Search results for: trend equations

Authors: M. Y. Malika, Farzana, Abdul Rehman

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The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs.

Keywords: boundary layer flow, exponentially stretched surface, Maxwell fluid, numerical solution

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: Sandhyarani Guggilla

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For several reasons no two individuals can be considered identical and hence individualization of therapy is the current trend in treating the patients. Influence of menstrual cycle on the pharmacokinetics of Doxycycline. Twelve healthy female volunteers have been included in the study after obtaining written informed consent. The age ranged from 16 to 25 years. Experimental design: The volunteer selection and recruitment will be carried out after obtaining informed consent from each volunteer. The drug administration will be done to each volunteer at 7 a.m along with a glass of water after an overnight fasting on 3rd, 13th and 23rd day of menstrual cycle. These saliva samples will be stored under frozen conditions until HPLC analysis. Results: In the present study the changes in estrogen levels during ovulatory phase have not shown any influence onAUCo-t of Doxycycline. Only AUCo-t of doxycycline showed an increasing trend with increasing levels of estrogen in ovulatory phase, but not in other phases. Even though the FSH levels differed significantly among volunteers during different phases FSH does not seem to influence the overall pharmacokinetic behavior of Doxycycline during different phases. The present study indicated only the trend that the hormone levels may influence the pharmacokinetic behavior of the Doxycycline. Conclusion: In the present study the changes in hormones have shown an increasing C-max, increasing AUCo-t of Doxycycline pharmacokinetics significantly in follicular phase than ovulatory and luteal phases among volunteers during different phases. In other pharmacokinetic properties like clearance, biological half-life, volume of distribution, mean residence time the change was not significant.

Keywords: menstrual cycle, doxycycline, estrogen, FSH, ovulatory phase

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Authors: Muhammad Omer Farooq Saeed

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The purpose of the proposal is to find out what time actually is! And to understand the natural phenomenon of the behavior of time and light corresponding to the motion of the bodies at relatively high speeds. The utmost concern of the paper is to deal with the possible demerits in the equations of relativity, thereby providing some valuable extensions in those equations and concepts. The idea used develops the most basic conception of the relative motion of the body with respect to space and a real understanding of time and the variation of energy of the body in different frames of reference. The results show the development of a completely new understanding of time, relative motion and energy, along with some extensions in the equations of special relativity most importantly the time dilation and the mass-energy relationship that will explain all frames of a body, all in one go. The proposal also raises serious questions on the validity of the “Principle of Equivalence” on which the General Relativity is based, most importantly a serious case of the bending light that eventually goes against its own governing concepts of space-time being proposed in the theory. The results also predict the existence of a completely new field that explains the fact just how and why bodies acquire energy in space-time. This field explains the production of gravitational waves based on time. All in all, this proposal challenges the formulas and conceptions of Special and General Relativity, respectively.

Keywords: time, relative motion, energy, speed, frame of reference, photon, curvature, space-time, time –differentials

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Pranitha Janapatla, Venkata Suman Gontla

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The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Fehmeada Bibi, Shafqat Nawaz Qaisrani, Masood Akhtar, Zulfiqar Ali

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Population trends learning is an important tool for conservation programs in rare as well as in common species of birds. A study was conducted to assess annual decline in species of birds and to identify the causes of this decline at Taunsa Barrage wildlife Sanctuary, Punjab, Pakistan. Data were collected by direct census method during wintering and breeding periods (2001 to 2002 and 2008 to 2011). The results indicated an increasing trend in 157, whereas a decreasing trend in 14 species of birds. Among the species with declining trend, there was a 92% decrease in White-backed Vulture (Gyps bengalensis), 60% in Greater Painted Snipe (Rostratula benghalensis), 57% in Garganey (Anas querquedula), Pallas’s Fish Eagle and Long-legged Buzzard (Buteo rufinus) 50% each, 41% in Grey Heron (Ardea cinerea), 39% in Little Cormorant (Phalacrocorax niger), 37% in Gadwall (Anas strepera), 33% in Marsh Harrier (Circus aeruginosus), 30% in Black Drongo (Dicrurus macrocercus) and 26% in Red-crested Pochard (Netta rufina) population. Habitat exploitation, hunting and grazing were found the main causes of this decline. In conclusion, conservation and management of the study area is foremost to interests of declining bird population. It is suggested, therefore, to take immediate steps for the protection of the sanctuary to conserve the declining population of birds.

