Computational Modeling of Microchannel Flows on Laboratory Compact Disk (LABCD)

2010 ◽  
Vol 26 (2) ◽  
pp. 239-247
Author(s):  
C.-M. Lin ◽  
T.-C. Lin ◽  
C.-M. Tan ◽  
T.-H. Tsai
Keyword(s):  
Numerical Solutions ◽  
Flow Behavior ◽  
Piecewise Linear ◽  
Linear Method ◽  
Mathematical Expression ◽  
Compact Disk ◽  
Governing Equations ◽  
Transform Method ◽  
The Laplace Transform ◽  
Numerical Program

AbstractThis paper models and analyzes flows in linear and curved microchannels on a rotating Laboratory Compact Disk (LabCD). The effects of centrifugal force are introduced into the governing equations of the microchannel flow to promote the fluidic velocity in the microchannel. The microchannel types on the LabCD must be designed following a process of mathematical identification. A flow model which takes into account the combined effects of viscosity, capillary forces, pressure difference and rotation is developed. A reduction-order technique is applied to obtain linear and nonlinear governing equations for flows in straight and curviform microchannels, respectively. The analytical solutions for the flow in the tubular microchannel are obtained using the Laplace transform method, while the numerical solutions for the curviform microchannel or microchannel with a varying cross-section are obtained using a piecewise linear method. The results show that the analyzed models are easily presented by a mathematical expression for the case of a tubular microchannel and simulated using a numerical program for the case of special microchannels. The modeling presented in this paper enables the performance of LabCD devices to be significantly enhanced by providing insights into the fluid flow behavior in microchannels of varying configurations under different rotational velocities.

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

scholarly journals Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Limei Yan
Keyword(s):  
Laplace Transform ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Space Time ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Promising Tool ◽  
The Laplace Transform ◽  
Fokker Planck Equations ◽  
Fokker Planck

A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.

scholarly journals A Reliable Iterative Transform Method for Solving an Epidemic Model

2021 ◽  
pp. 4839-4846
Author(s):  
Reem Waleed Huisen ◽  
Sinan H. Abd Almjeed ◽  
Areej Salah Mohammed
Keyword(s):  
Epidemic Model ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Absolute Error ◽  
Maximum Error ◽  
Disease Spread ◽  
Approximate Analytic Solution ◽  
Transform Method ◽  
Epidemic Period ◽  
The Laplace Transform

    The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

Fractional modelling arising in unidirectional propagation of long waves in dispersive media

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Sunil Kumar ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Numerical Solutions ◽  
Simple Algorithm ◽  
Nonlinear Problems ◽  
Convergent Series ◽  
Dispersive Media ◽  
Transform Method ◽  
Adomian Polynomials ◽  
Modified Method ◽  
Homotopy Analysis ◽  
The Laplace Transform

AbstractThe purpose of this paper is to propose a modified and simple algorithm for fractional modelling arising in unidirectional propagation of long wave in dispersive media by using the fractional homotopy analysis transform method (FHATM). This modified method is an innovative adjustment in the Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method. This modified method yields an analytical and approximate solution in terms of a rapidly convergent series with easily computable terms. The numerical solutions obtained by the proposed algorithm indicate that the approach is easy to implement and computationally very attractive. Comparing our solution with the existing ones, we note an excellent agreement.

Turbulent Flow of Incompressible Mixtures

1985 ◽  
Vol 107 (2) ◽  
pp. 224-231 ◽  
Author(s):  
M. C. Roco ◽  
C. A. Shook
Keyword(s):  
Turbulent Flow ◽  
Finite Volume ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Local Scale ◽  
Weighted Averaging ◽  
Time Averaging ◽  
Multicomponent Systems ◽  
Governing Equations ◽  
Slurry Flows

The spatial nonuniformities and the interactions between the components determine the flow behavior of multicomponent systems. A space/time averaging approach of the governing equations modeling these factors is presented in this paper. It is defined for a weighted averaging volume whose size is related to the local scale of turbulence. Numerical solutions for concentration and velocity distributions are obtained using integral finite volume techniques. The predictions are comapred with good results to multi-species particle slurry flows in pipelines.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

scholarly journals Analysis of Flow Behavior for Acid Fracturing Wells in Fractured-Vuggy Carbonate Reservoirs

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Mingxian Wang ◽  
Zifei Fan ◽  
Xuyang Dong ◽  
Heng Song ◽  
Wenqi Zhao ◽  
...  
Keyword(s):  
Composite System ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Flow Behavior ◽  
Outer Region ◽  
Carbonate Reservoirs ◽  
Single Fracture ◽  
Specific Flow ◽  
Type Curves ◽  
Acid Fracturing

This study develops a mathematical model for transient flow analysis of acid fracturing wells in fractured-vuggy carbonate reservoirs. This model considers a composite system with the inner region containing finite number of artificial fractures and wormholes and the outer region showing a triple-porosity medium. Both analytical and numerical solutions are derived in this work, and the comparison between two solutions verifies the model accurately. Flow behavior is analyzed thoroughly by examining the standard log-log type curves. Flow in this composite system can be divided into six or eight main flow regimes comprehensively. Three or two characteristic V-shaped segments can be observed on pressure derivative curves. Each V-shaped segment corresponds to a specific flow regime. One or two of the V-shaped segments may be absent in particular cases. Effects of interregional diffusivity ratio and interregional conductivity ratio on transient responses are strong in the early-flow period. The shape and position of type curves are also influenced by interporosity coefficients, storativity ratios, and reservoir radius significantly. Finally, we show the differences between our model and the similar model with single fracture or without acid fracturing and further investigate the pseudo-skin factor caused by acid fracturing.

Sign in / Sign up

Export Citation Format

Share Document