A new Reynolds analogy equation is presented, which is based on flow and thermal behavior in a rectangular cross-section channel with real component surface roughness. This roughness is similar to that which exists on some turbine surfaces under extreme operating conditions, or on surfaces of other industrial devices, with deposit accumulation such as heat exchangers. Skin friction coefficient, Nusselt number, Stanton number, and performance factor experimental results are given over a range of Reynolds numbers for one polished smooth surface, and for two other surfaces with different levels of irregularly shaped and irregularly distributed, three-dimensional surface roughness. The Reynolds analogy deduced from these data, with such roughness, is important because it is different from Reynolds analogy equations for surfaces with uniformly shaped elements arranged in a regular, periodic pattern.