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33 articles for “Laplace equation”
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Numerical Formulation of Solidification of Aluminum Casting in 2-D Green Sand Mould
Abstract: Unsteady numerical simulation of steady state and unsteady state conduction heat transfer has been done for solidification of pure Aluminium in green sand mould. As during the solidification heat transfer by conduction will dominate over convection and radiation. Heat conduction equation in two-dimensional Cartesian co-ordinate governs the problem. Convective boundary condition has been considered at the interface of the casting part and mould cavity. Heat conduction equation in unsteady state …
Published in Trends in Mechanical Engineering & Technology · Vol. 5, Issue 3, 2015 · pp. 38–41 Read article
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Effect of Flexibility on Aircraft Wing
Abstract: The shape of the aerofoil determines how the air circulates around it and how much moment and force will be the acting on it. When the body is rigid (fixed) flow around the geometry remains unchanged at particular A.O.A. (angle of attack), but if the body is allowed to be flexible (free) i.e., it can deform its shape, due to which there will be a significant change in the shape …
Published in Journal of Aerospace Engineering & Technology · Vol. 6, Issue 1, 2016 · pp. 45–50 Read article
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Analysis of Hydrodynamic Characteristics of a Squeeze Film in O-Ring Assembly Under the Oscillating Motion
Abstract: In the most of the non-contacting face seals, squeezing occurs in the fluid film between the O-ring surface and the mating surfaces in the gland assembly. Therefore, hydrodynamic characteristics are easily simulated by considering a fluid film between a rubber surface (O-ring surface) and a rigid surface (machined surface). In this paper, effects of surface roughness of rubber block on leakage flow rate and hydrodynamic force developed in fluid film …
Published in Journal of Experimental & Applied Mechanics · Vol. 6, Issue 2, 2015 · pp. 1–12 Read article
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Parametric Analysis of Oscillating Squeeze Film Using a New Dimensionless Parameter
Abstract: A comprehensive mathematical model has been established including a new dimensionless parameter Ω to investigate the effects of surface roughness and permeability of rubber block on leakage flow rate and hydrodynamic force generated in fluid film between annular porous rubber block and oscillating annular rigid block. The modified Reynolds equation, Laplace equation and governing equation for three-parameter viscoelastic model are solved simultaneously to obtain pressure developed in fluid film between …
Published in Journal of Experimental & Applied Mechanics · Vol. 3, Issue 2-3, 2012 · pp. 12–24 Read article
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Electromagnetic Transients in Compensated Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the analysis of the electromagnetic transients developed in an important class of non-uniform high-voltage power lines. It deals particularly with compensated long overhead high- voltage transmission lines composed of several tower spans, which are connected in cascade. The derived mathematical model leads to a system composed of simultaneous partial differential and algebraic equations, which can be solved numerically in terms of parametric functions using the software Mathematica’s …
Published in Trends in Electrical Engineering · Vol. 15, Issue 2, 2025 · pp. 1–9 Read article
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Direct Determination of the Frequency-Dependent Transmission Constants of Non-Uniform Two-Port Networks
Abstract: Due to space constraints and the expansion of electricity networks, transmission lines that cross close to one another are now commonplace. Power networks also commonly install higher operational voltage lines that share transmission corridors with lower voltage lines. Overhead transmission lines are the primary method for transmitting electrical energy across vast distances. This paper presents an efficient and direct technique for identifying the four frequency-dependent ABCD transmission constants of arbitrary …
Published in Journal of Power Electronics and Power Systems · Vol. 14, Issue 3, 2024 · pp. 1–8 Read article
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The Electromagnetic Transients in Compensated High Voltage Power Lines
Abstract: This paper addresses the simulation of the transients developed in high voltage lines, which are initiated by lightning discharges. The analysis allows for compensated and uncompensated lines. Both the individual and simultaneous series inductive and shunt capacitive compensation types can be dealt with. The sizes and locations of the compensating elements are included in the analysis. Numerous studies on the transient concentrated stresses across these elements and the related protection …
Published in International Journal of Electrical Power and Machine Systems · Vol. 1, Issue 2, 2023 · pp. 1–8 Read article
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Time and Frequency Response of Non-uniform Overhead Lines Under Corona
Abstract: This study presents an efficient and direct technique for determining both the time and frequency responses of non-uniform overhead power transmission lines operating under corona conditions. The assumed-line's non-uniformity is due to the conductors’ sag. Expressions will be presented for the location-dependent line surge impedance and the unevenly distributed lines’ electrical parameters. The analysis starts with solving the relevant system of differential and algebraic equations, subject to the boundary conditions. …
Published in International Journal of Electrical Machine Analysis and Design · Vol. 2, Issue 2, 2024 · pp. 25–33 Read article
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A Contribution to the Frequency and Transient Analysis of High Voltage Bushings
Abstract: The paper suggests a method for determining the frequency characteristics and transient response of capacitively graded high voltage bushings. It is based on an s-domain circuit model that describes the grading conducting foils and the insulating layers. In most cases, they are of different axial lengths. A system of simultaneous differential and algebraic equations is derived taking these differences into account. Its closed-form solution, subject to the boundary conditions, can …
Published in Journal of Power Electronics and Power Systems · Vol. 9, Issue 1, 2019 · pp. 15–26 Read article
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The Frequency and Transient Analyses of a High Voltage Bushing/Transformer Cascade
