An Integral Model for Natural Convection From an Isothermal Right Circular Cone

2007 ◽  
Author(s):  
Chris J. Kobus ◽  
Yu-Hsien Wu
Keyword(s):  
Boundary Layer Thickness ◽  
Closed Form Solution ◽  
Approximate Model ◽  
Form Solution ◽  
Circular Cone ◽  
Integral Model ◽  
Numerical Techniques ◽  
System Parameters ◽  
Integral Technique ◽  
Individual System

An integral technique approximate model is developed in the current research to predict the convective heat transfer from a right circular cone. Much research has been done regarding stationary circular cones, but all of this prior research was achieved utilizing numerical techniques. As will be shown, the integral model predicts with almost the same precision as the former research. The advantage of the integral technique is its simplicity, culminating in a closed-form solution where the influence of individual system parameters and variables is directly observable. In addition, boundary layer thickness appreas explicitly in the analysis, which again tends to yield more insight at the expense of some accuracy.

Calculation of Discharge Current Waveforms in High Voltage Spark Sources. II. Extensions and Limitations of Closed-Form Solution

1982 ◽  
Vol 36 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Alexander Scheeline ◽  
T. V. Tran
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Closed Form ◽  
High Voltage ◽  
Discharge Current ◽  
Closed Form Solution ◽  
Approximate Model ◽  
Form Solution ◽  
Dynamic Impedance ◽  
Numerical Integration Methods

Simulation of gap breakdown and dynamic impedance effects in high voltage spark sources is performed using an algebraically exact solution to an approximate model of source behavior. The importance of diode shunt capacitance in determining gap breakdown behavior is shown. Limitations in generality and implicit use of numerical methods in dynamic situations lead naturally to consideration of numerical integration methods. Comparisons to hardware sources are made.

Criterion for Preventing Self-Loosening of Preloaded Cap Screws Under Transverse Cyclic Excitation

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xianjie Yang ◽  
Sayed A. Nassar ◽  
Zhijun Wu
Keyword(s):  
Closed Form ◽  
Test Procedure ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Self ◽  
Experimental Setup ◽  
Transverse Loading ◽  
System Parameters ◽  
Transverse Excitation ◽  
Key Variables

In this paper, a novel criterion is developed for preventing the self-loosening of preloaded threaded cap screws under cyclic transverse loading. For a known cyclic excitation, the system parameters are used in the formulation of a closed form solution for the minimum fastener preload required for preventing self-loosening. The effect of several key variables is investigated; this includes bearing and thread friction coefficients, cap screw grip length, thread pitch, material, and cyclic amplitude of the transverse excitation. An experimental setup and test procedure are established. Comparison between the experimental and analytical clamp load variation results shows that the proposed criterion can accurately predict the requirements for preventing self-loosening.

Formulation of a Criterion for Preventing Self-Loosening of Threaded Fasteners Due to Cyclic Transverse Loading

2010 ◽  
Author(s):  
Xianjie Yang ◽  
Sayed Nassar ◽  
Zhijun Wu
Keyword(s):  
Test Procedure ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Self ◽  
Experimental Setup ◽  
Transverse Loading ◽  
System Parameters ◽  
Threaded Fasteners ◽  
Transverse Excitation ◽  
Key Variables

In the paper, a novel criterion is developed for preventing the self-loosening of preloaded threaded fasteners under cyclic transverse loading. For a known cyclic excitation, the system parameters are used in the formulation of a closed form solution for the minimum fastener preload required for preventing self-loosening. The effect of several key variables is investigated; this includes bearing and thread friction coefficients, bolt grip length, thread pitch, material, and the cyclic amplitude of the transverse excitation. An experimental setup and test procedure is established. Comparison between the experimental and analytical clamp load variation results shows that the proposed criterion can accurately predict the requirements for preventing self-loosening.

scholarly journals A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance

2013 ◽  
Vol 49 (3) ◽  
pp. 245-256
Author(s):  
U.C. Singh ◽  
A. Prasad ◽  
A. Kumar
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Freezing Temperature ◽  
Bath Temperature ◽  
Layer Growth ◽  
Form Solution ◽  
Integral Model ◽  
Interface Temperature ◽  
Short Times

In a theoretical analysis, a lump-integral model for freezing and melting of the bath material onto a cylindrical additive having its thermal resistance negligible with respect to that of the bath is developed. It is regulated by independent nondimensional parameters, namely the Stefan number, St the heat capacity ratio, Cr and the modified conduction factor, Cofm. Series solutions associated with short times for time variant growth of the frozen layer and rise in interface temperature between the additive and the frozen layer are obtained. For all times, numerical solutions concerning the frozen layer growth with its melting and increase in the interface temperature are also found. Time for freezing and melting is estimated for different values of Cr, St and Cofm. It is predicted that for lower total time of freezing and melting Cofm<2 or Cr<1 needs to be maintained. When the bath temperature equals the freezing temperature of the bath material, the model is governed by only Cr and St and gives closed-form expressions for the growth of the frozen layer and the interface temperature. For the interface attaining the freezing temperature of the bath material the maximum thickness of the frozen layer becomes ?max-?Cr(Cr+St). The model is validated once it is reduced to a problem of heating of the additive without freezing of the bath material onto the additive. Its closed-form solution is exactly the same as that reported in the literature.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

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