AN APPROXIMATE SOLUTION PROCEDURE FOR “OPEN” MOMENT EVOLUTION EQUATIONS

1992 ◽  
pp. 542-544
Keyword(s):  
Approximate Solution ◽  
Evolution Equations ◽  
Solution Procedure

Thermal Analysis of the Hot Dip-Coating Process

1993 ◽  
Vol 115 (2) ◽  
pp. 453-460 ◽  
Author(s):  
Hui Zhang ◽  
M. Karim Moallemi ◽  
Sunil Kumar
Keyword(s):  
Experimental Data ◽  
Thermal Analysis ◽  
Approximate Solution ◽  
Dip Coating ◽  
Solution Procedure ◽  
Heat Diffusion ◽  
Coating Process ◽  
Parametric Effects ◽  
Simplifying Assumptions ◽  
Axial Heat

In this study a thermal analysis is performed on the hot dip-coating process where solidification of metal occurs on a bar moving through a finite molten bath. A continuum model is considered that accounts for important transport mechanisms such as axial heat diffusion, buoyancy, and shear-induced melt motion in the bath. A numerical solution procedure is developed, and its predictions are compared with those of an analytical approximate solution, as well as available experimental data. The predictions of the numerical scheme are in good agreement with the experimental data. The results of the approximate solution, however, exhibit significant disagreement with the data, which is attributed to the simplifying assumptions used in its development. Parametric effects of the bath geometry, and initial and boundary temperatures and solid velocity, as characterized by the Reynolds number, Grashof number, and Stefan numbers, are presented.

An Efficient Technique for the Approximate Analysis of Vibro-Impact

1983 ◽  
Vol 105 (3) ◽  
pp. 332-336 ◽  
Author(s):  
R. K. Miller ◽  
B. Fatemi
Keyword(s):  
Approximate Solution ◽  
Substantial Reduction ◽  
Solution Procedure ◽  
Computational Effort ◽  
Mean Square ◽  
Base Excitation ◽  
Weighted Mean ◽  
Linearization Technique ◽  
Adjacent Structures ◽  
Impact Problems

An approximate solution procedure is presented for a class of steady vibro-impact problems consisting of adjacent structures separated by a gap and subjected to harmonic base excitation. The procedure is based on a weighted mean-square linearization technique, and is capable of substantial reduction of computational effort over that required for an exact numerical simulation. As an illustration of the general approach, a detailed analysis of an example problem is presented, together with a comparison of results with an exact solution. It is shown for the example problem that the level of accuracy of the approximate solution is adequate for many applications.

Approximate Solution Procedure for Dynamic Traffic Assignment

2013 ◽  
Vol 139 (8) ◽  
pp. 822-832 ◽  
Author(s):  
Anna C. Y. Li ◽  
Linda Nozick ◽  
Rachel Davidson ◽  
Nathanael Brown ◽  
Dean A. Jones ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Traffic Assignment ◽  
Dynamic Traffic Assignment ◽  
Solution Procedure ◽  
Dynamic Traffic

Frequency–Amplitude Relationship of Coupled Anharmonic Oscillators

2011 ◽  
Vol 105-107 ◽  
pp. 271-274
Author(s):  
Zheng Biao Li ◽  
Wei Hong Zhu
Keyword(s):  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Parameter Method ◽  
Anharmonic Oscillators ◽  
First Order ◽  
Linear And Nonlinear ◽  
Relationship Of

The frequency–amplitude relationship of coupled anharmonic oscillators is an important problem. Many powerful methods for solving this problem have been proposed. He’s parameter-expanding method is an important one. It holds the advantages of modified Lindstedt–Poincare parameter method and bookkeeping parameter method. The first iteration is enough. It is very effective and convenient and quite accurate to both linear and nonlinear problems. In this paper, He’s parameter-expanding method is applied to coupled anharmonic oscillators. The frequency-amplitude relationship and the first-order approximate solution of the oscillators are obtained respectively. The solution procedure shows that the method is very powerful and convenient to nonlinear oscillator. This method has great potential and can be applied to other types of nonlinear oscillator problems.

scholarly journals Double trials method for nonlinear problems arising in heat transfer

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 153-155 ◽  
Author(s):  
Chun-Hui He ◽  
Ji-Huan He
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Differential Equations ◽  
Unknown Parameter ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Second Century ◽  
Algebraic Equations ◽  
False Position

According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.

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