scholarly journals New developments and explicit results for the thermal constriction resistance of a circular contact under mixed axisymmetric boundary conditions

2021 ◽  
Vol 163 ◽  
pp. 106806
Author(s):  
Najib Laraqi ◽  
Taïssir Kasraoui ◽  
Jean-Gabriel Bauzin
Keyword(s):  
Boundary Conditions ◽  
New Developments ◽  
Constriction Resistance ◽  
Circular Contact

Constriction Resistance in Rectangular Bodies

1991 ◽  
Vol 113 (4) ◽  
pp. 392-396 ◽  
Author(s):  
Matthew John M. Krane
Keyword(s):  
Boundary Conditions ◽  
Constant Temperature ◽  
Three Dimensional ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Flux Lines ◽  
Constriction Resistance ◽  
Opposite Face ◽  
Overall Resistance

Steady conduction equations are solved for two and three-dimensional rectangular bodies with a constant temperature sink and heat applied over a portion of the opposite face. The solutions, with previously published solutions to similar bodies with convective boundary conditions at the sink, are presented as dimensionless resistances in such a way that a designer can easily use them to predict the effect of constriction of flux lines on the overall resistance of the bodies.

Thermal constriction resistance of a contact on a circular cylinder with mixed convective boundaries

1988 ◽  
Vol 420 (1859) ◽  
pp. 323-354 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Thermal Contact ◽  
Circuit Board ◽  
Asperity Contact ◽  
Convective Boundary ◽  
Aspect Ratios ◽  
Constriction Resistance ◽  
Plane Face ◽  
Wide Range

Numerous important heat-transfer problems make use of a cylinder as the basic element: these include the conduction of heat between two bodies in asperity contact; the heat transfer in a convectively cooled printed circuit board; the thermal analysis of fin coolers. This paper presents a unified treatment of the steady-state axisymmetric temperature distribution in a cylinder of radius b and height h . Thermal contact occurs over a circle of radius a (≼ b ) on the top plane face of the cylinder, and is governed by a general convective boundary condition. The remainder of the top plane face, the curved surface and the bottom may be insulated, isothermal, or subject to other convective boundary conditions. If the boundary conditions on the two parts of the top surface are unmixed, the problem is reduced by Hankel, Fourier and Abel transform techniques to a quadrature and the summation of an infinite series. If they are mixed, the problem is reduced to the solution of an integro-differential equation. Extensive numerical results are presented for the thermal constriction resistance over a wide range of dimensionless Biot numbers and aspect ratios b / a and h / a .

8. Quantum mechanics

2019 ◽  
pp. 99-110
Author(s):  
Eric R. Scerri
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Electron Energy ◽  
Energy Levels ◽  
Single Electron ◽  
Electron Systems ◽  
New Developments

‘Quantum mechanics’ shows how Bohr’s quantum theory was a stepping stone for the development of quantum mechanics. Bohr’s quantum theory worked well in single electron systems, but not in multi-electron systems. Quantum mechanics allowed the development of Schrödinger’s equation, which could theoretically predict the determination of electron energy levels in any system. The advantage of quantum mechanics over quantum theory lies in its treatment of electrons as waves. This allowed Schrödinger to apply mathematical boundary conditions to his equation and quantize the energy levels of electrons. Further work by Heisenberg showed that electrons are spread around a spherical shell. New developments on atomic configurations by Eugen Schwarz are also discussed.

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