Thermal Constriction Resistance of a Contact on a Circular Cylinder with Mixed Convective Boundaries

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 (<=slant 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.