Abstract: This paper investigates the frequency characteristics and electromagnetic transients of a typical system composed of a high voltage bushing and a power transformer connected in cascade. Detailed distributed-parameter Laplace-domain models are adopted for the digital simulations. These parameters include, among others, the transformer winding’s series inductance, its capacitance to ground and the inter-turn capacitances. Moreover, the number, the geometrical data of the capacitively-graded bushing’s conducting foils and the dielectric insulating …
Published in Journal of Power Electronics and Power Systems · Vol. 9, Issue 1, 2019 · pp. 42–53 Read article
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Analyzing The Electromagnetic Transients and Corona Performance of Long Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the simulation of the electromagnetic transients developed in an important class of non-uniform high voltage power lines. The resulting information is of paramount importance for the proper planning, design, operation and protection of electric power networks. It deals particularly with long overhead high voltage transmission lines composed of several tower spans which are connected in cascade. The presented approach considers eventually existing localized corona discharges at some …
Published in International Journal of Electrical and Communication Engineering Technology · Vol. 3, Issue 1, 2025 · pp. 35–44 Read article
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Solidification of Brass Casting in Green Sand Mould: A Numerical and Experimental Study
Abstract: Casting which is also known as founding, is one of the earliest metal shaping methods. It means the pouring of molten metal into the refractory mould then allowing it to solidify. After solidification removing of part from the mould either by breaking the mould or ejecting the mould part. Present study has been focused on solidification of brass in green sand mould formulation. Two-dimensional heat conduction equation in cartesian co-ordinate …
Published in Journal of Mechatronics and Automation · Vol. 2, Issue 3, 2015 · pp. 24–30 Read article
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Computable Extension of New Advanced Fractional Kinetic Equation
Abstract: AbstractFirst, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 26–32 Read article
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Advanced Computable Extension of New Fractional Kinetic Equation
Abstract: AbstractThe aim of this work is to find advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 74–80 Read article
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Uniform Beam Dynamics Under Exponentially Moving Load on Bi-paeametric Foundation with Time-dependent Boundary Effects
Abstract: This study investigates the problem of a uniform elastic beam subjected to exponentially varying moving load with time dependent boundary conditions. A complex structural dynamic problem that has very significant implications for various applications such as railway systems, bridge structures, industrial machinery will be addressed in this research. A damping term is built into the uniform beam model to give a more realistic picture of the structural behaviour, while the …
Published in Journal of Experimental & Applied Mechanics · Vol. 17, Issue 2, 2026 · pp. 53–64 Read article
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An Application of Fractional Calculus in L-R and C-R Circuit
Abstract: In this paper, we proposed a Fractional differential equation for the electrical L-R and C-R Circuit and obtained the solution in the form of Mittag-Leffler function.Keywords: Circuit analysis, L-R and C-R circuit, Fractional differential equation, Riemann-Liouville Fractional derivative, Laplace transform, Inverse Laplace transform.Mathematical Subject Classification: -26A33, 33E12, 44A10Cite this Article: Laxmi Morya, Manoj Sharma, Rajshree Mishra. An Application of Fractional Calculus in L-R andC-R Circuit. Research & Reviews: Discrete Mathematical …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 2, 2020 · pp. 14–17 Read article
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Fractional Homotopy Analysis Transform Method for a Fin Having Temperature Dependent Internal Heat Generation
Abstract: Fractional Homotopy Analysis Transform Method (FHATM) is a new analytical tool for solving homogeneous and non-homogeneous fin equations. FHATM is a novel and innovative modification in Laplace Transform Algorithm (LTA) thus making analysis easier. Non-linear problems are solved by proposed technique without using Adomian and He’s polynomial which is a clear benefit of this new algorithm over decomposition and homotopy perturbation transform methods. This is an elementary technique which gives …
Published in Journal of Experimental & Applied Mechanics · Vol. 10, Issue 1, 2019 · pp. 23–34 Read article
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On The Time-Domain Analysis of the Electromagnetic Transients in High-Voltage Line Towers
Abstract: This paper presents an efficient and direct method for the time-domain transient analysis of high voltage power line towers. A Mathematica-based numerical solution of the governing set of simultaneous partial differential and algebraic equations is proposed. The results of a corresponding computer code are presented and discussed. A comparison with other more sophisticated analytical time-and Laplace-domain approaches is presented. In addition to the possible use of the EMTP transients’ program, …
Published in Journal of Nuclear Engineering & Technology · Vol. 13, Issue 2, 2023 · pp. 12–20 Read article
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Review on Fractional Order Sliding Mode Control of Nonlinear System
Abstract: This paper presents review fractional order sliding mode control of nonlinear system.Sliding mode control (SMC) may be a variable structure control (VSC). It is a nonlinear manipulates approach that approaches in supplied,an impact action andrestricts plant to manage to feature in accordance to some pre-defined ordinary dynamic. This desired dynamic is mentioned as sliding surface. When plant follows sliding surface, it is in sliding mode.Fractional sliding mode control (FSMC) is …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 1, 2021 · pp. 8–16 Read article
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Animated Transient Response of High Voltage Power Line Towers Equipped with Nonlinear Footing Resistances
Abstract: This study focuses, among other objectives, on the use of animation techniques for visualizing the electromagnetic transients in high voltage power line towers. The model includes parameters such as the tower’s footing resistance and its location-dependent surge impedance. It describes the governing algebraic/partial differential equations expressed in terms of the current and voltage distributions as functions of time and location. The transients are assumed initiated by a lightning discharge of …
Published in Trends in Electrical Engineering · Vol. 14, Issue 1, 2024 · pp. 44–52 Read article