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20 articles for “Differential Equations”
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Effect of the Conductor Sag on the Electromagnetic Transients in High Voltage Lines
Abstract: This paper addresses the effect of the conductor sag on the electromagnetic transients in high voltage lines. A time-domain model for their simulation is presented. It yields a set of simultaneous partial differential equations governing the voltage and current distributions in terms of both the time and location, as well as the corresponding initial and boundary conditions. An efficient Mathematica code is suggested for their numerical solution. The presented model …
Published in International Journal of Analog Integrated Circuits · Vol. 10, Issue 1, 2024 · pp. 8–16 Read article
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Predictive Evaluation of Erema Community Groundwater in Egi for the Purpose of Agricultural Use
Abstract: The investigation in this research is to study the developed sodium absorption ratio model for predicting and monitoring SAR concentration of Erema community groundwater by Ukpaka, 2016 given as, SAR = – + with coefficient of determination of that is modified in this research as + = 0 which is now the modified differential equation of sodium absorption ratio for Erema community it fitness in assessing SAR concentration. Validation of …
Published in International Journal of Water Resources Engineering · Vol. 3, Issue 2, 2017 · pp. 91–96 Read article
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Consequence of Hall and Ion-slip Currents on Boundary Layer Flow with Power-law Deviation Wall Temperature
Abstract: MHD boundary layer flow in permeable medium along vertical plate with power-law deviation wall temperature in a gyratory system for the effects of Hall and ion-slip currents have investigated numerically. The ordinary differential equations are obtained from considered system of partial differential equations using usual transform. The Nachtsheim- Swigert shooting iteration method along with sixth order Runge-Kutta integration technique has employed to solve the non-dimensional system of ordinary differential equations. …
Published in International Journal of Structural Mechanics and Finite Elements · Vol. 6, Issue 2, 2020 · pp. 10–20 Read article
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Analysis Of Non-Uniform Damped Rayleigh Beam Resting on Pasternak Foundation Subjected to Distributed Load With Variable Axial Force
Abstract: In this paper, damped non-uniform Rayleigh beam resting on Pasternak foundation and subjected to distributed load with variable axial force has been investigated. The solution techniques to the governing equation describing the dynamical system are based on Galerkin’s method, Laplace integral transformation in conjunction with convolution theorem. Galerkin’s method is explored to reduce the fourth order non-homogeneous partial differential equation to a second order ordinary differential equation. The resulting equation …
Published in International Journal of Composite Materials and Matrices · Vol. 11, Issue 2, 2025 · pp. 6–16 Read article
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Analysis of Non-Uniform Damped Rayleigh BeamResting on Pasternak Foundation Subjected toDistributed Load with Variable Axial Force
Abstract: In this paper, damped non-uniform Rayleigh beam resting on Pasternak foundation and subjected to distributed load with variable axial force has been investigated. The solution techniques to the governing equation describing the dynamical system are based on Galerkin’s method, Laplace integral transformation in conjunction with convolution theorem. Galerkin’s method is explored to reduce the fourth order non-homogeneous partial differential equation to a second order ordinary differential equation. The resulting equation …
Published in International Journal of Composite Materials and Matrices · Vol. 11, Issue 2, 2025 · pp. 26–35 Read article
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Distribution Parameter Concentration of Alkalinity and Total hardness in Stagnant Water Environment: The Concepts of Oil and Gas Emission Influence
Abstract: Model for predicting the distribution parameter concentration of alkalinity and total hardness in stagnant water environment upon the influence of oil and gasemission was investigated in this paper. The model was formulated from the basic principle of mass and momentum concept which was resolved to obtain an ordinary differential equation. A mathematical tool known as the least square method was applied to resolve the differential equation to obtain quadratic equation …
Published in International Journal of Chemical Separation Technology · Vol. 6, Issue 1, 2020 · pp. 14–22 Read article
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Flexure of Thick Fixed Beams Subjected to Varying Load using Shear Deformation Theory
Abstract: A refined shear deformation theory for flexural analysis of thick beams, considering transverse shear deformation effects, is developed. The number of variables as in the first order shear deformation theory is kept in present theory. The important feature of present theory is that the transverse shear stresses can directly be obtained using constitutive relations. The theory does not demand shear correction factors. The principle of virtual work is used to …
Published in International Journal of Structural Engineering and Analysis · Vol. 2, Issue 1, 2016 · pp. 23–31 Read article
