Search results for: energy equation

Authors: Muhammad Umar Khan, Mahesh Kumar, Faraz Neakakhtar

Abstract:

Although industrialization marks to the economy of a country yet it increases the pollution and temperature of the environment. The world is now shifting towards green energy because the utilization of fossil fuels is resulting in global warming. So we need to develop systems that can operate on renewable energy resources and have low heat losses. The combined solar and geothermal multigeneration system can solve this issue. Rather than making rankine cycle purely a solar-driven, heat from solar is used to drive vapour absorption cycle and reheated to generate power using geothermal reservoir. The results are displayed by using Engineering Equation Solver software, where inputs are varied to optimize the energy and exergy efficiencies of the system. The cooling effect is 348.2 KW, while the network output is 23.8 MW and reducing resultant emission of 105553 tons of CO₂ per year. This eco-friendly multigeneration system is capable of eliminating the use of fossil fuels and increasing the geothermal energy efficiency.

Keywords: cooling effect, eco-friendly, green energy, heat loses, multigeneration system, renewable energy, work output

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Shane D. Inder, Mehrdad Khamooshi

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Efficient energy storage is a crucial factor in facilitating the uptake of renewable energy resources. Among the many options available for energy storage systems required to balance imbalanced supply and demand cycles, compressed air energy storage (CAES) is a proven technology in grid-scale applications. This paper reviews the current state of micro scale CAES technology and describes a micro-scale advanced adiabatic CAES (A-CAES) system, where heat generated during compression is stored for use in the discharge phase. It will also describe a thermodynamic model, developed in EES (Engineering Equation Solver) to evaluate the performance and critical parameters of the discharge phase of the proposed system. Three configurations are explained including: single turbine without preheater, two turbines with preheaters, and three turbines with preheaters. It is shown that the micro-scale A-CAES is highly dependent upon key parameters including; regulator pressure, air pressure and volume, thermal energy storage temperature and flow rate and the number of turbines. It was found that a micro-scale AA-CAES, when optimized with an appropriate configuration, could deliver energy input to output efficiency of up to 70%.

Keywords: CAES, adiabatic compressed air energy storage, expansion phase, micro generation, thermodynamic

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Suprit Pradhan, Sushil Pradhan

Abstract:

Photosynthesis is a physiological process where green plants prepare their food from carbon dioxide from the atmosphere and water being absorbed from the soil in presence of sun light and chlorophyll. From this definition it is clear that four reactants (Carbon Dioxide, Water, Light and Chlorophyll) are essential for the process to proceed and the product is a sugar or carbohydrate ultimately stored as starch. The entire process has “Light Reaction” (Photochemical) and “Dark Reaction” (Biochemical). Biochemical reactions are very much complicated being catalysed by various enzymes and the path of carbon is known as “Calvin Cycle” according to the name of its discover. The overall reaction which is now universally accepted can be explained like this. Six molecules of carbon dioxide react with twelve molecules of water in presence of chlorophyll and sun light to give only one molecule of sugar (Carbohydrate) six molecules of water and six molecules of oxygen is being evolved in gaseous form. This is the accepted equation and also chemically balanced. However while teaching the subject the author came across a new balanced equation from among the students who happened to be the daughter of the author. In the new balanced equation in place of twelve water molecules in the reactant side seven molecules can be expressed and accordingly in place of six molecules of water in the product side only one molecule of water is produced. The energetics of the photosynthesis as related to the environment and the newly reported balanced chemical equation has been discussed in detail in the present research paper presentation in this international conference on energy, environmental and chemical engineering.

Keywords: biochemistry, enzyme , isotope, photosynthesis

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Authors: Sh. Heidari, A. J. Andrews, A. Oberoi

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Electrochemical storage of hydrogen in activated carbon electrodes as part of a reversible fuel cell offers a potentially attractive option for storing surplus electrical energy from inherently variable solar and wind energy resources. Such a system – which we have called a proton flow battery – promises to have a roundtrip energy efficiency comparable to lithium ion batteries, while having higher gravimetric and volumetric energy densities. In this paper, a theoretical model is presented of the process of H+ ion (proton) conduction through an acid electrolyte into a highly porous activated carbon electrode where it is neutralised and absorbed on the inner surfaces of pores. A Butler-Volmer type equation relates the rate of adsorption to the potential difference between the activated carbon surface and the electrolyte. This model for the hydrogen storage electrode is then incorporated into a more general computer model based on MATLAB software of the entire electrochemical cell including the oxygen electrode. Hence a theoretical voltage-current curve is generated for given input parameters for a particular activated carbon electrode. It is shown that theoretical VI curves produced by the model can be fitted accurately to experimental data from an actual electrochemical cell with the same characteristics. By obtaining the best-fit values of input parameters, such as the exchange current density and charge transfer coefficient for the hydrogen adsorption reaction, an improved understanding of the adsorption reaction is obtained. This new model will assist in designing improved proton flow batteries for storing solar and wind energy.

