages of using emitters made of graphene, carbon nanotube and metals respectively in a STEC.

Keywords: graphene, high temperature, modified Richardson-Dushman equation, solar thermionic energy converter

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Authors: Y. Pala, M. O. Ertas

Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

Abstract:

A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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