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Study of Heavy Metal ion adsorption from Synthetic Wastewater with the help of biomass and analysis of Mathematical Model
Abstract: The biofilm matrix is a mixture of secreted polymers, metabolites and nutrients ingested, lysis solution products, and even particle debris. This matrix, which is polyanionic by nature, is essential for the activated carbon of metal cations. In this study, the heavy metal adsorption mechanism in biofilms is modelled in one spatial dimension. The numerical method is a free-boundary value issue for nonlinear parabolic and quadratic partial differential equations. Parabolic equations …
Published in International Journal of Polymer Science and Engineering · Vol. 8, Issue 1, 2022 · pp. 45–56 Read article
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Transient Circuit Breaker Stresses in Networks Including Long Overhead Lines with Multiple Tower Spans
Abstract: Abstract: This paper proposes a new technique for analyzing the recovery voltages in circuit breakers of high voltage networks comprising strongly non-uniform lines. As a representative example, the model considers transmission lines comprising multiple cascade-connected tower spans the resulting information is crucial for assessing the proper operation and protection of those networks. The mathematical model is based on a system composed of simultaneous partial differential and algebraic equations. They formulate …
Published in International Journal of Microelectronics and Digital integrated circuits · Vol. 11, Issue 1, 2025 Read article
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Radiative Flow of Energy Consumption with Varying Building Structures
Abstract: The current study deals with Radiative flow of energy consumption with varying building structures solved by boundary value problem. Application of heat transfer takes place in Industrial and Engineering sectors to overcome the difficulties which arise from radiations in building construction. This is shown by taking few unique shapes of buildings as examples which are ellipsoid, isohemi hexagon, isohemisphere and torus ring. The heat transfer taking places of these structural …
Published in International Journal of Applied Nanotechnology · Vol. 8, Issue 1, 2022 · pp. 30–43 Read article
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Application of Three-dimensional Differential Transform Method to Dynamic Vibration Analysis of Rectangular Plate Resting on Elastic Foundation
Abstract: Research on vibration analysis of non-homogenous and varying thickness plate has gained a tremendous increment in recent year due to its vast application in many fields of engineering. This study investigate the dynamic behavior of rectangular plate with varying thickness resting on two-parameter foundation under simply supported free edge condition. The governing differential equation is analyzed using three-dimensional differential transform method. The accuracies of the established solutions are verified by …
Published in International Journal of Structural Mechanics and Finite Elements · Vol. 5, Issue 2, 2019 · pp. 20–35 Read article
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Study and Characterisitics of Different GVF Profile of Rectangular Channel
Abstract: This technical note presents the equation for one-dimensional gradually-varied steady flow profiles with constant discharge, in a rectangular-section prismatic channel of constant roughness and small longitudinal slope. The flow profile differential equation was transformed by means of a polynomial approximation and then, by an algebraic procedure followed by the integration of the equation, the solution was obtained. This solution was applied to a particular case which, through a comparative analysis, …
Published in International Journal of Construction Engineering and Planning · Vol. 3, Issue 1, 2017 · pp. 24–34 Read article
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A Review on Distribution Feeder and Designs
Abstract: An increase in the number of inverter-interfaced photovoltaic (PV) generators on existing distribution feeders affects the design, operation, and control of the distribution systems. The existing distribution system analysis tools are capable of supporting only snapshot and quasi-static analyses. Capturing the dynamic effects of the PV generators during the variation in the distribution system states is necessary when studying the effects of controller bandwidths, multiple voltage correction devices, and anti-islanding. …
Published in International Journal of Electrical Power System and Technology · Vol. 5, Issue 2, 2019 · pp. 13–23 Read article
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Flexural Analysis of Thick Beam Subjected to Sine Load Using Refined Shear Deformation Theory
Abstract: A Hyperbolic Shear Deformation Theory (HPSDT) taking into account transverse shear deformation effects is used for the static flexure analysis of thick isotropic beams. The displacement field of the theory contains two variables. The hyperbolic sine and cosine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the …
Published in International Journal of Structural Engineering and Analysis · Vol. 2, Issue 2, 2016 · pp. 8–19 Read article
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Application of Mathematics to Electric Circuits
Abstract: In this paper, we explain the application of differential equations of first order and first degree, which are helpful to find the rate of change of current flowing in closed circuit with respect to the constraints (resistance, inductance, and capacitance).
