Thermal constriction resistance: effects of boundary conditions and contact geometries

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.

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1988.0129 ◽

1988 ◽

Vol 420 (1859) ◽

pp. 323-354 ◽

Cited By ~ 6

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 .

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Thermal constriction resistance of circular contacts on coated surfaces - Effect of contact boundary conditions

10.2514/6.1985-1014 ◽

1985 ◽

Cited By ~ 5

Author(s):

K. NEGUS ◽

M. YOVANOVICH ◽

J. THOMPSON

Keyword(s):

Boundary Conditions ◽

Contact Boundary ◽

Constriction Resistance ◽

Coated Surfaces

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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