Effect of gap size and spacing on heat conduction between materials with irregularly spaced plane strip contacts

Abstract

A previous paper developed solutions for conductive heat flow in the x, y plane where there is a uniform flow at infinite values of y and where y = 0 represents the interface between two materials. This interface consists of an arbitrary pattern of perfectly conducting strips and non-conducting gaps. It was assumed that thermoelastic effects are negligible. The solution took the form of an equation with one unknown parameter per gap, which can be found by a simple process involving numerical integration. Using this method, the present paper gives solutions for a range of gap sizes and spacings. These are compared with approximate solutions determined by simplifying the general solutions sufficiently for them to be solved analytically. It is shown that the sizes of the gaps are the dominant parameters. The spacings are relatively unimportant unless two gaps are very close. The extent to which the approximate forms can be used to give solutions for random patterns of gaps, using the statistics of gap sizes, is discussed.