Use of hydrodynamic theory to estimate electrical current redistribution in metals

Using the analogy between hydrodynamic and electrical current flow, we study how electrical current density j redistributes and amplifies due to two commonly encountered inhomogeneities in metals. First, we consider flow around a spherical resistive inclusion and find significant j amplification, independent of inclusion size. Hence, even mu m-scale inclusions can affect performance in applications by creating localized regions of enhanced Joule heating. Next, we investigate j redistribution due to surface roughness, idealized as a sinusoidal perturbation with amplitude A and wavelength lambda. Theory predicts that j amplification is determined by the ratio A / lambda, so that even "smooth" surface finishes (i.e., small A) can generate significant amplification, if lambda is correspondingly small. We compare theory with magnetohydrodynamic simulation to illustrate both the utility and limitations of the steady-state theory.