Centrifugal forces break the degenerate closed-streamline configuration that occurs in simple shear flow past a neutrally buoyant torque-free particle in the inertialess limit. The broken symmetry allows heat or mass to be convected away in an efficient manner in sharp contrast to the inertialess diffusion-limited scenario. The dimensionless transfer rate, characterized by the Nusselt number, is found to be Nu = 0.33(RePe)(1/3) + O(1) for small but finite Re when RePe >> 1. Here, the particle Reynolds number (Re) is a dimensionless measure of the inertial forces, while the Peclet number (Pe) measures the relative importance of the convective and the diffusive transfer mechanisms. The symmetry-breaking bifurcation is expected to occur in generic shearing flows, and represents a possible means for heat or mass transfer enhancement from the dispersed phase in multiphase systems.