Roughness measurements of solid surfaces, such as thin films and machined metals, at microscales and nanoscales show that the surfaces are rough and disordered over several decades of length scales. Similar features have been observed in turbulent fluid interfaces. Such disordered structures strongly influence thermal phenomena at interfaces. Previous studies on thermal phenomena at such interfaces have conventionally made either oversimplifying idealizations of smoothness of an interface or resorted to empirical and semi- empirical methods of analysis. This lack of physical understanding of the phenomena was mainly due to an inability to quantify the disorder in these structures. This study proposes to use the novel concepts of fractal geometry to understand and characterize the fundamental nature of disordered surfaces. Such a characterization quantifies the structure of surfaces at every length scale within certain limits. This is particularly important in providing key insight into the interactions of thermal phenomena with interfaces at relevant length scales. Preliminary studies on applying fractals in contact conductance have explained several previous experimental results. Based on these encouraging prospects, this study proposes to use fractals to study interfacial thermal phenomena of scientific and engineering importance such as contact conductance, frictional heating, and interactions of radiation with surfaces.
