Thermal constriction resistance : effects of boundary conditions and contact geometries

Abstract The problem of steady-state thermal constriction resistance is modeled by means of various spatially periodic arrangements of circular disks (contact regions) on the surface of a semi-infinite solid. Three cases of disk boundary condition are considered : uniform flux, the ‘equivalent isothermal flux’, and the condition of isothermal disks. Analytical expressions for the resistance are derived as power series of K 1 4 , where k is the fraction of the solid surface occupied by the disks. The behavior of the resistance is then studied as a function of disk boundary condition, spatial arrangement and concentration.