Keywords: population trends, wildlife sanctuary, bird, habitat exploitation

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Ishiyaku Abdulkadir, Satish Kumar J

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Land Productivity is a measure of the greenness of above-ground biomass in health and potential gain and is not related to agricultural productivity. Monitoring land productivity dynamics is essential to identify, especially when and where the trend is characterized degraded for mitigation measures. This research aims to monitor the land productivity trend of Gombe State between 2001 and 2015. QGIS was used to compute NDVI from AVHRR/MODIS datasets in a cloud-based method. The result appears that land area with improving productivity account for 773sq.km with 4.31%, stable productivity traced to 4,195.6 sq.km with 23.40%, stable but stressed productivity represent 18.7sq.km account for 0.10%, early sign of decline productivity occupied 5203.1sq.km with 29%, declining productivity account for 7019.7sq.km, represent 39.2%, water bodies occupied 718.7sq.km traced to 4% of the state’s area.

Keywords: above-ground biomass, dynamics, land productivity, man-environment relationship

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Authors: Roudane Mohamed

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In this study we are interested in improving the efficiency of a steam boiler to 4.5T/h and minimize fume discharge temperature by the addition of a heat exchanger against the current in the energy system, the output of the boiler. The mathematical approach to the problem is based on the use of heat transfer by convection and conduction equations. These equations have been chosen because of their extensive use in a wide range of application. A software and developed for solving the equations governing these phenomena and the estimation of the thermal characteristics of boiler through the study of the thermal characteristics of the heat exchanger by both LMTD and NUT methods. Subsequently, an analysis of the thermal performance of the steam boiler by studying the influence of different operating parameters on heat flux densities, temperatures, exchanged power and performance was carried out. The study showed that the behavior of the boiler is largely influenced. In the first regime (P = 3.5 bar), the boiler efficiency has improved significantly from 93.03 to 99.43 at the rate of 6.47% and 4.5%. For maximum speed, the change is less important, it is of the order of 1.06%. The results obtained in this study of great interest to industrial utilities equipped with smoke tube boilers for the preheating air temperature intervene to calculate the actual temperature of the gas so the heat exchanged will be increased and minimize temperature smoke discharge. On the other hand, this work could be used as a model of computation in the design process.

Keywords: numerical simulation, efficiency, fire tube, heat exchanger, convection and conduction

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Authors: Igor Filikhin, Vladimir M. Suslov, Roman Ya. Kezerashvili, Branislav Vlahivic

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The mass-polarization term of the three-body kinetic energy operator is evaluated for different systems which include two identical particles: A+A+B. The term has to be taken into account for the analysis of AB- and AA-interactions based on experimental data for two- and three-body ground state energies. In this study, we present three-body calculations within the framework of a potential model for the kaonic clusters K−K−p and ppK−, nucleus 3H and hypernucleus 6 ΛΛHe. The systems are well clustering as A+ (A+B) with a ground state energy E2 for the pair A+B. The calculations are performed using the method of the Faddeev equations in configuration space. The phenomenological pair potentials were used. We show a correlation between the mass ratio mA/mB and the value δB of the mass-polarization term. For bosonic-like systems, this value is defined as δB = 2E2 − E3, where E3 is three-body energy when VAA = 0. For the systems including three particles with spin(isospin), the models with average AB-potentials are used. In this case, the Faddeev equations become a scalar one like for the bosonic-like system αΛΛ. We show that the additional energy conected with the mass-polarization term can be decomposite to a sum of the two parts: exchenge related and reduced mass related. The state of the system can be described as the following: the particle A1 is bound within the A + B pair with the energy E2, and the second particle A2 is bound with the pair with the energy E3 − E2. Due to the identity of A particles, the particles A1 and A2 are interchangeable in the pair A + B. We shown that the mass polarization δB correlates with a type of AB potential using the system αΛΛ as an example.

Keywords: three-body systems, mass polarization, Faddeev equations, nuclear interactions