Keywords: electrochemical hydrogen storage, proton flow battery, butler-volmer equation, activated carbon

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Authors: Karlijn Van Den Broek, Ian Walker, Christian Klöckner

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Campaigns aiming to induce energy-saving behaviour among householders use a wide range of approaches that address many different drivers thought to underpin this behaviour. However, little research has compared the relative importance of the different factors that influence energy behaviour, meaning campaigns are not informed about where best to focus resources. Therefore, this study applies the Comprehensive Action Determination Model (CADM) to compare the role of normative, intentional, habitual, and situational processes on energy-saving behaviour. An online survey on a sample of households (N = 247) measured the CADM variables and the data was analysed using structural equation modelling. Results showed that situational and habitual processes were best able to account for energy saving behaviour while normative and intentional processes had little predictive power. These findings suggest that policymakers should move away from motivating householders to save energy and should instead focus their efforts on changing energy habits and creating environments that facilitate energy saving behaviour. These findings add to the wider development in social and environmental psychology that emphasizes the importance of extra-personal variables such as the physical environment in shaping behaviour.

Keywords: energy consumption, behavioural modelling, environmental psychology theory, habits, values

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Yuanjun Chen, Yongjiang Shi

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Rising energy prices have drawn a focus to global energy issues, and the severe pollution that has resulted from energy-intensive industrial sectors has yet to be addressed. By combining Energy Efficiency with Industrial Symbiosis, the practices of efficient energy utilization and improvement can be not only enriched at the factory level but also upgraded into “within and/or between firm level”. The academic contribution of this paper provides a conceptual framework of energy management through IS. The management of waste energy within/between firms can contribute to the reduction of energy consumption and provides a solution to the environmental issues.

Keywords: energy efficiency, energy management, industrial symbiosis, energy-intensive industry

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Authors: Sami M. Alshareef

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In the rapidly evolving energy landscape, the integration of renewable energy sources and the electrification of transportation are essential steps toward achieving sustainability goals. However, these advancements introduce new challenges, particularly in maintaining frequency stability due to variable photovoltaic (PV) generation and the growing demand for fast charging stations. The variability of photovoltaic (PV) generation due to weather conditions can disrupt the balance between generation and load, resulting in frequency deviations. To ensure the stability of power systems, it is imperative to develop effective under frequency load-shedding schemes. This research proposal presents an adaptive under-frequency load shedding scheme based on the power swing equation, designed explicitly for the IEEE-9 Bus Test System, that includes PV generation and fast charging stations. This research aims to address these challenges by developing an advanced scheme that dynamically disconnects fast charging stations based on power imbalances. The scheme prioritizes the disconnection of stations near affected areas to expedite system frequency stabilization. To achieve these goals, the research project will leverage the power swing equation, a widely recognized model for analyzing system dynamics during under-frequency events. By utilizing this equation, the proposed scheme will adaptively adjust the load-shedding process in real-time to maintain frequency stability and prevent power blackouts. The research findings will support the transition towards sustainable energy systems by ensuring a reliable and uninterrupted electricity supply while enhancing the resilience and stability of power systems during under-frequency events.

Keywords: load shedding, fast charging stations, pv generation, power system resilience

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Kunpeng Wang, Hongchun, Wu, Liangzhi Cao, Chuanqi Zhao

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The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions which satisfy the diffusion equation at any point in a triangular-z node for each energy group, and nodes were coupled with each other with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form which is the same with the neutron diffusion equation; therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. Four benchmark problems are tested by this method to verify its feasibility, the results show good agreement with the references which demonstrates the efficiency and feasibility of this method.

Keywords: analytic basis function expansion method, arbitrary triangular-z node, adjoint neutron flux, complicated geometry

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Authors: Samuel Ahamefula Mba

Abstract:

Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: Ilija Plecas, Dalibor Arbutina

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

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

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Authors: Bahadır Aydın

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Being one of the most important elements of social evolution, energy has a vital role for a sustainable economy and development. Energy has great importance to level up the welfare. By this importance, countries having rich resources can apply energy as an political instrument. While needs of energy is increasing, sources to respond this need is very limited. Therefore, countries seek for alternative resources to meet their needs. Renewable energy sources have firstly taken into consideration. Being clean and belonging to countries own sources, renewable energy resources have been widely applied during the last decades. However, renewable energy cannot meet all the expectation of energy needs. In this respect, energy efficiency can be seen as an alternative. Energy efficiency can minimize energy consumption without degrading standard of living, lessening quality of products and without increasing energy bills. In this article, energy resources, SWOT analysis of renewable sources, and energy efficiency topics are mainly discussed.

Keywords: energy efficiency, renewable energy, energy regulations, oil, international relations

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: S. Etaig, R. Hasan, N. Perera

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This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.

Keywords: computational fluid dynamics, natural convection, nanofluid and thermal conductivity

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Basant K. Jha, M. L. Kaurangini

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An approximate analytical solution is presented for convective flow in a horizontal channel filled with porous material. The Brinkman-Forchheimer extension of Darcy equation is utilized to model the fluid flow while the energy equation is utilized to model temperature distribution in the channel. The solutions were obtained utilizing the newly suggested technique and compared with those obtained from an implicit finite-difference solution.

Keywords: approximate analytical, convective flow, porous material, Brinkman-Forchiemer

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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