An explanation of thermal rectification

In an effort to understand the physical basis of thermal rectification, a semiquantitative study of a greatly idealized contact between two smooth, frictionless spheres has been undertaken. Hertzian methods were employed to express the contact length as a function of the spheres' radii, the compressive force on the spheres, and the spheres' mechanical properties. Then, an expression defining the relationship between the contact length and the heat flux through the junction was derived. The results of this analysis reveal that distortion at the contact surfaces of the two spheres due to thermal strains within the spheres can explain the observed behavior of thermal rectification reported in the literature, including: (1) the increase in thermal rectification as the contact load is increased, (2) the dependence of thermal rectification upon the contact geometry, (3) the dependence of thermal rectification upon the heat flux magnitude, and (4) thermal rectification at similar material junctions.