Published in International Journal of Analog Integrated Circuits · Vol. 2, Issue 2, 2016 · pp. 1–4 Read article
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Simulation and Design of Closed Loop Controlled Buck - Boost Converter
Abstract: In this paper we propose to model some practical power electronic converters used in the intermediate power conversion process for e.g. wind, solar, and battery system. The small-signal models are derived from the differential equations. Based on the models, simulation and experimental results is be provided to validate the proposed controllers. A mathematical and simulation model of a practical Buck-Boost converter is developed, it will be employed for closed loop …
Published in International Journal of Electrical Power System and Technology · Vol. 7, Issue 1, 2021 · pp. 13–23 Read article
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A Study on Method and Modelling of Structural Analysis and Finite Elements: A Review
Abstract: The finite element method (FEM) or finite element analysis (FEA), is a numerical method usually employed for solving engineering (structural mechanics) and mathematical physics problems. Generally, the analytical solution of these problems require the solution to boundary value problems for partial differential equations. Specimens are usually tested and analysed using finite element method (FEM) for investigating the behaviour of square concrete columns confined by fibre reinforced polymer (FRP) and sheets.
Published in International Journal of Structural Mechanics and Finite Elements · Vol. 3, Issue 2, 2017 · pp. 29–33 Read article
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Analysis of Electronic Circuits Equipped with Free Wheel Diodes
Abstract: This paper addresses the important role of the flyback or freewheel diodes in the protection of electronic circuits as well as their impact on the transient response of these circuits. Sample case studies are presented and analyzed in the time domain using the software Mathematica (Version12.1). Without any loss of generality, a delayed step- voltage source starting at the time point 2 seconds and a single diode are assumed. The …
Published in International Journal of Microelectronics and Digital integrated circuits · Vol. 7, Issue 2, 2021 · pp. 24–32 Read article
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Structural Mechanics: Its Boundary Conditions and Applications
Abstract: Structural mechanics is the study of the calculation of deformations, deflections, internal forces, orstresses (stress equivalents) within structures, either for design or for performance assessment ofalready-existing structures. An area of structural analysis is this. Structural loads, the geometricrepresentation and support circumstances of the structure, as well as the material properties, are allinput variables for structural mechanics analyses. Support responses, strains, and displacementscould all be included in the output numbers. The …
Published in International Journal of Structural Mechanics and Finite Elements · Vol. 8, Issue 1, 2022 · pp. 19–23 Read article
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Thermodynamic Analysis of an Adsorption Refrigeration System
Abstract: In this paper, thermodynamics analysis of an adsorption refrigeration pair (activated carbon and methanol) at adsorption equilibrium conditions has been proposed. Similar analyses have been done by different scientists for different combinations of adsorbent-adsorbate pairs. Adsorption refrigeration processes normally occurs in physical adsorption condition and activated carbon molecules being nonpolar in nature, micropores approach of adsorption (Polanyi’s micropores theory and D-A equation) has been followed here. Analysis of the adsorption …
Published in International journal of Thermodynamics and Chemical Kinetics · Vol. 1, Issue 1, 2015 · pp. 1–9 Read article