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Ahmad Almajid

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The idea of unifying quantum mechanics with general relativity is still a dream for many researchers, as physics has only two paths, no more. Einstein's path, which is mainly based on particle mechanics, and the path of Paul Dirac and others, which is based on wave mechanics, the incompatibility of the two approaches is due to the radical difference in the initial assumptions and the mathematical nature of each approach. Logical thinking in modern physics leads us to two problems: - In quantum mechanics, despite its success, the problem of measurement and the problem of wave function interpretation is still obscure. - In special relativity, despite the success of the equivalence of rest-mass and energy, but at the speed of light, the fact that the energy becomes infinite is contrary to logic because the speed of light is not infinite, and the mass of the particle is not infinite too. These contradictions arise from the overlap of relativistic and quantum mechanics in the neighborhood of the speed of light, and in order to solve these problems, one must understand well how to move from relativistic mechanics to quantum mechanics, or rather, to unify them in a way different from Dirac's method, in order to go along with God or Nature, since, as Einstein said, "God doesn't play dice." From De Broglie's hypothesis about wave-particle duality, Léon Brillouin's definition of the new proper time was deduced, and thus the quantum Lorentz factor was obtained. Finally, using the Euler-Lagrange equation, we come up with new equations in quantum mechanics. In this paper, the two problems in modern physics mentioned above are solved; it can be said that this new approach to quantum mechanics will enable us to unify it with general relativity quite simply. If the experiments prove the validity of the results of this research, we will be able in the future to transport the matter at speed close to the speed of light. Finally, this research yielded three important results: 1- Lorentz quantum factor. 2- Planck energy is a limited case of Einstein energy. 3- Real quantum mechanics, in which new equations for quantum mechanics match and exceed Dirac's equations, these equations have been reached in a completely different way from Dirac's method. These equations show that quantum mechanics is a limited case of relativistic mechanics. At the Solvay Conference in 1927, the debate about quantum mechanics between Bohr, Einstein, and others reached its climax, while Bohr suggested that if particles are not observed, they are in a probabilistic state, then Einstein said his famous claim ("God does not play dice"). Thus, Einstein was right, especially when he didn't accept the principle of indeterminacy in quantum theory, although experiments support quantum mechanics. However, the results of our research indicate that God really does not play dice; when the electron disappears, it turns into amicable particles or an elastic medium, according to the above obvious equations. Likewise, Bohr was right also, when he indicated that there must be a science like quantum mechanics to monitor and study the motion of subatomic particles, but the picture in front of him was blurry and not clear, so he resorted to the probabilistic interpretation.

Keywords: lorentz quantum factor, new, planck’s energy as a limiting case of einstein’s energy, real quantum mechanics, new equations for quantum mechanics

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

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Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers' equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile

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Authors: M. Ghanbari, S. Hossainpour, G. Rezazadeh

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In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

Keywords: micro-polar theory, Galerkin method, MEMS, micro-fluid

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Authors: Yao Song, Danni Cheng, Jianjun Ren

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Objectives: We aimed to explore the prognostic effects of absolute values and dynamic changes of common hematological indices on oropharynx squamous cell carcinoma (OPSCC) patients treated with radiation. Methods and materials: The absolute values of white blood cell (WBC), absolute neutrophil count (ANC), absolute lymphocyte count (ALC), hemoglobin (Hb), platelet (Plt), albumin (Alb), neutrophil-to-lymphocyte ratio (NLR) and platelet-to-lymphocyte ratio (PLR) at baseline (within 45 days before radiation), 1-, 3-, 6- and 12-months after the start of radiotherapy were retrospectively collected. Locally-estimated smoothing scatterplots were used to describe the smooth trajectory of each index. A mixed-effect model with a random slope was fitted to describe the changing rate and trend of indices over time. Cox proportional hazard analysis was conducted to assess the correlation between hematological indices and treatment outcomes. Results: Of the enrolled 85 OPSCC patients, inflammatory indices, such as WBC and ALC, dropped rapidly during acute treatment and gradually recovered, while NLR and PLR increased at first three months and subsequently declined within 3-12 months. Higher absolute value or increasing trend of nutritional indices (Alb and Hb) was associated with better prognosis (all p<0.05). In contrast, patients with higher absolute value or upward trend of inflammatory indices (WBC, ANC, Plt, PLR and NLR) had worse survival (all p<0.05). Conclusions: The absolute values and dynamic changes of hematological indices were valuable prognostic factors for OPSCC patients who underwent radiotherapy.

Keywords: hematological indices, oropharyngeal cancer, radiotherapy, NLR, PLR

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Authors: Revytia Tanera

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This research is a pilot study to examine the rise of selfie trend in dealing with individual self representation and identity building in social media. The symbolic interactionism theory is used as the concept of the desired self image, and Cooley’s looking glass-self concept is used to analyze the mechanical reflection of ourselves; how do people perform their “digital self” in social media. In-depth interviews were conducted in the study with a non-random sample who owns a smartphone with a front camera feature and are active in social media. This research is trying to find out whether the selfie trend brings any influence on identity building on each individual. Through analysis of interview results, it can be concluded that people take selfie photos in order to express themselves and to boost their confidence. This study suggests a follow up and more in depth analysis on identity and self representation from various age groups.

