Heat transfer from a vibrating circular cylinder

Theoretical results are obtained for heat transfer from a circular cylinder oscillating in an unbounded viscous fluid which is otherwise at rest. The amplitude of the oscillation is assumed small compared to the radius of the cylinder, which for most of the examples considered is assumed to be at a constant temperature. The analysis is based upon use of the acoustic streaming flow field and consideration is given to the cases of small and large streaming Reynolds numbers. For large streaming Reynolds numbers, a solution for the previously undetermined steady streaming flow field is computed. The results obtained cover a wide range of Prandtl number. The method of matched asymptotic expansions is exploited in the analysis and the computed results are also supplemented by an approximate method based on an integrated form of the governing equations. The relationship between the present work and other relevant contributions in the literature is discussed. In a final section, attention is devoted to a technique for determining the temperature distribution which results when a line source of heat is embedded at the centre of the oscillating cylinder.