Papers by Keyword: Laplace Transform

Abstract: The time-dependent hydromagnetic boundary layer flow across a vertical surface with internal heat regeneration in porous media is investigated. The flow problem has been modelled mathematically in partial differential equations along with appropriate defined boundary conditions. These equations were expressed in dimensionless form using suitable similarity variables. The resulting dimensionless equations along with the conditions defined at the boundaries are solved by means of the Laplace transform methods. Results of the study are graphically illustrated for various quantities of practical importance. It was concluded that time positively influence the flow as a reduced skin friction coefficient was observed. Furthermore, the magnetic parameter, the radiation parameter, the heat absorption parameter and the permeability of the porous media can be used to influence the characteristics of a flow in porous media.

Abstract: In this paper, we will compare the methods of solving with explicit or implicit finite difference of the partial differential equations that define the mechanical models of hydrodynamics movements, thermodynamics or those that define the vibration movements with the ones that use integral transforms. By applying the Laplace and Fourier transforms, finite in sine or cosine, depending on the boundary conditions of the real physical problem, it leads to the algebraic approach of the problem, which reduces the difficulty of solving partial differential equations. The errors obtained for the solution of partial differential equations using different methods are within the standard norms. However, in terms of calculus precision, the use of integral transforms is more advantageous.

Abstract: This paper presents results of the test of methods for numerical inversion of the Laplace Transform for solving the one-dimensional advection-diffusion equation, which describes solute transport processes, focusing on the contaminant transport in a porous medium. The performance of Stehfest and Power Series Expansion methods is analyzed, for diffusion-dominated and advection-dominated transport problems under linear flow condition. Numerical results are compared to the analytical solution by means of the absolute error. Based on these results, we concluded that both methods, Stehfest and Power Series Expansion, are recommended only for diffusion-dominated cases.

Abstract: An analytical study of transient natural convective flow of a viscous incompressible optically thick radiating fluid past a moving vertical plate with ramped heat and mass fluxes in the presence of thermal radiation is performed. Exact solution of the governing equations under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The expressions for the shear stress and at the plate temperature and concentration are also derived. The velocity profiles, temperature and species concentration are studied as functions of different physical parameters like radiation parameter, thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number and time. The physical aspects of the problem are discussed.

Abstract: Electrical discharge machining (EDM) is one of the earliest non-traditional machining processes and controlled process where pulsed electrical discharge is used to erode metal in a workpiece. EDM pulsed power generator applies voltage pulse discharge occurs in a small gap between the work piece and the electrode and removes the unwanted material from the parent metal through melting and vaporization. The essential requirement for EDM system is to obtain the output waveform similar to the ideal EDM waveform. This paper seeks to discuss on the design and simulation based on RC (resistance-capacitance) power generator circuit. Based on the findings of the study, from the equation gained, the simulation is constructed through using electrical model in Matlab Simulink software and circuit analysis in Lapels transform in EDM system process. Also this procedure simulated in Matlab software.

Abstract: One of the latest non-traditional machining processes and controlled process is presented as Electrical Discharge Machining (EDM) that the pulsed electrical discharge is used to erode metal in a work piece. The voltage pulse discharge occurs when EDM pulsed power generator is applied on a workpiece. The discharge happens in a small gap between the work piece and the electrode. The important function of EDM is to obtain the output waveform parallel with the ideal EDM waveform. Additionally, the EDM design is according to the transistor kind pulse power generator circuit. The present paper seeks to discuss on the current modeling and voltage gap waveform intended for the system in EDM process. Based on the derived equation, the simulation is done using electrical model in Matlab Simulink software and circuit analysis in Lapels transform in EDM process.

Abstract: This paper described the mathematical modeling of chrome shavings drying by performing a microscopic balance for water content to describe the unidimensional transfer of water within the solid at a certain temperature. The deterministic model was solved using Laplace transformation and separation of variables methods in order to determine the average free moisture content at different intervals of time during the drying period. Agreement was observed between both, experimental and modeling data. The effective diffusion coefficient of water molecules during the drying of chrome shavings in a tunnel dryer was determined to be 5.8 x 10^-6 m²/h.

Abstract: In the full power wind power system, the cage induction wind generator-rectifier system can be regarded as a independent part if the DC voltage could be always controlled constant by inverter part. The prospective AC voltage and frequency of induction generator is dependent on the specific speed and input power, which is obtained by use of SPWM. All rectifier switching state and the alternating moments can be calculated by switching function given by SPWM control. This paper focuses on how to use analytical methods to calculate the process of alternately switching the state of the system. Furthermore, the dynamic mathematical model of induction generator is studied and derived under different states, which is suitable for analytical method on base of Laplace transform.

Abstract: The authors consider the problem of numerical inversion of Laplace transform using its values of the Laplace-image defined on the positive real half-axis of the complex plane. The main distinction of the proposed path associated with the method of forming these values. This path is based on a special case of the direct formula of the Laplace transform, when complex variable degenerates into a real variable. As a result, they continue getting image-function, but these functions have an important feature for numerical problems – they have a real argument. The presence of a continuous-time function allows implementing her sampling more reasonably, for example, taking into account the properties of the differentiating features. One more attractive possibility – generalization sampling, conversion and interpolation algorithms for transfer functions with irrational and transcendental expressions. The paper presents the necessary information about obtaining of real functions images and their usage in problems of the Laplace transform inversion. The method is based on the representation of function originals as a segment of series on the exponential Chebyshev polynomials. An example is given.

Abstract: The velocity field and the associated tangential tension corresponding to the flow of the viscoelastic fluid over an infinite rigid plate are determined in this paper. The characteristic of the non-Newtonian viscoelastic fluid flow is analyzed using the Stehfest method of the numerical inversion of Laplace transform. It indicates that the flow of the viscoelastic fluid is very sensitive to the material constants. Finally, some comparative diagrams concerning the velocity and tangential tension profiles are presented.