Keywords: self representation, selfie, social media, symbolic interaction, looking glass-self

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Authors: Rachid Fermous, Rima Mebrek

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Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamic multi-fluid equations, we investigated the expansion of dense plasma. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. It is shown that dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

Keywords: plasma expansion, quantum degeneracy, weakly relativistic, under-dense plasma

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Authors: Adamu S. Salawu, Ibrahim O. Isah

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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: Rodrigo Costa, Thomas Mazzuchi, Shahram Sarkani

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This study analyzes the evolution of Bitcoin Improvement Proposals (BIPs), the self-governing mechanism that enables updates to the Bitcoin protocol. By modeling BIP submission frequencies with a Negative Binomial distribution and detecting change points with the Pelt Rupture model, we identify three distinct intervals of proposal activity, suggesting shifts in development priorities over time. Long-term growth patterns, captured by Gompertz and Weibull models, indicate an S-shaped trend in cumulative BIP counts, pointing toward a maturation phase in Bitcoin’s protocol. Our findings suggest that Bitcoin may be entering a stable stage, with fewer fundamental changes and more incremental enhancements. This trend highlights the need for further research into BIP content and more studies into its dynamics to better understand decentralized protocol governance and maturation.

Keywords: bitcoin improvement proposals, innovation management, change point detection, systems modeling, simulation

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Authors: Minoo Ghasemzadeh, Rouzbeh Riazi, Shidvash Vakilipour, Alireza Ramezani

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In this study, thermo acoustic oscillations of a lean premixed combustor has been investigated, and a mono-dimensional code was developed in this regard. The linearized equations of motion are solved for perturbations with time dependence〖 e〗^iwt. Two flame models were considered in this paper and the effect of mean flow and boundary conditions were also investigated. After manipulation of flame heat release equation together with the equations of flow perturbation within the main components of the combustor model (i.e., plenum/ premixed duct/ and combustion chamber) and by considering proper boundary conditions between the components of model, a system of eight homogeneous equations can be obtained. This simplification, for the main components of the combustor model, is convenient since low frequency acoustic waves are not affected by bends. Moreover, some elements in the combustor are smaller than the wavelength of propagated acoustic perturbations. A convection time is also assumed to characterize the required time for the acoustic velocity fluctuations to travel from the point of injection to the location of flame front in the combustion chamber. The influence of an extended flame model on the acoustic frequencies of combustor was also investigated, assuming the effect of flame speed as a function of equivalence ratio perturbation, on the rate of flame heat release. The abovementioned system of equations has a related eigenvalue equation which has complex roots. The sign of imaginary part of these roots determines whether the disturbances grow or decay and the real part of these roots would give the frequency of the modes. The results show a reasonable agreement between the predicted values of dominant frequencies in the present model and those calculated in previous related studies.

Keywords: combustion instability, dominant frequencies, flame speed, premixed combustor

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Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

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General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

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Authors: Oscar Bautista, Jose Arcos

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In this work, we conduct a theoretical analysis of an oscillatory electroosmotic flow in a parallel-plate microchannel taking into account slippage at the microchannel walls. The governing equations given by the Poisson-Boltzmann (with the Debye-Huckel approximation) and momentum equations are nondimensionalized from which four dimensionless parameters appear; a Reynolds angular number, the ratio between the zeta potentials of the microchannel walls, the electrokinetic parameter and the dimensionless slip length which measures the competition between the Navier slip length and the half height microchannel. The principal results indicate that the slippage has a strong influence on the magnitude of the oscillatory electroosmotic flow increasing the velocity magnitude up to 50% for the numerical values used in this work.

Keywords: electroosmotic flows, oscillatory flow, slippage, microchannel

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Authors: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

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Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

Abstract:

This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Mohammadreza Akbari, Leila Abdollahpour, Sara Akbari, Pooya Soleimani

Abstract:

Transferring thermo at the field of solid materials for instance tube-shaped structures, causing dynamical vibration at them. Majority of thermal and fluid processes are done engineering science at solid materials, for example, thermo-transferred pipes, fluids, chemical and nuclear reactors, include thermal processes, so, they need to consider the moment solid-fundamental structural strength unto these thermal interactions. Fluid and thermo retentive materials in front of external force to it like thermodynamical force, hydrodynamical force and static force continuously according to a function of time vibrated, and this action causes relative displacement of the structural materials elements, as a result, the moment resistance analysis preservation materials in thermal processes, the most important parameters for design are discussed. Including structural substrate holder temperature and fluid of the administrative and industrial center, is a cylindrical tube that for vibration analysis of cylindrical cells with heat and fluid transfer requires the use of vibration differential equations governing the structure of a tubular and thermal differential equations as the vibrating motive force at double-glazed cylinders.

Keywords: heat transfer, elements in cylindrical coordinates, analytical solving the governing equations, structural vibration

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Authors: Giovanni Incerti

Abstract:

In this paper the dynamic behavior of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the mathematical model here proposed also takes into consideration the electrical behaviour of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations of the mathematical model without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the abovementioned software.

Keywords: belt drive, vibrations, startup, DC motor

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Authors: Xuezhang Hou

Abstract:

A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

Procedia PDF Downloads 87