On the Nondimensionalization of Constriction Resistance for Semi-infinite Heat Flux Tubes

The insulated semi-infinite cylinder with heat supplied uniformly through a coaxial contact area is an important unit cell in the theory of contact resistance. In the past, several investigators have examined the problem of the thermal constriction resistance of a circular contact area on an insulated semi-infinite, coaxial circular cylinder. Recently the case of a circular contact on a square cylinder has been investigated. By using a new approximate technique as well as double-infinite series solution to Laplace's equation in Cartesian coordinates, the case of a square contact area on a square cylinder can also be solved. Previously the nondimensionalization technique employed for the results has varied with different configurations and researchers. However, the similarity of these three configurations in terms of their integrated parameter, the thermal constriction resistance, will only be seen when nondimensionalization is made using a characteristic dimension that best describes these geometries.