The problem of heat and mass transfer from small spheres and cylinders freely suspended in a shear flow is considered in the limit of Reynolds number Re → 0. Asymptotic formulas are derived which relate the Nusselt number Nu to the Pe´clet number Pe in the limit Pe → 0, and for the case of the cylinder, Pe → ∞. At high Pe, the Nusselt number is found to approach a constant value, whereas, at low Pe it is shown to increase withPe12for the sphere and with—(log Pe)−1for the cylinder. These results indicate the existence of a fundamental difference at high Pe between the shear flow problem studied here and the corresponding classical problem of uniform flow at infinity.