The Temperature Distribution Around a Spherical Particle on a Planar Surface

1990 ◽  
Vol 112 (3) ◽  
pp. 561-566 ◽  
Author(s):  
J. Fransaer ◽  
M. De Graef ◽  
J. Roos
Keyword(s):  
Temperature Distribution ◽  
Boundary Value Problems ◽  
Spherical Particle ◽  
Stream Function ◽  
Potential Field ◽  
Flat Surface ◽  
Series Expansions ◽  
Planar Surface ◽  
The Third ◽  
Integral Solutions

The solutions for three related boundary value problems in tangent sphere coordinates are presented; two of these problems involve a conducting and a nonconducting sphere on a conducting flat surface when the field at infinity is linear. The third problem describes the potential field around a conducting sphere on an insulating surface where the field at infinity vanishes. Depending on the nature of the problem, either the Laplace equation or the Stokes stream function formalism is used. The integral solutions are rewritten as series expansions, which are numerically easier to evaluate.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary

Steady Motion of a Thread Over a Rotating Roller

1994 ◽  
Vol 61 (1) ◽  
pp. 16-22 ◽  
Author(s):  
R.-J. Yang
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Steady Motion ◽  
Dynamic Equations ◽  
Initial Value ◽  
Perturbation Result ◽  
The Third

Dynamic equations of steady motion governing the behavior of threads over rotating arbitrary-axisymmetric rollers are derived. Various types of boundary conditions resulting in initial value or boundary value problems are discussed. Analytical solutions for the case of a circular cylinder are found. Two of the integrals obtained are exact. The third one, being a perturbation result, is thus approximate. Comparisons of results for a circular cylinder with those for tapered and parabolic rollers are made.

Temperature Buildup in Bonded Rubber Blocks Due to Hysteresis

1977 ◽  
Vol 50 (1) ◽  
pp. 186-193
Author(s):  
B. P. Holownia
Keyword(s):  
Temperature Distribution ◽  
Cyclic Loading ◽  
Theoretical Analysis ◽  
Poisson’S Ratio ◽  
Experimental Results ◽  
Poisson's Ratio ◽  
The Third ◽  
Significant Figure ◽  
Rubber Block

Abstract The comparison between theoretical and experimental results of the temperature distribution in bonded cyclindrical rubber blocks due to compressive cyclic loading was largely dependent on the value of Poisson's ratio. It was found that, for thin rubber blocks (D/h>6), the third significant figure in the value of v appreciably altered the temperature distribution, while for thick blocks (D/h<4), the same change in v had much smaller effect on the temperature distribution within the rubber block. The theoretical analysis used in the paper can easily be adapted for blocks of different geometries, and hence the temperature distribution within a desirable limit can be achieved by changing the geometry of the rubber block.

Milton on Learning and Wisdom

PMLA ◽  
1949 ◽  
Vol 64 (4) ◽  
pp. 708-723 ◽  
Author(s):  
Irene Samuel
Keyword(s):  
Flat Surface ◽  
Greek Philosophy ◽  
Front View ◽  
Paradise Regained ◽  
Philosophy And Literature ◽  
The Third ◽  
The World ◽  
The Many ◽  
The Rose ◽  
Cut Rose

The longer I live, the more I am satisfied of two things: first, that the truest lives are those that are cut rose-diamond fashion, with many facets answering to the many-planed aspects to the world about them; secondly, that society is always trying in some way or other to grind us down to a single flat surface. … People who honestly mean to be true really contradict themselves much more rarely than those who try to be “consistent.” But a great many things we say can be made to appear contradictory, simply because they are partial views of a truth, and many often look unlike at first, as a front view of a face and its profile often do.—Holmes, The Professor at the Breakfast-TableThe rose-diamond cut of Milton's thought often disconcerts his reader, but perhaps nowhere so completely as in his views on learning. After the high enthusiasm for unrestricted inquiry, after all the “intent study” which he took as his own “portion in life”, in Paradise Lost and Paradise Regained, the ripe products of his learning, he gives to Raphael, Michael, and Jesus speeches that seem a wholesale repudiation of studies of all sorts. The three passages are too well known to quote. In the first (P.L., viii, 66–178)1 Raphael disparages Adam's inquiries about astronomy, but answers them, and then comments, “Solicit not thy thoughts with matters hid.” In the second (P.L., XII, 575–587) Michael commends Adam for the inference he has drawn from his preview of universal history (that “to obey is best, / And love with fear the only God”), and admonishes him, “This having learnt, thou hast attain'd the sum / Of wisdom; hope no higher.” In the third (P.R., iv, 286–364) Jesus spurns Satan's offer of Greek learning, with an analysis of the defects of Greek philosophy and literature and a thrust at learning in general: “Many books / Wise men have said are wearisome.”

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