Natural Convection in a Vertical Annulus Containing Water Near the Density Maximum

1987 ◽  
Vol 109 (4) ◽  
pp. 899-905 ◽  
Author(s):  
D. S. Lin ◽  
M. W. Nansteel
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Density Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Flow ◽  
Density Maximum ◽  
Vertical Annulus

Steady natural convection of water near the density extremum in a vertical annulus is studied numerically. Results for flow in annuli with aspect ratio 1≤A≤8 and varying degrees of curvature are given for 103≤Ra≤105. It is shown that both the density distribution parameter R and the annulus curvature K have a strong effect on the steady flow structure and heat transfer in the annulus. A closed-form solution for the vertical flow in a very tall annulus is compared with numerical results for finite-aspect-ratio annuli.

On Murphy’s Integrated Circuit Yield Integral

1995 ◽  
Vol 117 (2) ◽  
pp. 159-164
Author(s):  
John H. Lau
Keyword(s):  
Density Distribution ◽  
Closed Form ◽  
Integrated Circuit ◽  
Defect Density ◽  
Closed Form Solution ◽  
Form Solution ◽  
Simple Equation ◽  
Multichip Module ◽  
Yield Formula ◽  
Circuit Yield

An approximated closed-form integrated circuit (IC) yield formula based on a Gaussian defect density distribution for the compounder in Murphy’s yield integral is presented. Also, a closed-form solution for the average number of faults (AD0) in an IC is obtained for a given IC yield (Y). Furthermore, based on the new IC yield formula a simple equation for determining the number of yielded chips in a wafer is given. Finally, the multichip module yield (Ym) and resultant shipped multichip module yield (Yms) based on the new IC yield formula are provided.

The gravity anomaly of two‐dimensional sources with continuous density distribution and bounded by continuous surfaces

Geophysics ◽  
1992 ◽  
Vol 57 (4) ◽  
pp. 623-628 ◽  
Author(s):  
Tapio Ruotoistenmäki
Keyword(s):  
Density Distribution ◽  
Closed Form ◽  
Gravity Anomaly ◽  
Closed Form Solution ◽  
Vertical Direction ◽  
Form Solution ◽  
Two Dimensional ◽  
Layered Intrusions ◽  
Integration Interval ◽  
Closed Form Solutions

The gravity anomaly of a complicated two‐dimensional (2-D) source having arbitrary surfaces and density varying in either horizontal or vertical direction is calculated using a combination of closed form solutions and numerical integration. The surfaces and density can be defined by continuous or piecewise continuous two‐dimensional functions in the integration interval. For example, the anomalies for intrusions or folded sedimentary units, having an arbitrary density in the horizontal direction and a polynomial density distribution in the vertical direction, can be calculated using surfaces represented by functions of the horizontal dimension. When modeling dipping layered intrusions or sedimentary beds the surfaces are represented by functions of the vertical dimension in which case the density can be an arbitrary function of depth and a polynome function of horizontal coordinate. The accuracy of the method is defined by the user. The method gives simple and general equations to calculate anomalies of complicated sources which have no closed form solution, thus reducing the number of algorithms needed in interpretation programs.

Sign in / Sign up

Export Citation Format

Share Document