On the Analytical Solution of the Multi-Group Neutron Diffusion Kinetic Equation in One-Dimensional Cartesian Geometry by an Integral Transform Technique

2011 ◽  
pp. 59-67 ◽  
Author(s):  
C. Ceolin ◽  
M. T. Vilhena ◽  
B. E. J. Bodmann
Keyword(s):  
Kinetic Equation ◽  
Analytical Solution ◽  
Integral Transform ◽  
Neutron Diffusion ◽  
Diffusion Kinetic ◽  
One Dimensional ◽  
Cartesian Geometry ◽  
Integral Transform Technique

Analytical Solution for Solute Transport in Semi-Infinite Heterogeneous Porous Media

2011 ◽  
Vol 312-315 ◽  
pp. 495-499
Author(s):  
B.Q. Deng ◽  
Y.F. Qiu ◽  
C.N. Kim
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Solute Transport ◽  
Integral Transform ◽  
Integral Transforms ◽  
Heterogeneous Porous Media ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Integral Transform Technique ◽  
Linear Decay

Solute transport in porous media concerns advection, dispersion, sorption, and reaction. Since porous media is commonly heterogeneous, the properties of porous media are spatially and temporally variable. In this paper, one dimensional unsteady solute transport in semi-infinite heterogeneous porous media is investigated. Both linear and nonlinear decay is considered. Analytical solution is obtained for linear decay with spatially and temporally diffusion coefficient and velocity by using generalized integral transform technique. The inverse integral transforms are developed for the problems in semi-infinite space based on some weighted functions. Some examples are given to show the application of the method and analytical solutions.

Analytical Solution of Forced Vibration of a Column Subjected to Conservative and Nonconservative Forces

2001 ◽  
Author(s):  
Zhixiang Xu ◽  
Kunisato Seto ◽  
Hideyuki Tamura
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Integral Transform ◽  
Boundary Value ◽  
Suspension Bridge ◽  
Follower Force ◽  
Analysis Process ◽  
Finite Integral ◽  
Excitation Force ◽  
Integral Transform Technique

Abstract This paper presents analytical results of forced transverse vibration of a column with a mass attached at free-end subjected to a tangential follower force and a transverse distributed excitation force, that is a simplified model of some structures in civil and mechanical engineering, e.g., a column of a suspension bridge, a launched rocket in the atmosphere. Because the tangential follower force is nonconservative, it is very difficult to get the analytical solution of the problem by usually-used analysis methods with which the adjoint boundary value problem can not be directly obtained. However, by applying the finite integral transform technique, we directly obtained the adjoint boundary value problem in the analysis process, and successfully obtained the analytical solution of the column’s vibration excited by the transverse distributed force.

On the solution of the neutron diffusion kinetic equation in planar geometry free of stiffness with convergence analysis

2019 ◽  
Vol 125 ◽  
pp. 272-282
Author(s):  
Fernanda Tumelero ◽  
Bardo Bodmann ◽  
Marco Túllio Vilhena ◽  
Celso M.F. Lapa
Keyword(s):  
Kinetic Equation ◽  
Convergence Analysis ◽  
Planar Geometry ◽  
Neutron Diffusion ◽  
Diffusion Kinetic

scholarly journals Response of Groundwater Levels in a Coastal Aquifer to Tidal Waves and Rainfall Recharge

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 625
Author(s):  
Ping-Cheng Hsieh ◽  
Jing-Lun Huang ◽  
Ming-Chang Wu
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Groundwater Level ◽  
Integral Transform ◽  
Decay Length ◽  
Groundwater Levels ◽  
Tidal Waves ◽  
New Finding ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Groundwater level in coastal aquifers is usually affected by tidal waves and rainfall recharge. Therefore, the objective of this study is to present a mathematical model to account for the effects of tidal waves and rainfall recharge simultaneously. The model is based on the Dupuit–Forchheimer assumptions and is separated into a tidal waves component and rainfall recharge component. A new more general analytical solution for the recharge component is acquired by the generalized integral transform technique. The beach slope, the inclination of an impermeable base of an aquifer, and any randomly distributed rainfall recharge are taken into account in the model. A new finding is that the highest fluctuation in groundwater levels might occur when the range of rainfall recharge is larger than the decay length.

scholarly journals Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique

2021 ◽  
Vol 7 (1) ◽  
pp. 41-55
Author(s):  
Jabbar Hussein Mohmmed ◽  
Mauwafak Ali Tawfik ◽  
Qasim Abbas Atiyah
Keyword(s):  
Analytical Solution ◽  
Temperature Variation ◽  
Integral Transform ◽  
Fluid Velocity ◽  
Harmful Effect ◽  
Fluid System ◽  
Flowing Fluid ◽  
Time Domain Response ◽  
The Stability ◽  
Integral Transform Technique

This study proposes an analytical solution of natural frequencies for an inclined fixed supported Euler-Bernoulli pipe containing the flowing fluid subjected to thermal loads. The integral transform technique is employed to obtain the spatial displacement-time domain response of the pipe-fluid system. Then, a closed-form analytical expression is presented. The effects of various geometric and system parameters on the vibration characteristics of pipe-fluid system with different flow velocities are discussed. The results illustrate that the proposed analytical solution agrees with the solutions achieved in previous works. The proposed model predicts that the pipe loses the stability by divergence with the increasing flow velocity. It is evident that the influences of inclination angle and temperature variation are dramatically increased at a higher aspect ratio. Additionally, it is demonstrated that the temperature variation becomes a more harmful effect than the internal fluid velocity on the stability of the pipe at elevated temperature.

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