The work described in this thesis falls into five parts. Four of these parts deal with the extension of the Danckwerts-Mickley surface renewal concept for turbulent mixing, to the problem of calculating the convective and condensation· heat transfer coefficients from surfaces which are in mechanical oscillation, or are maintained in an acoustic field. The fifth part discusses experiments carried out by the author on the condensation of steam at atmospheric pressure on a horizontal tube subjected to mechanical oscillations in the vertical plane. A perturbation analysis of the problem has also been carried out and compared with experiment.